File: testsetgenerator.cpp

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#include "testsetgenerator.h"

#include <iostream>
#include <sstream>

#include <math.h>

#include "../../structures/image2d.h"
#include "../../msio/pngfile.h"

#include "../../util/logger.h"
#include "../../util/ffttools.h"
#include "../../util/stopwatch.h"

#include "../../imaging/model.h"
#include "../../imaging/observatorium.h"

#include "combinatorialthresholder.h"
#include "localfitmethod.h"

void TestSetGenerator::AddBroadbandLine(Image2D& data, Mask2D& rfi,
                                        double lineStrength, size_t startTime,
                                        size_t duration, double frequencyRatio,
                                        double frequencyOffsetRatio) {
  size_t frequencyCount = data.Height();
  unsigned fStart = (size_t)(frequencyOffsetRatio * frequencyCount);
  unsigned fEnd =
      (size_t)((frequencyOffsetRatio + frequencyRatio) * frequencyCount);
  AddBroadbandLinePos(data, rfi, lineStrength, startTime, duration, fStart,
                      fEnd, UniformShape);
}

void TestSetGenerator::AddBroadbandLinePos(Image2D& data, Mask2D& rfi,
                                           double lineStrength,
                                           size_t startTime, size_t duration,
                                           unsigned frequencyStart,
                                           double frequencyEnd,
                                           enum BroadbandShape shape) {
  const double s = (frequencyEnd - frequencyStart);
  for (size_t f = frequencyStart; f < frequencyEnd; ++f) {
    // x will run from -1 to 1
    const double x = (double)((f - frequencyStart) * 2) / s - 1.0;
    double factor = shapeLevel(shape, x);
    for (size_t t = startTime; t < startTime + duration; ++t) {
      data.AddValue(t, f, lineStrength * factor);
      if (lineStrength > 0.0) rfi.SetValue(t, f, true);
    }
  }
}

void TestSetGenerator::AddSlewedBroadbandLinePos(
    Image2D& data, Mask2D& rfi, double lineStrength, double slewrate,
    size_t startTime, size_t duration, unsigned frequencyStart,
    double frequencyEnd, enum BroadbandShape shape) {
  const double s = (frequencyEnd - frequencyStart);
  for (size_t f = frequencyStart; f < frequencyEnd; ++f) {
    // x will run from -1 to 1
    const double x = (double)((f - frequencyStart) * 2) / s - 1.0;
    double factor = shapeLevel(shape, x);
    double slew = slewrate * (double)f;
    size_t slewInt = (size_t)slew;
    double slewRest = slew - slewInt;

    data.AddValue(startTime + slewInt, f,
                  lineStrength * factor * (1.0 - slewRest));
    if (lineStrength > 0.0) rfi.SetValue(startTime + slewInt, f, true);
    for (size_t t = startTime + 1; t < startTime + duration; ++t) {
      data.AddValue(t + slewInt, f, lineStrength * factor);
      if (lineStrength > 0.0) rfi.SetValue(t + slewInt, f, true);
    }
    data.AddValue(startTime + duration + slewInt, f,
                  lineStrength * factor * slewRest);
    if (lineStrength > 0.0)
      rfi.SetValue(startTime + duration + slewInt, f, true);
  }
}

void TestSetGenerator::AddRfiPos(Image2D& data, Mask2D& rfi,
                                 double lineStrength, size_t startTime,
                                 size_t duration, unsigned frequencyPos) {
  for (size_t t = startTime; t < startTime + duration; ++t) {
    data.AddValue(t, frequencyPos, lineStrength);
    if (lineStrength > 0) rfi.SetValue(t, frequencyPos, true);
  }
}

Image2D TestSetGenerator::MakeRayleighData(unsigned width, unsigned height) {
  Image2D image = Image2D::MakeUnsetImage(width, height);
  for (unsigned y = 0; y < height; ++y) {
    for (unsigned x = 0; x < width; ++x) {
      image.SetValue(x, y, RNG::Rayleigh());
    }
  }
  return image;
}

Image2D TestSetGenerator::MakeGaussianData(unsigned width, unsigned height) {
  Image2D image = Image2D::MakeUnsetImage(width, height);
  for (unsigned y = 0; y < height; ++y) {
    for (unsigned x = 0; x < width; ++x) {
      image.SetValue(x, y, RNG::Gaussian());
    }
  }
  return image;
}

std::string TestSetGenerator::GetTestSetDescription(int number) {
  switch (number) {
    case 0:
      return "Image of all zero's";
    case 1:
      return "Image of all ones";
    case 2:
      return "Noise";
    case 3:
      return "Several broadband RFI contaminating all channels";
    case 4:
      return "Several broadband RFI contaminating a part of channels";
    case 5:
      return "Several broadband RFI contaminating a random part of channels";
    case 6:
      return "Several broadband RFI on a sine wave background";
    case 7:
      return "Several broadband lines on a background of rotating sine waves";
    case 8:
      return "Testset 7 with a background fit on the background";
    case 9:
      return "Testset 7 in the time-lag domain";
    case 10:
      return "Identity matrix";
    case 11:
      return "FFT of Identity matrix";
    case 12:
      return "Broadband RFI contaminating all channels";
    case 13:
      return "Model of three point sources with broadband RFI";
    case 14:
      return "Model of five point sources with broadband RFI";
    case 15:
      return "Model of five point sources with partial broadband RFI";
    case 16:
      return "Model of five point sources with random broadband RFI";
    case 17:
      return "Background-fitted model of five point sources with random "
             "broadband RFI";
    case 18:
      return "Model of three point sources with random RFI";
    case 19:
      return "Model of three point sources with noise";
    case 20:
      return "Model of five point sources with noise";
    case 21:
      return "Model of three point sources";
    case 22:
      return "Model of five point sources";
    case 26:
      return "Gaussian lines";
    default:
      return "?";
  }
}

Image2D TestSetGenerator::MakeTestSet(int number, Mask2D& rfi, unsigned width,
                                      unsigned height, int gaussianNoise) {
  Image2D image;
  switch (number) {
    case 0:  // Image of all zero's
      return Image2D::MakeZeroImage(width, height);
    case 1:  // Image of all ones
      image = Image2D::MakeUnsetImage(width, height);
      image.SetAll(1.0);
      break;
    case 2:  // Noise
      return MakeNoise(width, height, gaussianNoise);
    case 3: {  // Several broadband lines
      image = MakeNoise(width, height, gaussianNoise);
      AddBroadbandToTestSet(image, rfi, 1.0);
    } break;
    case 4: {  // Several broadband lines
      image = MakeNoise(width, height, gaussianNoise);
      AddBroadbandToTestSet(image, rfi, 0.5);
    } break;
    case 5: {  // Several broadband lines of random length
      image = MakeNoise(width, height, gaussianNoise);
      AddVarBroadbandToTestSet(image, rfi);
    } break;
    case 6: {  // Different broadband lines + low freq background
      image = MakeNoise(width, height, gaussianNoise);
      AddVarBroadbandToTestSet(image, rfi);
      for (unsigned y = 0; y < image.Height(); ++y) {
        for (unsigned x = 0; x < image.Width(); ++x) {
          image.AddValue(x, y,
                         sinn(num_t(x) * M_PIn * 5.0 / image.Width()) + 0.1);
        }
      }
    } break;
    case 7: {  // Different broadband lines + high freq background
      image = MakeNoise(width, height, gaussianNoise);
      for (unsigned y = 0; y < image.Height(); ++y) {
        for (unsigned x = 0; x < image.Width(); ++x) {
          image.AddValue(
              x, y,
              sinn((long double)(x + y * 0.1) * M_PIn * 5.0L / image.Width() +
                   0.1));
          image.AddValue(x, y,
                         sinn((long double)(x + pown(y, 1.1)) * M_PIn * 50.0L /
                                  image.Width() +
                              0.1));
        }
      }
      AddVarBroadbandToTestSet(image, rfi);
      for (unsigned y = 0; y < image.Height(); ++y) {
        for (unsigned x = 0; x < image.Width(); ++x) {
          image.AddValue(x, y, 1.0);
        }
      }
    } break;
    case 8: {  // Different droadband lines + smoothed&subtracted high freq
               // background
      image = MakeNoise(width, height, gaussianNoise);
      for (unsigned y = 0; y < image.Height(); ++y) {
        for (unsigned x = 0; x < image.Width(); ++x) {
          image.AddValue(
              x, y,
              sinn((num_t)(x + y * 0.1) * M_PIn * 5.0 / image.Width() + 0.1));
          image.AddValue(
              x, y,
              sinn((num_t)(x + pown(y, 1.1)) * M_PIn * 50.0 / image.Width() +
                   0.1));
        }
      }
      SubtractBackground(image);
      AddVarBroadbandToTestSet(image, rfi);
    } break;
    case 9: {  // FFT of 7
      image = MakeTestSet(7, rfi, width, height);
      Image2D copy(image);
      FFTTools::CreateHorizontalFFTImage(image, copy, false);
      for (unsigned y = 0; y < rfi.Height(); ++y) {
        for (unsigned x = 0; x < rfi.Width(); ++x) {
          image.SetValue(x, y, image.Value(x, y) / sqrtn(image.Width()));
        }
      }
    } break;
    case 10: {  // Identity matrix
      image = Image2D::MakeZeroImage(width, height);
      unsigned min = width < height ? width : height;
      for (unsigned i = 0; i < min; ++i) {
        image.SetValue(i, i, 1.0);
        rfi.SetValue(i, i, true);
      }
    } break;
    case 11: {  // FFT of identity matrix
      image = MakeTestSet(10, rfi, width, height);
      Image2D copy(image);
      FFTTools::CreateHorizontalFFTImage(image, copy, false);
      for (unsigned y = 0; y < rfi.Height(); ++y) {
        for (unsigned x = 0; x < rfi.Width(); ++x) {
          image.SetValue(x, y, image.Value(x, y) / sqrtn(width));
        }
      }
    } break;
    case 12: {  // Broadband contaminating all channels
      image = MakeNoise(width, height, gaussianNoise);
      for (unsigned y = 0; y < image.Height(); ++y) {
        for (unsigned x = 0; x < image.Width(); ++x) {
          image.AddValue(
              x, y,
              sinn((num_t)(x + y * 0.1) * M_PIn * 5.0 / image.Width() + 0.1));
          image.AddValue(
              x, y,
              sinn((num_t)(x + powl(y, 1.1)) * M_PIn * 50.0 / image.Width() +
                   0.1));
        }
      }
      AddBroadbandToTestSet(image, rfi, 1.0);
    } break;
    case 13: {  // Model of three point sources with broadband RFI
      SetModelData(image, rfi, 3, width, height);
      Image2D noise = MakeNoise(image.Width(), image.Height(), gaussianNoise);
      image += noise;
      AddBroadbandToTestSet(image, rfi, 1.0);
    } break;
    case 14: {  // Model of five point sources with broadband RFI
      SetModelData(image, rfi, 5, width, height);
      Image2D noise = MakeNoise(image.Width(), image.Height(), gaussianNoise);
      image += noise;
      AddBroadbandToTestSet(image, rfi, 1.0);
    } break;
    case 15: {  // Model of five point sources with partial broadband RFI
      SetModelData(image, rfi, 5, width, height);
      Image2D noise = MakeNoise(image.Width(), image.Height(), gaussianNoise);
      image += noise;
      AddBroadbandToTestSet(image, rfi, 0.5);
    } break;
    case 16: {  // Model of five point sources with random broadband RFI
      SetModelData(image, rfi, 5, width, height);
      Image2D noise = MakeNoise(image.Width(), image.Height(), gaussianNoise);
      image += noise;
      AddVarBroadbandToTestSet(image, rfi);
    } break;
    case 17: {  // Background-fitted model of five point sources with random
                // broadband RFI
      SetModelData(image, rfi, 5, width, height);
      Image2D noise = MakeNoise(image.Width(), image.Height(), gaussianNoise);
      image += noise;
      SubtractBackground(image);
      AddVarBroadbandToTestSet(image, rfi);
    } break;
    case 18: {  // Model of three point sources with random RFI
      SetModelData(image, rfi, 3, width, height);
      Image2D noise = MakeNoise(image.Width(), image.Height(), gaussianNoise);
      image += noise;
      AddVarBroadbandToTestSet(image, rfi);
    } break;
    case 19: {  // Model of three point sources with noise
      SetModelData(image, rfi, 3, width, height);
      Image2D noise = MakeNoise(image.Width(), image.Height(), gaussianNoise);
      image += noise;
    } break;
    case 20: {  // Model of five point sources with noise
      SetModelData(image, rfi, 5, width, height);
      Image2D noise = MakeNoise(image.Width(), image.Height(), gaussianNoise);
      image += noise;
    } break;
    case 21: {  // Model of three point sources
      SetModelData(image, rfi, 3, width, height);
    } break;
    case 22: {  // Model of five point sources
      image = Image2D::MakeZeroImage(width, height);
      SetModelData(image, rfi, 5, width, height);
    } break;
    case 23:
      image = MakeNoise(width, height, gaussianNoise);
      AddBroadbandToTestSet(image, rfi, 0.5, 0.1, true);
      break;
    case 24:
      image = MakeNoise(width, height, gaussianNoise);
      AddBroadbandToTestSet(image, rfi, 0.5, 10.0, true);
      break;
    case 25:
      image = MakeNoise(width, height, gaussianNoise);
      AddBroadbandToTestSet(image, rfi, 0.5, 1.0, true);
      break;
    case 26: {  // Several Gaussian broadband lines
      image = MakeNoise(width, height, gaussianNoise);
      AddBroadbandToTestSet(image, rfi, 1.0, 1.0, false, GaussianShape);
    } break;
    case 27: {  // Several Sinusoidal broadband lines
      image = MakeNoise(width, height, gaussianNoise);
      AddBroadbandToTestSet(image, rfi, 1.0, 1.0, false, SinusoidalShape);
    } break;
    case 28: {  // Several slewed Gaussian broadband lines
      image = MakeNoise(width, height, gaussianNoise);
      AddSlewedBroadbandToTestSet(image, rfi, 1.0);
    } break;
    case 29: {  // Several bursty broadband lines
      image = MakeNoise(width, height, gaussianNoise);
      AddBurstBroadbandToTestSet(image, rfi);
    } break;
    case 30: {  // noise + RFI ^-2 distribution
      image = sampleRFIDistribution(width, height, 1.0);
      rfi.SetAll<true>();
    } break;
    case 31: {  // noise + RFI ^-2 distribution
      image = sampleRFIDistribution(width, height, 0.1);
      rfi.SetAll<true>();
    } break;
    case 32: {  // noise + RFI ^-2 distribution
      image = sampleRFIDistribution(width, height, 0.01);
      rfi.SetAll<true>();
    } break;
  }
  return image;
}

void TestSetGenerator::AddBroadbandToTestSet(Image2D& image, Mask2D& rfi,
                                             long double length,
                                             double strength, bool align,
                                             enum BroadbandShape shape) {
  size_t frequencyCount = image.Height();
  unsigned step = image.Width() / 11;
  if (align) {
    // see vertevd.h why this is:
    unsigned n = (unsigned)floor(0.5 + sqrt(0.25 + 2.0 * frequencyCount));
    unsigned affectedAntennas = (unsigned)n * (double)length;
    unsigned index = 0;
    Logger::Debug << affectedAntennas << " of " << n << " antennas effected."
                  << '\n';
    Logger::Debug << "Affected  baselines: ";
    for (unsigned y = 0; y < n; ++y) {
      for (unsigned x = y + 1; x < n; ++x) {
        double a1, a2;
        if (x < affectedAntennas)
          a1 = 1.0;
        else
          a1 = 0.0;
        if (y < affectedAntennas)
          a2 = 1.0;
        else
          a2 = 0.0;

        if (y < affectedAntennas || x < affectedAntennas) {
          Logger::Debug << x << " x " << y << ", ";
          AddRfiPos(image, rfi, 3.0 * strength * a1 * a2, step * 1, 3, index);
          AddRfiPos(image, rfi, 2.5 * strength * a1 * a2, step * 2, 3, index);
          AddRfiPos(image, rfi, 2.0 * strength * a1 * a2, step * 3, 3, index);
          AddRfiPos(image, rfi, 1.8 * strength * a1 * a2, step * 4, 3, index);
          AddRfiPos(image, rfi, 1.6 * strength * a1 * a2, step * 5, 3, index);

          AddRfiPos(image, rfi, 3.0 * strength * a1 * a2, step * 6, 1, index);
          AddRfiPos(image, rfi, 2.5 * strength * a1 * a2, step * 7, 1, index);
          AddRfiPos(image, rfi, 2.0 * strength * a1 * a2, step * 8, 1, index);
          AddRfiPos(image, rfi, 1.8 * strength * a1 * a2, step * 9, 1, index);
          AddRfiPos(image, rfi, 1.6 * strength * a1 * a2, step * 10, 1, index);
        }
        ++index;
      }
    }
    Logger::Debug << ".\n";
  } else {
    unsigned fStart = (unsigned)((0.5 - length / 2.0) * frequencyCount);
    unsigned fEnd = (unsigned)((0.5 + length / 2.0) * frequencyCount);
    AddBroadbandLinePos(image, rfi, 3.0 * strength, step * 1, 3, fStart, fEnd,
                        shape);
    AddBroadbandLinePos(image, rfi, 2.5 * strength, step * 2, 3, fStart, fEnd,
                        shape);
    AddBroadbandLinePos(image, rfi, 2.0 * strength, step * 3, 3, fStart, fEnd,
                        shape);
    AddBroadbandLinePos(image, rfi, 1.8 * strength, step * 4, 3, fStart, fEnd,
                        shape);
    AddBroadbandLinePos(image, rfi, 1.6 * strength, step * 5, 3, fStart, fEnd,
                        shape);

    AddBroadbandLinePos(image, rfi, 3.0 * strength, step * 6, 1, fStart, fEnd,
                        shape);
    AddBroadbandLinePos(image, rfi, 2.5 * strength, step * 7, 1, fStart, fEnd,
                        shape);
    AddBroadbandLinePos(image, rfi, 2.0 * strength, step * 8, 1, fStart, fEnd,
                        shape);
    AddBroadbandLinePos(image, rfi, 1.8 * strength, step * 9, 1, fStart, fEnd,
                        shape);
    AddBroadbandLinePos(image, rfi, 1.6 * strength, step * 10, 1, fStart, fEnd,
                        shape);
  }
}

void TestSetGenerator::AddSlewedBroadbandToTestSet(Image2D& image, Mask2D& rfi,
                                                   long double length,
                                                   double strength,
                                                   double slewrate,
                                                   enum BroadbandShape shape) {
  size_t frequencyCount = image.Height();
  unsigned step = image.Width() / 11;
  unsigned fStart = (unsigned)((0.5 - length / 2.0) * frequencyCount);
  unsigned fEnd = (unsigned)((0.5 + length / 2.0) * frequencyCount);
  AddSlewedBroadbandLinePos(image, rfi, 3.0 * strength, slewrate, step * 1, 3,
                            fStart, fEnd, shape);
  AddSlewedBroadbandLinePos(image, rfi, 2.5 * strength, slewrate, step * 2, 3,
                            fStart, fEnd, shape);
  AddSlewedBroadbandLinePos(image, rfi, 2.0 * strength, slewrate, step * 3, 3,
                            fStart, fEnd, shape);
  AddSlewedBroadbandLinePos(image, rfi, 1.8 * strength, slewrate, step * 4, 3,
                            fStart, fEnd, shape);
  AddSlewedBroadbandLinePos(image, rfi, 1.6 * strength, slewrate, step * 5, 3,
                            fStart, fEnd, shape);

  AddSlewedBroadbandLinePos(image, rfi, 3.0 * strength, slewrate, step * 6, 1,
                            fStart, fEnd, shape);
  AddSlewedBroadbandLinePos(image, rfi, 2.5 * strength, slewrate, step * 7, 1,
                            fStart, fEnd, shape);
  AddSlewedBroadbandLinePos(image, rfi, 2.0 * strength, slewrate, step * 8, 1,
                            fStart, fEnd, shape);
  AddSlewedBroadbandLinePos(image, rfi, 1.8 * strength, slewrate, step * 9, 1,
                            fStart, fEnd, shape);
  AddSlewedBroadbandLinePos(image, rfi, 1.6 * strength, slewrate, step * 10, 1,
                            fStart, fEnd, shape);
}

void TestSetGenerator::AddVarBroadbandToTestSet(Image2D& image, Mask2D& rfi) {
  // The "randomness" should be reproducable randomness, so calling
  // the random number generator to generate the numbers is not a good
  // idea.
  unsigned step = image.Width() / 11;
  AddBroadbandLine(image, rfi, 3.0, step * 1, 3, 0.937071, 0.0185952);
  AddBroadbandLine(image, rfi, 2.5, step * 2, 3, 0.638442, 0.327689);
  AddBroadbandLine(image, rfi, 2.0, step * 3, 3, 0.859308, 0.0211675);
  AddBroadbandLine(image, rfi, 1.8, step * 4, 3, 0.418327, 0.324842);
  AddBroadbandLine(image, rfi, 1.6, step * 5, 3, 0.842374, 0.105613);

  AddBroadbandLine(image, rfi, 3.0, step * 6, 1, 0.704607, 0.163653);
  AddBroadbandLine(image, rfi, 2.5, step * 7, 1, 0.777955, 0.0925143);
  AddBroadbandLine(image, rfi, 2.0, step * 8, 1, 0.288418, 0.222322);
  AddBroadbandLine(image, rfi, 1.8, step * 9, 1, 0.892462, 0.0381083);
  AddBroadbandLine(image, rfi, 1.6, step * 10, 1, 0.444377, 0.240526);
}

void TestSetGenerator::SetModelData(Image2D& image, Mask2D& rfi,
                                    unsigned sources, size_t width,
                                    size_t height) {
  class Model model;
  if (sources >= 5) {
    model.AddSource(0.1, 0.1, 0.5);
    model.AddSource(0.1, 0.0, 0.35);
    model.AddSource(.101, 0.001, 0.45);
    model.AddSource(1.0, 0.0, 1.0);
    model.AddSource(4.0, 3.0, 0.9);
  } else {
    if (sources >= 1) model.AddSource(0.1, 0.1, 0.7);
    if (sources >= 2) model.AddSource(0.1, 0.0, 0.5);
    if (sources >= 3) model.AddSource(1.0, 0.0, 1.0);
  }
  WSRTObservatorium wsrt(size_t(0), size_t(1), height);
  std::pair<TimeFrequencyData, TimeFrequencyMetaDataCPtr> data =
      model.SimulateObservation(width, wsrt, 0.05, 0.05, 0, 1);
  image = *data.first.GetRealPart();
  rfi = Mask2D::MakeSetMask<false>(width, height);
}

void TestSetGenerator::SubtractBackground(Image2D& image) {
  Mask2DPtr zero =
      Mask2D::CreateSetMaskPtr<false>(image.Width(), image.Height());
  LocalFitMethod fittedImage;
  fittedImage.SetToWeightedAverage(20, 40, 7.5, 15.0);
  Image2DPtr imagePtr = Image2D::MakePtr(image);
  TimeFrequencyData data(TimeFrequencyData::AmplitudePart,
                         aocommon::Polarization::StokesI, imagePtr);
  data.SetGlobalMask(zero);
  fittedImage.Initialize(data);
  for (unsigned i = 0; i < fittedImage.TaskCount(); ++i)
    fittedImage.PerformFit(i);
  image =
      Image2D::MakeFromDiff(image, *fittedImage.Background().GetSingleImage());
  for (unsigned y = 0; y < image.Height(); ++y) {
    for (unsigned x = 0; x < image.Width(); ++x) {
      image.AddValue(x, y, 1.0);
    }
  }
}

Image2D TestSetGenerator::sampleRFIDistribution(unsigned width, unsigned height,
                                                double ig_over_rsq) {
  Image2D image = Image2D::MakeUnsetImage(width, height);
  const double sigma = 1.0;

  for (size_t f = 0; f < height; ++f) {
    for (size_t t = 0; t < width; ++t) {
      image.SetValue(t, f,
                     Rand(Gaussian) * sigma + ig_over_rsq / RNG::Uniform());
    }
  }
  return image;
}

TimeFrequencyData TestSetGenerator::MakeSpike() {
  constexpr size_t width = 7, height = 10, pols = 8;
  Image2DPtr images[pols];
  for (size_t p = 0; p != pols; ++p) {
    images[p] = Image2D::CreateUnsetImagePtr(width, height);
    for (size_t y = 0; y != height; ++y) {
      for (size_t x = 0; x != width; ++x) {
        images[p]->SetValue(x, y, ((x + y) % 2 == 0) ? -1 : 2);
      }
    }
  }
  // We set one absurdly high value which all strategies should detect
  size_t rfiX = width / 2, rfiY = height / 2;
  images[5]->SetValue(rfiX, rfiY, 1000.0);
  return TimeFrequencyData::FromLinear(images[0], images[1], images[2],
                                       images[3], images[4], images[5],
                                       images[6], images[7]);
}