MagickExport Image *WaveletDenoiseImage(const Image *image,
  const double threshold,const double softness,ExceptionInfo *exception)
{
  CacheView
    *image_view,
    *noise_view;

  float
    *kernel,
    *pixels;

  Image
    *noise_image;

  MagickBooleanType
    status;

  MagickSizeType
    number_pixels;

  MemoryInfo
    *pixels_info;

  size_t
    max_channels;

  ssize_t
    channel;

  static const double
    noise_levels[]= {
      0.8002, 0.2735, 0.1202, 0.0585, 0.0291, 0.0152, 0.0080, 0.0044 };

  /*
    Initialize noise image attributes.
  */
  assert(image != (const Image *) NULL);
  assert(image->signature == MagickCoreSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  assert(exception != (ExceptionInfo *) NULL);
  assert(exception->signature == MagickCoreSignature);
  noise_image=(Image *) NULL;
#if defined(MAGICKCORE_OPENCL_SUPPORT)
  noise_image=AccelerateWaveletDenoiseImage(image,threshold,exception);
  if (noise_image != (Image *) NULL)
    return(noise_image);
#endif
  noise_image=CloneImage(image,0,0,MagickTrue,exception);
  if (noise_image == (Image *) NULL)
    return((Image *) NULL);
  if (SetImageStorageClass(noise_image,DirectClass) == MagickFalse)
    {
      noise_image=DestroyImage(noise_image);
      return((Image *) NULL);
    }
  if (AcquireMagickResource(WidthResource,3*image->columns) == MagickFalse)
    ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
  pixels_info=AcquireVirtualMemory(3*image->columns,image->rows*
    sizeof(*pixels));
  kernel=(float *) AcquireQuantumMemory(MagickMax(image->rows,image->columns)+1,
    GetOpenMPMaximumThreads()*sizeof(*kernel));
  if ((pixels_info == (MemoryInfo *) NULL) || (kernel == (float *) NULL))
    {
      if (kernel != (float *) NULL)
        kernel=(float *) RelinquishMagickMemory(kernel);
      if (pixels_info != (MemoryInfo *) NULL)
        pixels_info=RelinquishVirtualMemory(pixels_info);
      ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
    }
  pixels=(float *) GetVirtualMemoryBlob(pixels_info);
  status=MagickTrue;
  number_pixels=image->columns*image->rows;
  max_channels=(size_t) (image->colorspace == CMYKColorspace ? 4 : 3);
  image_view=AcquireAuthenticCacheView(image,exception);
  noise_view=AcquireAuthenticCacheView(noise_image,exception);
  for (channel=0; channel < (ssize_t) max_channels; channel++)
  {
    ssize_t
      i;

    size_t
      high_pass,
      low_pass;

    ssize_t
      level,
      y;

    if (status == MagickFalse)
      continue;
    /*
      Copy channel from image to wavelet pixel array.
    */
    i=0;
    for (y=0; y < (ssize_t) image->rows; y++)
    {
      const IndexPacket
        *magick_restrict indexes;

      const PixelPacket
        *magick_restrict p;

      ssize_t
        x;

      p=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
      if (p == (const PixelPacket *) NULL)
        {
          status=MagickFalse;
          break;
        }
      indexes=GetCacheViewVirtualIndexQueue(image_view);
      for (x=0; x < (ssize_t) image->columns; x++)
      {
        switch (channel)
        {
          case 0: pixels[i]=(float) GetPixelRed(p); break;
          case 1: pixels[i]=(float) GetPixelGreen(p); break;
          case 2: pixels[i]=(float) GetPixelBlue(p); break;
          case 3: pixels[i]=(float) indexes[x]; break;
          default: break;
        }
        i++;
        p++;
      }
    }
    /*
      Low pass filter outputs are called approximation kernel & high pass
      filters are referred to as detail kernel. The detail kernel
      have high values in the noisy parts of the signal.
    */
    high_pass=0;
    for (level=0; level < 5; level++)
    {
      double
        magnitude;

      ssize_t
        x,
        y;

      low_pass=(size_t) (number_pixels*((level & 0x01)+1));
#if defined(MAGICKCORE_OPENMP_SUPPORT)
      #pragma omp parallel for schedule(static,1) \
        magick_number_threads(image,image,image->rows,1)
#endif
      for (y=0; y < (ssize_t) image->rows; y++)
      {
        const int
          id = GetOpenMPThreadId();

        float
          *magick_restrict p,
          *magick_restrict q;

        ssize_t
          x;

        p=kernel+id*image->columns;
        q=pixels+y*image->columns;
        HatTransform(q+high_pass,1,image->columns,(size_t) (1UL << level),p);
        q+=low_pass;
        for (x=0; x < (ssize_t) image->columns; x++)
          *q++=(*p++);
      }
#if defined(MAGICKCORE_OPENMP_SUPPORT)
      #pragma omp parallel for schedule(static,1) \
        magick_number_threads(image,image,image->columns,1)
#endif
      for (x=0; x < (ssize_t) image->columns; x++)
      {
        const int
          id = GetOpenMPThreadId();

        float
          *magick_restrict p,
          *magick_restrict q;

        ssize_t
          y;

        p=kernel+id*image->rows;
        q=pixels+x+low_pass;
        HatTransform(q,image->columns,image->rows,(size_t) (1UL << level),p);
        for (y=0; y < (ssize_t) image->rows; y++)
        {
          *q=(*p++);
          q+=image->columns;
        }
      }
      /*
        To threshold, each coefficient is compared to a threshold value and
        attenuated / shrunk by some factor.
      */
      magnitude=threshold*noise_levels[level];
      for (i=0; i < (ssize_t) number_pixels; ++i)
      {
        pixels[high_pass+i]-=pixels[low_pass+i];
        if (pixels[high_pass+i] < -magnitude)
          pixels[high_pass+i]+=magnitude-softness*magnitude;
        else
          if (pixels[high_pass+i] > magnitude)
            pixels[high_pass+i]-=magnitude-softness*magnitude;
          else
            pixels[high_pass+i]*=softness;
        if (high_pass != 0)
          pixels[i]+=pixels[high_pass+i];
      }
      high_pass=low_pass;
    }
    /*
      Reconstruct image from the thresholded wavelet kernel.
    */
    i=0;
    for (y=0; y < (ssize_t) image->rows; y++)
    {
      MagickBooleanType
        sync;

      IndexPacket
        *magick_restrict noise_indexes;

      PixelPacket
        *magick_restrict q;

      ssize_t
        x;

      q=GetCacheViewAuthenticPixels(noise_view,0,y,noise_image->columns,1,
        exception);
      if (q == (PixelPacket *) NULL)
        {
          status=MagickFalse;
          break;
        }
      noise_indexes=GetCacheViewAuthenticIndexQueue(noise_view);
      for (x=0; x < (ssize_t) image->columns; x++)
      {
        float
          pixel;

        pixel=pixels[i]+pixels[low_pass+i];
        switch (channel)
        {
          case 0: SetPixelRed(q,ClampToQuantum(pixel)); break;
          case 1: SetPixelGreen(q,ClampToQuantum(pixel)); break;
          case 2: SetPixelBlue(q,ClampToQuantum(pixel)); break;
          case 3: SetPixelIndex(noise_indexes+x,ClampToQuantum(pixel)); break;
          default: break;
        }
        i++;
        q++;
      }
      sync=SyncCacheViewAuthenticPixels(noise_view,exception);
      if (sync == MagickFalse)
        status=MagickFalse;
    }
    if (image->progress_monitor != (MagickProgressMonitor) NULL)
      {
        MagickBooleanType
          proceed;

        proceed=SetImageProgress(image,AddNoiseImageTag,(MagickOffsetType)
          channel,max_channels);
        if (proceed == MagickFalse)
          status=MagickFalse;
      }
  }
  noise_view=DestroyCacheView(noise_view);
  image_view=DestroyCacheView(image_view);
  kernel=(float *) RelinquishMagickMemory(kernel);
  pixels_info=RelinquishVirtualMemory(pixels_info);
  return(noise_image);
}