/// <summary>
/// Perform an inverse haar wavelet mel scaled transform. E.g. perform an ihaar2d and inverse Mel Filterbands and return stftdata
/// </summary>
/// <param name="wavelet">wavelet matrix</param>
/// <returns>matrix inverse wavelet'ed and mel removed (e.g. stftdata)</returns>
public Matrix InverseMelScaleWaveletPadding(ref Matrix wavelet)
{
using (new DebugTimer("InverseMelScaleWaveletPadding(wavelet)")) {
// 6. Perform the Inverse Wavelet Transform
Matrix mel = WaveletUtils.InverseHaarWaveletTransform2D(wavelet.MatrixData);
// Resize (remove padding)
mel = mel.Resize(melScaleFreqsIndex.Length - 2, wavelet.Columns);
// 5. Take Inverse Logarithm
// Divide with first triangle height in order to scale properly
for (int i = 0; i < mel.Rows; i++)
{
for (int j = 0; j < mel.Columns; j++)
{
mel.MatrixData[i][j] = Math.Pow(10, (mel.MatrixData[i][j] / 20)) / melScaleTriangleHeights[0];
}
}
// 4. Inverse Mel Scale using interpolation
// i.e. from e.g.
// mel=Rows: 40, Columns: 165 (average freq, time slice)
// to
// m=Rows: 1024, Columns: 165 (freq, time slice)
//Matrix m = filterWeights.Transpose() * mel;
var m = new Matrix(filterWeights.Columns, mel.Columns);
InverseMelScaling(mel, m);
return(m);
}
}
/// <summary>
/// Mel Scale Haar Wavelet Transform
/// </summary>
/// <param name="m">matrix (stftdata)</param>
/// <returns>matrix mel scaled and wavelet'ed</returns>
public Matrix ApplyMelScaleWaveletPadding(ref Matrix m)
{
using (new DebugTimer("ApplyMelScaleWaveletPadding(m)")) {
// 4. Mel Scale Filterbank
// Mel-frequency is proportional to the logarithm of the linear frequency,
// reflecting similar effects in the human's subjective aural perception)
Matrix mel = filterWeights * m;
// 5. Take Logarithm
for (int i = 0; i < mel.Rows; i++)
{
for (int j = 0; j < mel.Columns; j++)
{
mel.MatrixData[i][j] = (mel.MatrixData[i][j] < 1.0 ? 0 : (20.0 * Math.Log10(mel.MatrixData[i][j])));
}
}
// 6. Wavelet Transform
// make sure the matrix is square before transforming (by zero padding)
Matrix resizedMatrix;
if (!mel.IsSymmetric() || !MathUtils.IsPowerOfTwo(mel.Rows))
{
int size = (mel.Rows > mel.Columns ? mel.Rows : mel.Columns);
int sizePow2 = MathUtils.NextPowerOfTwo(size);
resizedMatrix = mel.Resize(sizePow2, sizePow2);
}
else
{
resizedMatrix = mel;
}
Matrix wavelet = WaveletUtils.HaarWaveletTransform2D(resizedMatrix.MatrixData, true);
return(wavelet);
}
}
/// <summary>
/// Perform an inverse haar wavelet mel scaled transform. E.g. perform an ihaar2d and inverse Mel Filterbands and return stftdata
/// </summary>
/// <param name="wavelet">wavelet matrix</param>
/// <returns>matrix inverse wavelet'ed and mel removed (e.g. stftdata)</returns>
public Matrix InverseMelScaleWaveletPadding(ref Matrix wavelet)
{
Mirage.DbgTimer t = new Mirage.DbgTimer();
t.Start();
// 6. Perform the Inverse Wavelet Transform
Matrix mel = WaveletUtils.InverseHaarWaveletTransform(wavelet.MatrixData);
// Resize (remove padding)
mel = mel.Resize(melScaleFreqsIndex.Length - 2, wavelet.Columns);
// 5. Take Inverse Logarithm
// Divide with first triangle height in order to scale properly
for (int i = 0; i < mel.Rows; i++)
{
for (int j = 0; j < mel.Columns; j++)
{
mel.MatrixData[i][j] = Math.Pow(10, (mel.MatrixData[i][j] / 20)) / melScaleTriangleHeights[0];
}
}
// 4. Inverse Mel Scale using interpolation
// i.e. from e.g.
// mel=Rows: 40, Columns: 165 (average freq, time slice)
// to
// m=Rows: 1024, Columns: 165 (freq, time slice)
//Matrix m = filterWeights.Transpose() * mel;
Matrix m = new Matrix(filterWeights.Columns, mel.Columns);
InverseMelScaling(mel, m);
Mirage.Dbg.WriteLine("Inverse Mel Scale And Wavelet Compression Padding - Execution Time: " + t.Stop().TotalMilliseconds + " ms");
return(m);
}
public static void TestDenoise(string imageInPath)
{
var image = ReadImageGrayscale(imageInPath);
// Normalize the pixel values to the range 0..1.0. It does this by dividing all pixel values by the max value.
double max = image.Max((b) => b.Max((v) => Math.Abs(v)));
double[][] imageNormalized = image.Select(i => i.Select(j => j / max).ToArray()).ToArray();
var normalizedMatrix = new Matrix(imageNormalized);
normalizedMatrix.DrawMatrixImage("lena-original.png", -1, -1, false);
// Add Noise using normally distributed pseudorandom numbers
// image_noisy = image_normalized + 0.1 * randn(size(image_normalized));
RandomUtils.Seed(Guid.NewGuid().GetHashCode());
double[][] imageNoisy = imageNormalized.Select(i => i.Select(j => j + (0.2 * RandomUtils.NextDouble())).ToArray()).ToArray();
var matrixNoisy = new Matrix(imageNoisy);
matrixNoisy.DrawMatrixImage("lena-noisy.png", -1, -1, false);
// Haar Wavelet Transform
Matrix haarMatrix = WaveletUtils.HaarWaveletTransform2D(imageNoisy);
// Thresholding
const double threshold = 0.10; // 0.15 seems to work well with the noise added above, 0.1
var yHard = Thresholding.PerformHardThresholding(haarMatrix.MatrixData, threshold);
var ySoft = Thresholding.PerformSoftThresholding(haarMatrix.MatrixData, threshold);
var ySemisoft = Thresholding.PerformSemisoftThresholding(haarMatrix.MatrixData, threshold, threshold * 2);
var ySemisoft2 = Thresholding.PerformSemisoftThresholding(haarMatrix.MatrixData, threshold, threshold * 4);
var yStrict = Thresholding.PerformStrictThresholding(haarMatrix.MatrixData, 100);
// Inverse 2D Haar Wavelet Transform
Matrix zHard = WaveletUtils.InverseHaarWaveletTransform2D(yHard);
Matrix zSoft = WaveletUtils.InverseHaarWaveletTransform2D(ySoft);
Matrix zSemisoft = WaveletUtils.InverseHaarWaveletTransform2D(ySemisoft);
Matrix zSemisoft2 = WaveletUtils.InverseHaarWaveletTransform2D(ySemisoft2);
Matrix zStrict = WaveletUtils.InverseHaarWaveletTransform2D(yStrict);
// Output the images
zHard.DrawMatrixImage("lena-thresholding-hard.png", -1, -1, false);
zSoft.DrawMatrixImage("lena-thresholding-soft.png", -1, -1, false);
zSemisoft.DrawMatrixImage("lena-thresholding-semisoft.png", -1, -1, false);
zSemisoft2.DrawMatrixImage("lena-thresholding-semisoft2.png", -1, -1, false);
zStrict.DrawMatrixImage("lena-thresholding-strict.png", -1, -1, false);
}
/// <summary>
/// Mel Scale Haar Wavelet Transform
/// </summary>
/// <param name="m">matrix (stftdata)</param>
/// <returns>matrix mel scaled and wavelet'ed</returns>
public Matrix ApplyMelScaleWaveletPadding(ref Matrix m)
{
Mirage.DbgTimer t = new Mirage.DbgTimer();
t.Start();
// 4. Mel Scale Filterbank
// Mel-frequency is proportional to the logarithm of the linear frequency,
// reflecting similar effects in the human's subjective aural perception)
Matrix mel = filterWeights * m;
// 5. Take Logarithm
for (int i = 0; i < mel.Rows; i++)
{
for (int j = 0; j < mel.Columns; j++)
{
mel.MatrixData[i][j] = (mel.MatrixData[i][j] < 1.0 ? 0 : (20.0 * Math.Log10(mel.MatrixData[i][j])));
}
}
// 6. Wavelet Transform
// make sure the matrix is square before transforming (by zero padding)
Matrix resizedMatrix;
if (!mel.IsSymmetric() || !MathUtils.IsPowerOfTwo(mel.Rows))
{
int size = (mel.Rows > mel.Columns ? mel.Rows : mel.Columns);
int sizePow2 = MathUtils.NextPowerOfTwo(size);
resizedMatrix = mel.Resize(sizePow2, sizePow2);
}
else
{
resizedMatrix = mel;
}
Matrix wavelet = WaveletUtils.HaarWaveletTransform(resizedMatrix.MatrixData, true);
Mirage.Dbg.WriteLine("Wavelet Mel Scale And Wavelet Compression Padding - Execution Time: " + t.Stop().TotalMilliseconds + " ms");
return(wavelet);
}
public static Matrix GetWaveletTransformedMatrix(double[][] image, WaveletMethod waveletMethod)
{
int width = image[0].Length;
int height = image.Length;
Matrix dwtMatrix = null;
Stopwatch stopWatch = Stopwatch.StartNew();
long startS = stopWatch.ElapsedTicks;
switch (waveletMethod)
{
case WaveletMethod.Haar:
Haar.Haar2D(image, height, width);
dwtMatrix = new Matrix(image);
break;
case WaveletMethod.HaarTransformTensor: // This is using the tensor product layout
dwtMatrix = WaveletUtils.HaarWaveletTransform2D(image);
break;
case WaveletMethod.HaarWaveletDecompositionTensor: // This is using the tensor product layout
var haar = new StandardHaarWaveletDecomposition();
haar.DecomposeImageInPlace(image);
dwtMatrix = new Matrix(image);
break;
case WaveletMethod.NonStandardHaarWaveletDecomposition: // JPEG 2000
var haarNonStandard = new NonStandardHaarWaveletDecomposition();
haarNonStandard.DecomposeImageInPlace(image);
dwtMatrix = new Matrix(image);
break;
case WaveletMethod.HaarCSharp:
ForwardWaveletTransform.Transform2D(image, false, 2);
dwtMatrix = new Matrix(image);
break;
case WaveletMethod.HaarWaveletCompress:
int lastHeight = 0;
int lastWidth = 0;
WaveletCompress.HaarTransform2D(image, 10000, out lastHeight, out lastWidth);
dwtMatrix = new Matrix(image);
break;
default:
break;
}
long endS = stopWatch.ElapsedTicks;
Console.WriteLine("WaveletMethod: {0} Time in ticks: {1}", Enum.GetName(typeof(WaveletMethod), waveletMethod), (endS - startS));
// increase all values
const int mul = 50;
double[][] haarImageNormalized5k = dwtMatrix.MatrixData.Select(i => i.Select(j => j * mul).ToArray()).ToArray();
// convert to byte values (0 - 255)
// duplicate the octave/ matlab method uint8
var uint8 = new double[haarImageNormalized5k.Length][];
for (int i = 0; i < haarImageNormalized5k.Length; i++)
{
uint8[i] = new double[haarImageNormalized5k.Length];
for (int j = 0; j < haarImageNormalized5k[i].Length; j++)
{
double v = haarImageNormalized5k[i][j];
if (v > 255)
{
uint8[i][j] = 255;
}
else if (v < 0)
{
uint8[i][j] = 0;
}
else
{
uint8[i][j] = (byte)haarImageNormalized5k[i][j];
}
}
}
var uint8Matrix = new Matrix(uint8);
return(uint8Matrix);
}