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	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	color:#272727;
	mso-themecolor:text1;
	mso-themetint:216;
	mso-ansi-language:EN-US;
	font-style:italic;}
p.MsoHeading9, li.MsoHeading9, div.MsoHeading9
	{mso-style-noshow:yes;
	mso-style-priority:9;
	mso-style-qformat:yes;
	mso-style-link:"Heading 9 Char";
	mso-style-next:Normal;
	margin:0cm;
	line-height:115%;
	mso-pagination:widow-orphan lines-together;
	page-break-after:avoid;
	mso-outline-level:9;
	font-size:11.0pt;
	font-family:"Arial",sans-serif;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	color:#272727;
	mso-themecolor:text1;
	mso-themetint:216;
	mso-ansi-language:EN-US;}
p.MsoTitle, li.MsoTitle, div.MsoTitle
	{mso-style-priority:10;
	mso-style-unhide:no;
	mso-style-qformat:yes;
	mso-style-link:"Title Char";
	mso-style-next:Normal;
	margin-top:0cm;
	margin-right:0cm;
	margin-bottom:4.0pt;
	margin-left:0cm;
	mso-add-space:auto;
	mso-pagination:widow-orphan;
	font-size:28.0pt;
	font-family:"Aptos Display",sans-serif;
	mso-ascii-font-family:"Aptos Display";
	mso-ascii-theme-font:major-latin;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-hansi-font-family:"Aptos Display";
	mso-hansi-theme-font:major-latin;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	letter-spacing:-.5pt;
	mso-font-kerning:14.0pt;
	mso-ansi-language:EN-US;}
p.MsoTitleCxSpFirst, li.MsoTitleCxSpFirst, div.MsoTitleCxSpFirst
	{mso-style-priority:10;
	mso-style-unhide:no;
	mso-style-qformat:yes;
	mso-style-link:"Title Char";
	mso-style-next:Normal;
	mso-style-type:export-only;
	margin:0cm;
	mso-add-space:auto;
	mso-pagination:widow-orphan;
	font-size:28.0pt;
	font-family:"Aptos Display",sans-serif;
	mso-ascii-font-family:"Aptos Display";
	mso-ascii-theme-font:major-latin;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-hansi-font-family:"Aptos Display";
	mso-hansi-theme-font:major-latin;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	letter-spacing:-.5pt;
	mso-font-kerning:14.0pt;
	mso-ansi-language:EN-US;}
p.MsoTitleCxSpMiddle, li.MsoTitleCxSpMiddle, div.MsoTitleCxSpMiddle
	{mso-style-priority:10;
	mso-style-unhide:no;
	mso-style-qformat:yes;
	mso-style-link:"Title Char";
	mso-style-next:Normal;
	mso-style-type:export-only;
	margin:0cm;
	mso-add-space:auto;
	mso-pagination:widow-orphan;
	font-size:28.0pt;
	font-family:"Aptos Display",sans-serif;
	mso-ascii-font-family:"Aptos Display";
	mso-ascii-theme-font:major-latin;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-hansi-font-family:"Aptos Display";
	mso-hansi-theme-font:major-latin;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	letter-spacing:-.5pt;
	mso-font-kerning:14.0pt;
	mso-ansi-language:EN-US;}
p.MsoTitleCxSpLast, li.MsoTitleCxSpLast, div.MsoTitleCxSpLast
	{mso-style-priority:10;
	mso-style-unhide:no;
	mso-style-qformat:yes;
	mso-style-link:"Title Char";
	mso-style-next:Normal;
	mso-style-type:export-only;
	margin-top:0cm;
	margin-right:0cm;
	margin-bottom:4.0pt;
	margin-left:0cm;
	mso-add-space:auto;
	mso-pagination:widow-orphan;
	font-size:28.0pt;
	font-family:"Aptos Display",sans-serif;
	mso-ascii-font-family:"Aptos Display";
	mso-ascii-theme-font:major-latin;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-hansi-font-family:"Aptos Display";
	mso-hansi-theme-font:major-latin;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	letter-spacing:-.5pt;
	mso-font-kerning:14.0pt;
	mso-ansi-language:EN-US;}
p.MsoSubtitle, li.MsoSubtitle, div.MsoSubtitle
	{mso-style-priority:11;
	mso-style-unhide:no;
	mso-style-qformat:yes;
	mso-style-link:"Subtitle Char";
	mso-style-next:Normal;
	margin:0cm;
	line-height:115%;
	mso-pagination:widow-orphan;
	font-size:14.0pt;
	font-family:"Arial",sans-serif;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	color:#595959;
	mso-themecolor:text1;
	mso-themetint:166;
	letter-spacing:.75pt;
	mso-ansi-language:EN-US;}
p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
	{mso-style-priority:34;
	mso-style-unhide:no;
	mso-style-qformat:yes;
	margin-top:0cm;
	margin-right:0cm;
	margin-bottom:0cm;
	margin-left:36.0pt;
	mso-add-space:auto;
	line-height:115%;
	mso-pagination:widow-orphan;
	font-size:11.0pt;
	font-family:"Arial",sans-serif;
	mso-fareast-font-family:Arial;
	mso-ansi-language:EN-US;}
p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst
	{mso-style-priority:34;
	mso-style-unhide:no;
	mso-style-qformat:yes;
	mso-style-type:export-only;
	margin-top:0cm;
	margin-right:0cm;
	margin-bottom:0cm;
	margin-left:36.0pt;
	mso-add-space:auto;
	line-height:115%;
	mso-pagination:widow-orphan;
	font-size:11.0pt;
	font-family:"Arial",sans-serif;
	mso-fareast-font-family:Arial;
	mso-ansi-language:EN-US;}
p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle
	{mso-style-priority:34;
	mso-style-unhide:no;
	mso-style-qformat:yes;
	mso-style-type:export-only;
	margin-top:0cm;
	margin-right:0cm;
	margin-bottom:0cm;
	margin-left:36.0pt;
	mso-add-space:auto;
	line-height:115%;
	mso-pagination:widow-orphan;
	font-size:11.0pt;
	font-family:"Arial",sans-serif;
	mso-fareast-font-family:Arial;
	mso-ansi-language:EN-US;}
p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast
	{mso-style-priority:34;
	mso-style-unhide:no;
	mso-style-qformat:yes;
	mso-style-type:export-only;
	margin-top:0cm;
	margin-right:0cm;
	margin-bottom:0cm;
	margin-left:36.0pt;
	mso-add-space:auto;
	line-height:115%;
	mso-pagination:widow-orphan;
	font-size:11.0pt;
	font-family:"Arial",sans-serif;
	mso-fareast-font-family:Arial;
	mso-ansi-language:EN-US;}
p.MsoQuote, li.MsoQuote, div.MsoQuote
	{mso-style-priority:29;
	mso-style-unhide:no;
	mso-style-qformat:yes;
	mso-style-link:"Quote Char";
	mso-style-next:Normal;
	margin-top:8.0pt;
	margin-right:0cm;
	margin-bottom:0cm;
	margin-left:0cm;
	text-align:center;
	line-height:115%;
	mso-pagination:widow-orphan;
	font-size:11.0pt;
	font-family:"Arial",sans-serif;
	mso-fareast-font-family:Arial;
	color:#404040;
	mso-themecolor:text1;
	mso-themetint:191;
	mso-ansi-language:EN-US;
	font-style:italic;}
p.MsoIntenseQuote, li.MsoIntenseQuote, div.MsoIntenseQuote
	{mso-style-priority:30;
	mso-style-unhide:no;
	mso-style-qformat:yes;
	mso-style-link:"Intense Quote Char";
	mso-style-next:Normal;
	margin-top:18.0pt;
	margin-right:43.2pt;
	margin-bottom:18.0pt;
	margin-left:43.2pt;
	text-align:center;
	line-height:115%;
	mso-pagination:widow-orphan;
	border:none;
	mso-border-top-alt:solid #0F4761 .5pt;
	mso-border-top-themecolor:accent1;
	mso-border-top-themeshade:191;
	mso-border-bottom-alt:solid #0F4761 .5pt;
	mso-border-bottom-themecolor:accent1;
	mso-border-bottom-themeshade:191;
	padding:0cm;
	mso-padding-alt:10.0pt 0cm 10.0pt 0cm;
	font-size:11.0pt;
	font-family:"Arial",sans-serif;
	mso-fareast-font-family:Arial;
	color:#0F4761;
	mso-themecolor:accent1;
	mso-themeshade:191;
	mso-ansi-language:EN-US;
	font-style:italic;}
span.MsoIntenseEmphasis
	{mso-style-priority:21;
	mso-style-unhide:no;
	mso-style-qformat:yes;
	color:#0F4761;
	mso-themecolor:accent1;
	mso-themeshade:191;
	font-style:italic;}
span.MsoIntenseReference
	{mso-style-priority:32;
	mso-style-unhide:no;
	mso-style-qformat:yes;
	font-variant:small-caps;
	color:#0F4761;
	mso-themecolor:accent1;
	mso-themeshade:191;
	letter-spacing:.25pt;
	font-weight:bold;}
span.Heading1Char
	{mso-style-name:"Heading 1 Char";
	mso-style-priority:9;
	mso-style-unhide:no;
	mso-style-locked:yes;
	mso-style-link:"Heading 1";
	mso-ansi-font-size:20.0pt;
	mso-bidi-font-size:20.0pt;
	font-family:"Aptos Display",sans-serif;
	mso-ascii-font-family:"Aptos Display";
	mso-ascii-theme-font:major-latin;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-hansi-font-family:"Aptos Display";
	mso-hansi-theme-font:major-latin;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	color:#0F4761;
	mso-themecolor:accent1;
	mso-themeshade:191;}
span.Heading2Char
	{mso-style-name:"Heading 2 Char";
	mso-style-priority:9;
	mso-style-unhide:no;
	mso-style-locked:yes;
	mso-style-link:"Heading 2";
	mso-ansi-font-size:16.0pt;
	mso-bidi-font-size:16.0pt;
	font-family:"Aptos Display",sans-serif;
	mso-ascii-font-family:"Aptos Display";
	mso-ascii-theme-font:major-latin;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-hansi-font-family:"Aptos Display";
	mso-hansi-theme-font:major-latin;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	color:#0F4761;
	mso-themecolor:accent1;
	mso-themeshade:191;}
span.Heading3Char
	{mso-style-name:"Heading 3 Char";
	mso-style-priority:9;
	mso-style-unhide:no;
	mso-style-locked:yes;
	mso-style-link:"Heading 3";
	mso-ansi-font-size:14.0pt;
	mso-bidi-font-size:14.0pt;
	font-family:"Times New Roman",serif;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	color:#0F4761;
	mso-themecolor:accent1;
	mso-themeshade:191;}
span.Heading4Char
	{mso-style-name:"Heading 4 Char";
	mso-style-noshow:yes;
	mso-style-priority:9;
	mso-style-unhide:no;
	mso-style-locked:yes;
	mso-style-link:"Heading 4";
	font-family:"Times New Roman",serif;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	color:#0F4761;
	mso-themecolor:accent1;
	mso-themeshade:191;
	font-style:italic;}
span.Heading5Char
	{mso-style-name:"Heading 5 Char";
	mso-style-noshow:yes;
	mso-style-priority:9;
	mso-style-unhide:no;
	mso-style-locked:yes;
	mso-style-link:"Heading 5";
	font-family:"Times New Roman",serif;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	color:#0F4761;
	mso-themecolor:accent1;
	mso-themeshade:191;}
span.Heading6Char
	{mso-style-name:"Heading 6 Char";
	mso-style-noshow:yes;
	mso-style-priority:9;
	mso-style-unhide:no;
	mso-style-locked:yes;
	mso-style-link:"Heading 6";
	font-family:"Times New Roman",serif;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	color:#595959;
	mso-themecolor:text1;
	mso-themetint:166;
	font-style:italic;}
span.Heading7Char
	{mso-style-name:"Heading 7 Char";
	mso-style-noshow:yes;
	mso-style-priority:9;
	mso-style-unhide:no;
	mso-style-locked:yes;
	mso-style-link:"Heading 7";
	font-family:"Times New Roman",serif;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	color:#595959;
	mso-themecolor:text1;
	mso-themetint:166;}
span.Heading8Char
	{mso-style-name:"Heading 8 Char";
	mso-style-noshow:yes;
	mso-style-priority:9;
	mso-style-unhide:no;
	mso-style-locked:yes;
	mso-style-link:"Heading 8";
	font-family:"Times New Roman",serif;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	color:#272727;
	mso-themecolor:text1;
	mso-themetint:216;
	font-style:italic;}
span.Heading9Char
	{mso-style-name:"Heading 9 Char";
	mso-style-noshow:yes;
	mso-style-priority:9;
	mso-style-unhide:no;
	mso-style-locked:yes;
	mso-style-link:"Heading 9";
	font-family:"Times New Roman",serif;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	color:#272727;
	mso-themecolor:text1;
	mso-themetint:216;}
span.TitleChar
	{mso-style-name:"Title Char";
	mso-style-priority:10;
	mso-style-unhide:no;
	mso-style-locked:yes;
	mso-style-link:Title;
	mso-ansi-font-size:28.0pt;
	mso-bidi-font-size:28.0pt;
	font-family:"Aptos Display",sans-serif;
	mso-ascii-font-family:"Aptos Display";
	mso-ascii-theme-font:major-latin;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-hansi-font-family:"Aptos Display";
	mso-hansi-theme-font:major-latin;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	letter-spacing:-.5pt;
	mso-font-kerning:14.0pt;}
span.SubtitleChar
	{mso-style-name:"Subtitle Char";
	mso-style-priority:11;
	mso-style-unhide:no;
	mso-style-locked:yes;
	mso-style-link:Subtitle;
	mso-ansi-font-size:14.0pt;
	mso-bidi-font-size:14.0pt;
	font-family:"Times New Roman",serif;
	mso-fareast-font-family:"Times New Roman";
	mso-fareast-theme-font:major-fareast;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:major-bidi;
	color:#595959;
	mso-themecolor:text1;
	mso-themetint:166;
	letter-spacing:.75pt;}
span.QuoteChar
	{mso-style-name:"Quote Char";
	mso-style-priority:29;
	mso-style-unhide:no;
	mso-style-locked:yes;
	mso-style-link:Quote;
	color:#404040;
	mso-themecolor:text1;
	mso-themetint:191;
	font-style:italic;}
span.IntenseQuoteChar
	{mso-style-name:"Intense Quote Char";
	mso-style-priority:30;
	mso-style-unhide:no;
	mso-style-locked:yes;
	mso-style-link:"Intense Quote";
	color:#0F4761;
	mso-themecolor:accent1;
	mso-themeshade:191;
	font-style:italic;}
span.SpellE
	{mso-style-name:"";
	mso-spl-e:yes;}
span.GramE
	{mso-style-name:"";
	mso-gram-e:yes;}
.MsoChpDefault
	{mso-style-type:export-only;
	mso-default-props:yes;
	font-family:"Aptos",sans-serif;
	mso-ascii-font-family:Aptos;
	mso-ascii-theme-font:minor-latin;
	mso-fareast-font-family:Aptos;
	mso-fareast-theme-font:minor-latin;
	mso-hansi-font-family:Aptos;
	mso-hansi-theme-font:minor-latin;
	mso-bidi-font-family:"Times New Roman";
	mso-bidi-theme-font:minor-bidi;
	mso-fareast-language:EN-US;}
.MsoPapDefault
	{mso-style-type:export-only;
	margin-bottom:8.0pt;
	line-height:115%;}
@page WordSection1
	{size:595.3pt 841.9pt;
	margin:72.0pt 72.0pt 72.0pt 72.0pt;
	mso-header-margin:35.4pt;
	mso-footer-margin:35.4pt;
	mso-paper-source:0;}
div.WordSection1
	{page:WordSection1;}
 /* List Definitions */
 @list l0
	{mso-list-id:419373671;
	mso-list-template-ids:376834320;}
@list l0:level1
	{mso-level-number-format:bullet;
	mso-level-text:●;
	mso-level-tab-stop:none;
	mso-level-number-position:left;
	text-indent:-18.0pt;
	mso-ascii-font-family:"Noto Sans Symbols";
	mso-fareast-font-family:"Noto Sans Symbols";
	mso-hansi-font-family:"Noto Sans Symbols";
	mso-bidi-font-family:"Noto Sans Symbols";}
@list l0:level2
	{mso-level-number-format:bullet;
	mso-level-text:o;
	mso-level-tab-stop:none;
	mso-level-number-position:left;
	text-indent:-18.0pt;
	mso-ascii-font-family:"Courier New";
	mso-fareast-font-family:"Courier New";
	mso-hansi-font-family:"Courier New";
	mso-bidi-font-family:"Courier New";}
@list l0:level3
	{mso-level-number-format:bullet;
	mso-level-text:▪;
	mso-level-tab-stop:none;
	mso-level-number-position:left;
	text-indent:-18.0pt;
	mso-ascii-font-family:"Noto Sans Symbols";
	mso-fareast-font-family:"Noto Sans Symbols";
	mso-hansi-font-family:"Noto Sans Symbols";
	mso-bidi-font-family:"Noto Sans Symbols";}
@list l0:level4
	{mso-level-number-format:bullet;
	mso-level-text:●;
	mso-level-tab-stop:none;
	mso-level-number-position:left;
	text-indent:-18.0pt;
	mso-ascii-font-family:"Noto Sans Symbols";
	mso-fareast-font-family:"Noto Sans Symbols";
	mso-hansi-font-family:"Noto Sans Symbols";
	mso-bidi-font-family:"Noto Sans Symbols";}
@list l0:level5
	{mso-level-number-format:bullet;
	mso-level-text:o;
	mso-level-tab-stop:none;
	mso-level-number-position:left;
	text-indent:-18.0pt;
	mso-ascii-font-family:"Courier New";
	mso-fareast-font-family:"Courier New";
	mso-hansi-font-family:"Courier New";
	mso-bidi-font-family:"Courier New";}
@list l0:level6
	{mso-level-number-format:bullet;
	mso-level-text:▪;
	mso-level-tab-stop:none;
	mso-level-number-position:left;
	text-indent:-18.0pt;
	mso-ascii-font-family:"Noto Sans Symbols";
	mso-fareast-font-family:"Noto Sans Symbols";
	mso-hansi-font-family:"Noto Sans Symbols";
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<body lang=en-PL style='tab-interval:36.0pt;word-wrap:break-word'>

<div class=WordSection1>

<h1><span lang=EN-US>J.S. Lee refined speckle filter<o:p></o:p></span></h1>

<h3><span lang=EN-US>Mathematical Description<o:p></o:p></span></h3>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US>Unlike optical remote sensing images, characterized by very neat and
uniform features, SAR images are affected by speckle. Even if speckle confers a
random aspect to SAR images, it may not be considered as a simple noise. It is,
in fact, tightly related to SAR measurement principle.<o:p></o:p></span></p>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US>Speckle phenomenon corrupts polarimetric observables (phase and
intensity) in an important way. Specific procedures <span class=GramE>have to</span>
be used to retrieve relevant polarimetric information and to reduce the
randomness of the acquired signals.<o:p></o:p></span></p>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US>Synthesized SAR data may be considered as the result of the
integration of a scene coherent response within each resolution cell, resulting
from the convolution of the SAR impulse response with the coherent contribution
of each elementary scatterer. As the number of contributing scatterers, within
a resolution cell, tends to be large (it is the case for common resolution SAR
measurements), the resulting integrated response is random in phase and
amplitude and is shown to follow, over homogeneous areas, a <span class=GramE>Normal</span>
distribution.<o:p></o:p></span></p>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US>A speckled response is usually represented under the form of a
simple product model: </span><sub><span lang=EN-US style='font-size:18.0pt;
line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
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style='mso-spacerun:yes'> </span>where </span><sub><span lang=EN-US
style='font-size:18.0pt;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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 <v:imagedata src="Refined_Lee_theory.fld/image003.wmz" o:title=""/>
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scattering coefficient, </span><sub><span lang=EN-US style='font-size:18.0pt;
line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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style='mso-spacerun:yes'> </span>the original <span class=SpellE>unspeckled</span>
scattering coefficient and </span><sub><span lang=EN-US style='font-size:18.0pt;
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style='mso-spacerun:yes'> </span>the multiplicative speckle contribution.<o:p></o:p></span></p>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US>The speckle term, </span><sub><span lang=EN-US style='font-size:
18.0pt;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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style='mso-spacerun:yes'> </span>is composed of independent real and imaginary
parts, following both real centered Normal distribution </span><sub><span
lang=EN-US style='font-size:18.0pt;line-height:115%'><span style='mso-no-proof:
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intensity, <span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="_x0000_i1045"
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<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US>The principle of speckle filtering <span class=GramE>consist</span>
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its mean. The sample mean, </span><sub><span lang=EN-US style='font-size:18.0pt;
line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
 id="_x0000_i1042" type="#_x0000_t75" alt="" style='width:21pt;height:18pt;
 mso-width-percent:0;mso-height-percent:0;mso-width-percent:0;
 mso-height-percent:0' o:ole="">
 <v:imagedata src="Refined_Lee_theory.fld/image018.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=21 height=18
src="Refined_Lee_theory.fld/image019.png" v:shapes="_x0000_i1042"><![endif]></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1042"
  DrawAspect="Content" ObjectID="_1824309912">
 </o:OLEObject>
</xml><![endif]--></span></sub><span lang=EN-US>, is defined as the empirical
average of L independent realizations of a speckled intensity as follows: </span><sub><span
lang=EN-US style='font-size:18.0pt;line-height:115%'><span style='mso-no-proof:
yes'><!--[if gte vml 1]><v:shape id="_x0000_i1041" type="#_x0000_t75" alt=""
 style='width:69pt;height:34pt;mso-width-percent:0;mso-height-percent:0;
 mso-width-percent:0;mso-height-percent:0' o:ole="">
 <v:imagedata src="Refined_Lee_theory.fld/image020.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=69 height=34
src="Refined_Lee_theory.fld/image021.png" v:shapes="_x0000_i1041"><![endif]></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1041"
  DrawAspect="Content" ObjectID="_1824309913">
 </o:OLEObject>
</xml><![endif]--></span></sub><span lang=EN-US><o:p></o:p></span></p>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US>The <b style='mso-bidi-font-weight:normal'>J. S. Lee speckle filter</b>
determines the <span class=SpellE>unspeckled</span> intensity estimate that
minimizes a mean squared error following </span><sub><span lang=EN-US
style='font-size:18.0pt;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
 id="_x0000_i1040" type="#_x0000_t75" alt="" style='width:56pt;height:29pt;
 mso-width-percent:0;mso-height-percent:0;mso-width-percent:0;
 mso-height-percent:0' o:ole="">
 <v:imagedata src="Refined_Lee_theory.fld/image022.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=56 height=29
src="Refined_Lee_theory.fld/image023.png" v:shapes="_x0000_i1040"><![endif]></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1040"
  DrawAspect="Content" ObjectID="_1824309914">
 </o:OLEObject>
</xml><![endif]--></span></sub><span lang=EN-US>. This MMSE filter is based on
a linearized speckle model leading to the following estimate expression </span><sub><span
lang=EN-US style='font-size:18.0pt;line-height:115%'><span style='mso-no-proof:
yes'><!--[if gte vml 1]><v:shape id="_x0000_i1039" type="#_x0000_t75" alt=""
 style='width:134pt;height:28pt;mso-width-percent:0;mso-height-percent:0;
 mso-width-percent:0;mso-height-percent:0' o:ole="">
 <v:imagedata src="Refined_Lee_theory.fld/image024.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=134 height=28
src="Refined_Lee_theory.fld/image025.png" v:shapes="_x0000_i1039"><![endif]></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1039"
  DrawAspect="Content" ObjectID="_1824309915">
 </o:OLEObject>
</xml><![endif]--></span></sub><span lang=EN-US><span
style='mso-spacerun:yes'> </span>where k is an adaptive filtering coefficient,
based on local statistics, given by </span><sub><span lang=EN-US
style='font-size:18.0pt;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
 id="_x0000_i1038" type="#_x0000_t75" alt="" style='width:182pt;height:40pt;
 mso-width-percent:0;mso-height-percent:0;mso-width-percent:0;
 mso-height-percent:0' o:ole="">
 <v:imagedata src="Refined_Lee_theory.fld/image026.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=182 height=40
src="Refined_Lee_theory.fld/image027.png" v:shapes="_x0000_i1038"><![endif]></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1038"
  DrawAspect="Content" ObjectID="_1824309916">
 </o:OLEObject>
</xml><![endif]--></span></sub><span lang=EN-US><span
style='mso-spacerun:yes'> </span>with </span><sub><span lang=EN-US
style='font-size:18.0pt;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
 id="_x0000_i1037" type="#_x0000_t75" alt="" style='width:40pt;height:32pt;
 mso-width-percent:0;mso-height-percent:0;mso-width-percent:0;
 mso-height-percent:0' o:ole="">
 <v:imagedata src="Refined_Lee_theory.fld/image028.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=40 height=32
src="Refined_Lee_theory.fld/image029.png" v:shapes="_x0000_i1037"><![endif]></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1037"
  DrawAspect="Content" ObjectID="_1824309917">
 </o:OLEObject>
</xml><![endif]--></span></sub><span lang=EN-US><span
style='mso-spacerun:yes'> </span>the a priori speckle variance. <o:p></o:p></span></p>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US>Over homogeneous areas, </span><sub><span lang=EN-US
style='font-size:18.0pt;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
 id="_x0000_i1036" type="#_x0000_t75" alt="" style='width:104pt;height:20pt;
 mso-width-percent:0;mso-height-percent:0;mso-width-percent:0;
 mso-height-percent:0' o:ole="">
 <v:imagedata src="Refined_Lee_theory.fld/image030.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=104 height=20
src="Refined_Lee_theory.fld/image031.png" v:shapes="_x0000_i1036"><![endif]></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1036"
  DrawAspect="Content" ObjectID="_1824309918">
 </o:OLEObject>
</xml><![endif]--></span></sub><span lang=EN-US><span
style='mso-spacerun:yes'> </span>and </span><sub><span lang=EN-US
style='font-size:18.0pt;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
 id="_x0000_i1035" type="#_x0000_t75" alt="" style='width:55pt;height:21pt;
 mso-width-percent:0;mso-height-percent:0;mso-width-percent:0;
 mso-height-percent:0' o:ole="">
 <v:imagedata src="Refined_Lee_theory.fld/image032.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=55 height=21
src="Refined_Lee_theory.fld/image033.png" v:shapes="_x0000_i1035"><![endif]></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1035"
  DrawAspect="Content" ObjectID="_1824309919">
 </o:OLEObject>
</xml><![endif]--></span></sub><span lang=EN-US>, whereas over point targets
and highly heterogeneous areas,</span><sub><span lang=EN-US style='font-size:
18.0pt;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
 id="_x0000_i1034" type="#_x0000_t75" alt="" style='width:76pt;height:18pt;
 mso-width-percent:0;mso-height-percent:0;mso-width-percent:0;
 mso-height-percent:0' o:ole="">
 <v:imagedata src="Refined_Lee_theory.fld/image034.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=76 height=18
src="Refined_Lee_theory.fld/image035.png" v:shapes="_x0000_i1034"><![endif]></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1034"
  DrawAspect="Content" ObjectID="_1824309920">
 </o:OLEObject>
</xml><![endif]--></span></sub><span lang=EN-US>and the pixel intensity remains
unaffected by the filtering procedure. <o:p></o:p></span></p>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
class=GramE><span lang=EN-US>In order to</span></span><span lang=EN-US> reduce
the sensitivity of the adaptive filtering coefficient, </span><sub><span
lang=EN-US style='font-size:18.0pt;line-height:115%'><span style='mso-no-proof:
yes'><!--[if gte vml 1]><v:shape id="_x0000_i1033" type="#_x0000_t75" alt=""
 style='width:11pt;height:14pt;mso-width-percent:0;mso-height-percent:0;
 mso-width-percent:0;mso-height-percent:0' o:ole="">
 <v:imagedata src="Refined_Lee_theory.fld/image036.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=11 height=14
src="Refined_Lee_theory.fld/image037.png" v:shapes="_x0000_i1033"><![endif]></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1033"
  DrawAspect="Content" ObjectID="_1824309921">
 </o:OLEObject>
</xml><![endif]--></span></sub><span lang=EN-US>, to isolated heterogeneities,
this filter uses directional masks to determine the most homogeneous part of
the sliding window where local statistics <span class=GramE>have to</span> be
estimated. This modification permits to preserve relatively sharp edges. This
filter is named the <b style='mso-bidi-font-weight:normal'>J.S. Lee refined
speckle filter</b>.<o:p></o:p></span></p>

<p class=MsoNormal style='text-align:justify'><span lang=EN-US><o:p>&nbsp;</o:p></span></p>

<div align=center>

<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0 width=476
 style='border-collapse:collapse;mso-table-layout-alt:fixed;mso-padding-alt:
 0cm 5.4pt 0cm 5.4pt'>
 <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
  <td width=476 valign=top style='width:356.75pt;padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=MsoNormal align=center style='text-align:center'><span lang=EN-US><span
  style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="_x0000_i1032"
   type="#_x0000_t75" alt="" style='width:344pt;height:137pt;
   mso-width-percent:0;mso-height-percent:0;mso-width-percent:0;
   mso-height-percent:0' o:ole="">
   <v:imagedata src="Refined_Lee_theory.fld/image038.wmz" o:title=""/>
  </v:shape><![endif]--><![if !vml]><img width=344 height=137
  src="Refined_Lee_theory.fld/image039.png" v:shapes="_x0000_i1032"><![endif]></span><!--[if gte mso 9]><xml>
   <o:OLEObject Type="Embed" ProgID="Word.Picture.8" ShapeID="_x0000_i1032"
    DrawAspect="Content" ObjectID="_1824309922">
   </o:OLEObject>
  </xml><![endif]--><o:p></o:p></span></p>
  </td>
 </tr>
 <tr style='mso-yfti-irow:1;mso-yfti-lastrow:yes'>
  <td width=476 valign=top style='width:356.75pt;padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=MsoNormal align=center style='text-align:center'><i
  style='mso-bidi-font-style:normal'><span lang=EN-US><o:p>&nbsp;</o:p></span></i></p>
  </td>
 </tr>
</table>

</div>

<p class=MsoNormal style='text-align:justify'><span lang=EN-US><o:p>&nbsp;</o:p></span></p>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US><o:p>&nbsp;</o:p></span></p>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US>Speckle filtering is based on incoherent averaging and requires <span
class=GramE>to handle</span> second order representations. The intensity
information used in the scalar case <span class=GramE>has to</span> be extended
to the vector case when dealing with two or more polarization channels <span
class=GramE>in order to</span> <span class=GramE>take into account</span> the
different intensities as well as the cross-correlation related information. <o:p></o:p></span></p>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US>A simple way to build an incoherent polarimetric representation
consists in vectorizing a scattering matrix to create a target vector and
computing the corresponding (3×3) covariance matrix </span><sub><span
lang=EN-US style='font-size:18.0pt;line-height:115%'><span style='mso-no-proof:
yes'><!--[if gte vml 1]><v:shape id="_x0000_i1031" type="#_x0000_t75" alt=""
 style='width:25pt;height:20pt;mso-width-percent:0;mso-height-percent:0;
 mso-width-percent:0;mso-height-percent:0' o:ole="">
 <v:imagedata src="Refined_Lee_theory.fld/image040.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=25 height=20
src="Refined_Lee_theory.fld/image041.png" v:shapes="_x0000_i1031"><![endif]></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1031"
  DrawAspect="Content" ObjectID="_1824309923">
 </o:OLEObject>
</xml><![endif]--></span></sub><span lang=EN-US><span
style='mso-spacerun:yes'> </span>or the (3×3) coherency matrix </span><sub><span
lang=EN-US style='font-size:18.0pt;line-height:115%'><span style='mso-no-proof:
yes'><!--[if gte vml 1]><v:shape id="_x0000_i1030" type="#_x0000_t75" alt=""
 style='width:23pt;height:20pt;mso-width-percent:0;mso-height-percent:0;
 mso-width-percent:0;mso-height-percent:0' o:ole="">
 <v:imagedata src="Refined_Lee_theory.fld/image042.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=23 height=20
src="Refined_Lee_theory.fld/image043.png" v:shapes="_x0000_i1030"><![endif]></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1030"
  DrawAspect="Content" ObjectID="_1824309924">
 </o:OLEObject>
</xml><![endif]--></span></sub><span lang=EN-US>.<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:17.4pt;text-align:justify'><span
lang=EN-US><o:p>&nbsp;</o:p></span></p>

<p class=MsoNormal style='margin-left:17.4pt;text-align:justify'><span
lang=EN-US>A polarimetric speckle filter should be developed based on the
following principle:<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:35.4pt;text-align:justify;text-indent:
-18.0pt;line-height:normal;mso-list:l3 level1 lfo1'><![if !supportLists]><span
lang=EN-US style='font-family:"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";
mso-bidi-font-family:"Noto Sans Symbols"'><span style='mso-list:Ignore'>●<span
style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span
lang=EN-US>To preserve polarimetric properties, each term of the covariance /
coherency matrix should be filtered in a manner <span class=GramE>similar to</span>
multi-look processing by averaging the covariance / coherency matrices of the
same neighboring pixels. Like that, all terms of the covariance / coherency
matrix should be filtered by the same amount. <o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:35.4pt;text-align:justify;text-indent:
-18.0pt;line-height:normal;mso-list:l3 level1 lfo1'><![if !supportLists]><span
lang=EN-US style='font-family:"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";
mso-bidi-font-family:"Noto Sans Symbols"'><span style='mso-list:Ignore'>●<span
style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span
lang=EN-US>To avoid <span class=GramE>cross-talk</span> between polarization
channels, each element of the covariance / coherency matrix <span class=GramE>has
to</span> be filtered independently in the spatial domain. <o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:35.4pt;text-align:justify;text-indent:
-18.0pt;line-height:normal;mso-list:l1 level1 lfo3'><![if !supportLists]><span
lang=EN-US style='font-family:"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";
mso-bidi-font-family:"Noto Sans Symbols"'><span style='mso-list:Ignore'>●<span
style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span
lang=EN-US>To preserve scattering characteristics, edge sharpness and point
targets, the filtering <span class=GramE>has to</span> be adaptive, and the
filtering should select neighboring pixels for averaging.<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:17.4pt;text-align:justify'><span
lang=EN-US><o:p>&nbsp;</o:p></span></p>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US>J. S. Lee proposed to estimate the <span class=SpellE>unspeckled</span>
covariance matrix and/or coherency matrix according to the following
corresponding expressions: </span><sub><span lang=EN-US style='font-size:18.0pt;
line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
 id="_x0000_i1029" type="#_x0000_t75" alt="" style='width:147pt;height:25pt;
 mso-width-percent:0;mso-height-percent:0;mso-width-percent:0;
 mso-height-percent:0' o:ole="">
 <v:imagedata src="Refined_Lee_theory.fld/image044.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=147 height=25
src="Refined_Lee_theory.fld/image045.png" v:shapes="_x0000_i1029"><![endif]></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029"
  DrawAspect="Content" ObjectID="_1824309925">
 </o:OLEObject>
</xml><![endif]--></span></sub><span lang=EN-US><span
style='mso-spacerun:yes'> </span>and </span><sub><span lang=EN-US
style='font-size:18.0pt;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
 id="_x0000_i1028" type="#_x0000_t75" alt="" style='width:2in;height:25pt;
 mso-width-percent:0;mso-height-percent:0;mso-width-percent:0;
 mso-height-percent:0' o:ole="">
 <v:imagedata src="Refined_Lee_theory.fld/image046.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=144 height=25
src="Refined_Lee_theory.fld/image047.png" v:shapes="_x0000_i1028"><![endif]></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028"
  DrawAspect="Content" ObjectID="_1824309926">
 </o:OLEObject>
</xml><![endif]--></span></sub><span lang=EN-US>.<o:p></o:p></span></p>

<p class=MsoNormal style='text-align:justify'><span lang=EN-US><o:p>&nbsp;</o:p></span></p>

<p class=MsoNormal style='text-align:justify'><span lang=EN-US>Where <b
style='mso-bidi-font-weight:normal'><i style='mso-bidi-font-style:normal'>k</i></b>
<span class=GramE>remains</span> a scalar coefficient computed from the span
statistics with: </span><sub><span lang=EN-US style='font-size:18.0pt;
line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
 id="_x0000_i1027" type="#_x0000_t75" alt="" style='width:188pt;height:18pt;
 mso-width-percent:0;mso-height-percent:0;mso-width-percent:0;
 mso-height-percent:0' o:ole="">
 <v:imagedata src="Refined_Lee_theory.fld/image048.wmz" o:title=""/>
</v:shape><![endif]--><![if !vml]><img width=188 height=18
src="Refined_Lee_theory.fld/image049.png" v:shapes="_x0000_i1027"><![endif]></span><!--[if gte mso 9]><xml>
 <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027"
  DrawAspect="Content" ObjectID="_1824309927">
 </o:OLEObject>
</xml><![endif]--></span></sub><span lang=EN-US>. <o:p></o:p></span></p>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US>This approximation <span class=GramE>is allows</span> to filter
polarimetric data in a fast and simple way and avoids additional coupling (or <span
class=GramE>cross-talk</span>) between the polarimetric channels.<o:p></o:p></span></p>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US><o:p>&nbsp;</o:p></span></p>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US>Once the edge-aligned window is selected based on the span, pixels
in the edge-aligned window are then used to compute the mean for each element
of the covariance / coherency matrix and the same filtering weights computed
for the span image are then applied to each element equally and independently.
The computation of the local variance is not required for each element of the
covariance / coherency matrix, because the filtering weights are determined by
the span. Only the local variance of the span image is required for the
computation of the filtering weight. The use of the same weights makes this
algorithm computationally efficient. Additionally, the polarimetric information
is preserved in homogeneous areas, and <span class=GramE>cross-talk</span>
between channels is avoided. This is because, for each pixel, each element of
the covariance matrix is filtered independently to avoid <span class=GramE>cross-talk</span>,
and the same edge-aligned window and the same filtering weight are applied to
filter all elements of the covariance / coherency matrix to preserve
polarimetric information. Furthermore, the image sharpness is maintained,
because of the use of edge-aligned windows. <o:p></o:p></span></p>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US>The following figure proposes a flowchart of the J.S. Lee refined
speckle filter when applied on a 3x3 coherency matrix </span><sub><span
lang=EN-US style='font-size:18.0pt;line-height:115%'><span style='mso-no-proof:
yes'><!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" alt=""
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</v:shape><![endif]--><![if !vml]><img width=23 height=20
src="Refined_Lee_theory.fld/image043.png" v:shapes="_x0000_i1026"><![endif]></span><!--[if gte mso 9]><xml>
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</xml><![endif]--></span></sub><span lang=EN-US>.<o:p></o:p></span></p>

<p class=MsoNormal style='text-align:justify;text-indent:14.2pt'><span
lang=EN-US><o:p>&nbsp;</o:p></span></p>

<p class=MsoNormal align=center style='text-align:center'><span lang=EN-US
style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="image367.png" o:spid="_x0000_i1025"
 type="#_x0000_t75" alt="A black background with blue text&#10;&#10;AI-generated content may be incorrect."
 style='width:454pt;height:296pt;visibility:visible;mso-wrap-style:square'
 o:bordertopcolor="blue" o:borderleftcolor="blue" o:borderbottomcolor="blue"
 o:borderrightcolor="blue">
 <v:imagedata src="Refined_Lee_theory.fld/image050.png" o:title="A black background with blue text&#10;&#10;AI-generated content may be incorrect"/>
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</v:shape><![endif]--><![if !vml]><img width=456 height=298
src="Refined_Lee_theory.fld/image051.png"
alt="A black background with blue text&#10;&#10;AI-generated content may be incorrect."
v:shapes="image367.png"><![endif]></span><span lang=EN-US><o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:35.4pt'><span lang=EN-US><o:p>&nbsp;</o:p></span></p>

<h2><span lang=EN-US>References<o:p></o:p></span></h2>

<p class=MsoNormal style='text-align:justify'><b style='mso-bidi-font-weight:
normal'><u><span lang=EN-US style='font-variant:small-caps'>Books:<o:p></o:p></span></u></b></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;mso-list:l2 level1 lfo2;border:none;mso-padding-alt:31.0pt 31.0pt 31.0pt 31.0pt;
mso-border-shadow:yes'><![if !supportLists]><span lang=EN-US style='font-family:
"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";mso-bidi-font-family:
"Noto Sans Symbols";color:black'><span style='mso-list:Ignore'>●<span
style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
style='mso-bidi-font-weight:normal'><span lang=EN-US style='color:black'>Jong-Sen
LEE – Eric POTTIER, </span></b><i style='mso-bidi-font-style:normal'><span
lang=EN-US style='color:black'>Polarimetric Radar Imaging: From basics to
applications, </span></i><span lang=EN-US style='color:black'>CRC Press; 1st
ed., February 2009, pp 422, ISBN: 978-1420054972 <o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;mso-list:l2 level1 lfo2;border:none;mso-padding-alt:31.0pt 31.0pt 31.0pt 31.0pt;
mso-border-shadow:yes'><![if !supportLists]><span lang=EN-US style='font-family:
"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";mso-bidi-font-family:
"Noto Sans Symbols";color:black'><span style='mso-list:Ignore'>●<span
style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
style='mso-bidi-font-weight:normal'><span lang=EN-US style='color:black'>Shane
R. CLOUDE,</span></b><i style='mso-bidi-font-style:normal'><span lang=EN-US
style='color:black'> <span class=SpellE>Polarisation</span>: Applications in
Remote Sensing</span></i><span lang=EN-US style='color:black'>, Oxford
University Press, October 2009, pp 352, ISBN: 978-0199569731<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;mso-list:l2 level1 lfo2;border:none;mso-padding-alt:31.0pt 31.0pt 31.0pt 31.0pt;
mso-border-shadow:yes'><![if !supportLists]><span lang=EN-US style='font-family:
"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";mso-bidi-font-family:
"Noto Sans Symbols";color:black'><span style='mso-list:Ignore'>●<span
style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
style='mso-bidi-font-weight:normal'><span lang=EN-US style='color:black'>Charles
ELACHI – Jakob J. VAN ZYL,</span></b><i style='mso-bidi-font-style:normal'><span
lang=EN-US style='color:black'> Introduction <span class=GramE>To</span> <span
class=GramE>The</span> Physics and Techniques of Remote Sensing, </span></i><span
lang=EN-US style='color:black'>Wiley-<span class=SpellE>Interscience</span>;
2nd edition (July 31, 2007), ISBN-10 0-471-47569-6, ISBN-13 978-0471475699<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;mso-list:l2 level1 lfo2;border:none;mso-padding-alt:31.0pt 31.0pt 31.0pt 31.0pt;
mso-border-shadow:yes'><![if !supportLists]><span lang=EN-US style='font-family:
"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";mso-bidi-font-family:
"Noto Sans Symbols";color:black'><span style='mso-list:Ignore'>●<span
style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
style='mso-bidi-font-weight:normal'><span lang=EN-US style='color:black'>Harold
MOTT<i style='mso-bidi-font-style:normal'>, </i></span></b><i style='mso-bidi-font-style:
normal'><span lang=EN-US style='color:black'>Remote Sensing with Polarimetric
Radar, </span></i><span lang=EN-US style='color:black'>Wiley-IEEE Press; 1st
edition (January 2, 2007), ISBN-10 0-470-07476-0, ISBN-13 978-0470074763<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;mso-list:l2 level1 lfo2;border:none;mso-padding-alt:31.0pt 31.0pt 31.0pt 31.0pt;
mso-border-shadow:yes'><![if !supportLists]><span lang=EN-US style='font-family:
"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";mso-bidi-font-family:
"Noto Sans Symbols";color:black'><span style='mso-list:Ignore'>●<span
style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
style='mso-bidi-font-weight:normal'><span lang=EN-US style='color:black'>Jakob
J. VAN ZYL – <span class=SpellE>Yunjin</span> KIM<i style='mso-bidi-font-style:
normal'>,</i> </span></b><i style='mso-bidi-font-style:normal'><span
lang=EN-US style='color:black'>Synthetic Aperture Radar Polarimetry, </span></i><span
lang=EN-US style='color:black'>Wiley; 1st edition (October 14, 2011), ISBN-10
1-118-11511-2, ISBN-13 978-1118115114<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;mso-list:l2 level1 lfo2;border:none;mso-padding-alt:31.0pt 31.0pt 31.0pt 31.0pt;
mso-border-shadow:yes'><![if !supportLists]><span lang=EN-US style='font-family:
"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";mso-bidi-font-family:
"Noto Sans Symbols";color:black'><span style='mso-list:Ignore'>●<span
style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
style='mso-bidi-font-weight:normal'><span lang=EN-US style='color:black'>Yoshio
Yamaguchi</span></b><span lang=EN-US style='color:black'>, <i style='mso-bidi-font-style:
normal'>Polarimetric SAR <span class=GramE>Imaging :</span> Theory and
Applications</i>, CRC Press; 1st ed., August 2020, pp 350, ISBN: 978-1003049753<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;mso-list:l2 level1 lfo2;border:none;mso-padding-alt:31.0pt 31.0pt 31.0pt 31.0pt;
mso-border-shadow:yes'><![if !supportLists]><span lang=EN-US style='font-family:
"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";mso-bidi-font-family:
"Noto Sans Symbols";color:black'><span style='mso-list:Ignore'>●<span
style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
style='mso-bidi-font-weight:normal'><span lang=EN-US style='color:black'>Irena
HAJNSEK – Yves-Louis DESNOS </span></b><span lang=EN-US style='color:black'>(editors)<b
style='mso-bidi-font-weight:normal'>, </b><i style='mso-bidi-font-style:normal'>Polarimetric
Synthetic Aperture <span class=GramE>Radar :</span> Principles and
applications, </i>Springer; 1st edition (Marsh 30, 2021), ISBN
978-3-030-56502-2<o:p></o:p></span></p>

<p class=MsoNormal style='text-align:justify'><span lang=EN-US><o:p>&nbsp;</o:p></span></p>

<p class=MsoNormal style='text-align:justify'><b style='mso-bidi-font-weight:
normal'><u><span lang=EN-US style='font-variant:small-caps'>Journals:<o:p></o:p></span></u></b></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;line-height:normal;mso-list:l0 level1 lfo4;tab-stops:326.05pt;
border:none;mso-padding-alt:31.0pt 31.0pt 31.0pt 31.0pt;mso-border-shadow:yes'><![if !supportLists]><span
lang=EN-US style='font-family:"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";
mso-bidi-font-family:"Noto Sans Symbols";color:black'><span style='mso-list:
Ignore'>●<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'><span
lang=EN-US style='font-family:"Cambria",serif;mso-fareast-font-family:Cambria;
mso-bidi-font-family:Cambria;color:black'>S. Goze, A. Lopes</span></b><span
lang=EN-US style='font-family:"Cambria",serif;mso-fareast-font-family:Cambria;
mso-bidi-font-family:Cambria;color:black'>, «&nbsp;A MMSE Speckle Filter for
Full Resolution SAR Polarimetric Data&nbsp;», J.E.W.A., vol 7, n°5, pp 717-737,
May 1993.<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;line-height:normal;mso-list:l0 level1 lfo4;border:none;mso-padding-alt:
31.0pt 31.0pt 31.0pt 31.0pt;mso-border-shadow:yes'><![if !supportLists]><span
lang=EN-US style='font-family:"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";
mso-bidi-font-family:"Noto Sans Symbols";color:black'><span style='mso-list:
Ignore'>●<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'><span
lang=EN-US style='color:black'>J.S. Lee</span></b><span lang=EN-US
style='color:black'>, «&nbsp;Digital Image Enhancement and Noise Filtering by
Use of Local Statistics&nbsp;», IEEE Transactions on Pattern Analysis and
Machine Intelligence, Vol PAMI-2, n°2, pp 165-168, March 1980.<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;line-height:normal;mso-list:l0 level1 lfo4;border:none;mso-padding-alt:
31.0pt 31.0pt 31.0pt 31.0pt;mso-border-shadow:yes'><![if !supportLists]><span
lang=EN-US style='font-family:"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";
mso-bidi-font-family:"Noto Sans Symbols";color:black'><span style='mso-list:
Ignore'>●<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'><span
lang=EN-US style='color:black'>J.S. Lee</span></b><span lang=EN-US
style='color:black'>, «&nbsp;Refined Filtering of Image Noise Using Local
Statistics&nbsp;», Computer Graphics and Image Processing, 15, pp 380-389,
1981.<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;line-height:normal;mso-list:l0 level1 lfo4;border:none;mso-padding-alt:
31.0pt 31.0pt 31.0pt 31.0pt;mso-border-shadow:yes'><![if !supportLists]><span
lang=EN-US style='font-family:"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";
mso-bidi-font-family:"Noto Sans Symbols";color:black'><span style='mso-list:
Ignore'>●<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'><span
lang=EN-US style='color:black'>J.S. Lee</span></b><span lang=EN-US
style='color:black'>, «&nbsp;Speckle Analysis and Smoothing of Synthetic
Aperture Radar Images&nbsp;», Computer Graphics and Image Processing, 17, pp
24-32, 1981.<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;line-height:normal;mso-list:l0 level1 lfo4;border:none;mso-padding-alt:
31.0pt 31.0pt 31.0pt 31.0pt;mso-border-shadow:yes'><![if !supportLists]><span
lang=EN-US style='font-family:"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";
mso-bidi-font-family:"Noto Sans Symbols";color:black'><span style='mso-list:
Ignore'>●<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'><span
lang=EN-US style='color:black'>J.S. Lee</span></b><span lang=EN-US
style='color:black'>, «&nbsp;A Simple Speckle Smoothing Algorithm for Synthetic
Aperture Radar Images&nbsp;», IEEE Transactions on Systems, Man and
Cybernetics, Vol SMC 13, n°1, pp 85-89, January/<span class=SpellE>february</span>
1983.<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;line-height:normal;mso-list:l0 level1 lfo4;border:none;mso-padding-alt:
31.0pt 31.0pt 31.0pt 31.0pt;mso-border-shadow:yes'><![if !supportLists]><span
lang=EN-US style='font-family:"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";
mso-bidi-font-family:"Noto Sans Symbols";color:black'><span style='mso-list:
Ignore'>●<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'><span
lang=EN-US style='color:black'>J.S. Lee</span></b><span lang=EN-US
style='color:black'>, «&nbsp;Speckle Suppression and Analysis for Synthetic
Aperture Radar Images&nbsp;», Optical Engineering 25(81), pp 636-643, May 1986.<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;line-height:normal;mso-list:l0 level1 lfo4;border:none;mso-padding-alt:
31.0pt 31.0pt 31.0pt 31.0pt;mso-border-shadow:yes'><![if !supportLists]><span
lang=EN-US style='font-family:"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";
mso-bidi-font-family:"Noto Sans Symbols";color:black'><span style='mso-list:
Ignore'>●<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'><span
lang=EN-US style='color:black'>J.S. Lee, M.R. <span class=SpellE>Grunes</span></span></b><span
lang=EN-US style='color:black'>, «&nbsp;Speckle Reduction in <span
class=SpellE>Multipolarization</span>, Multifrequency SAR Imagery&nbsp;», IEEE
Transactions on Geoscience and Remote Sensing, vol 29, n°4, pp 535-544, July
1991.<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;line-height:normal;mso-list:l0 level1 lfo4;border:none;mso-padding-alt:
31.0pt 31.0pt 31.0pt 31.0pt;mso-border-shadow:yes'><![if !supportLists]><span
lang=EN-US style='font-family:"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";
mso-bidi-font-family:"Noto Sans Symbols";color:black'><span style='mso-list:
Ignore'>●<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'><span
lang=EN-US style='color:black'>J.S. Lee, K.W. Hoppel, S.A. Mango, <span
class=SpellE><span class=GramE>A.Miller</span></span></span></b><span
lang=EN-US style='color:black'>, “Intensity and Phase Statistics of Multi-Look
Polarimetric and Interferometric SAR Imagery”, IEEE Trans GE-32, pp. 1017-1028,
1994.<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;line-height:normal;mso-list:l0 level1 lfo4;border:none;mso-padding-alt:
31.0pt 31.0pt 31.0pt 31.0pt;mso-border-shadow:yes'><![if !supportLists]><span
lang=EN-US style='font-family:"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";
mso-bidi-font-family:"Noto Sans Symbols";color:black'><span style='mso-list:
Ignore'>●<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'><span
lang=EN-US style='color:black'>J.S. Lee, I. <span class=SpellE>Jurkevich</span>,
P. Dewaele, P. <span class=SpellE>Wambacq</span>, A. <span class=SpellE>Oosterlinck</span></span></b><span
lang=EN-US style='color:black'>. «&nbsp;Speckle Filtering of Synthetic Aperture
Radar Images: A Review&nbsp;», Remote Sensing Review, 1994, Vol n°8, pp
313-340.<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;line-height:normal;mso-list:l0 level1 lfo4;border:none;mso-padding-alt:
31.0pt 31.0pt 31.0pt 31.0pt;mso-border-shadow:yes'><![if !supportLists]><span
lang=EN-US style='font-family:"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";
mso-bidi-font-family:"Noto Sans Symbols";color:black'><span style='mso-list:
Ignore'>●<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'><span
lang=EN-US style='color:black'>Lopes, R. Touzi, E. <span class=SpellE>Nezry</span></span></b><span
lang=EN-US style='color:black'>, «&nbsp;Adaptative Speckle Filters and Scene
Heterogeneity&nbsp;», IEEE Transactions on Geoscience and Remote Sensing, vol
28, n°6, pp 992-1000, November 1990.<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;line-height:normal;mso-list:l0 level1 lfo4;border:none;mso-padding-alt:
31.0pt 31.0pt 31.0pt 31.0pt;mso-border-shadow:yes'><![if !supportLists]><span
lang=EN-US style='font-family:"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";
mso-bidi-font-family:"Noto Sans Symbols";color:black'><span style='mso-list:
Ignore'>●<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'><span
lang=EN-US style='color:black'>Lopes, E. <span class=SpellE>Nezry</span>, R.
Touzi, H. Laur</span></b><span lang=EN-US style='color:black'>,
«&nbsp;Structure Detection and Statistical Adaptive Speckle Filtering in SAR
Images&nbsp;», International Journal of Remote Sensing, 1993, Vol 14, n°9, pp
1735-1758.<o:p></o:p></span></p>

<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-18.0pt;line-height:normal;mso-list:l0 level1 lfo4;border:none;mso-padding-alt:
31.0pt 31.0pt 31.0pt 31.0pt;mso-border-shadow:yes'><![if !supportLists]><span
lang=EN-US style='font-family:"Noto Sans Symbols";mso-fareast-font-family:"Noto Sans Symbols";
mso-bidi-font-family:"Noto Sans Symbols";color:black'><span style='mso-list:
Ignore'>●<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><b style='mso-bidi-font-weight:normal'><span
lang=EN-US style='color:black'>R. Touzi, A. Lopes</span></b><span lang=EN-US
style='color:black'>, «&nbsp;The Principle of Speckle Filtering in Polarimetric
SAR Imagery&nbsp;», IEEE Transactions on Geoscience and Remote Sensing, vol 32,
n°5, pp 1110-1114, September 1994.<o:p></o:p></span></p>

<p class=MsoNormal><span lang=EN-US><o:p>&nbsp;</o:p></span></p>

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