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Chapter 05 2-Dim Multiresolution Analysis (MRA)

Chapter 05 2-Dim Multiresolution Analysis (MRA). Haar Wavelet Transform - 1dim main. Haar Wavelet Transform - 1dim Result. Haar Wavelet Transform - 1dim printArray. Haar Wavelet Transform - 1dim Compute g-coefficients. Haar Wavelet Transform - 1dim Forward Transformation.

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Chapter 05 2-Dim Multiresolution Analysis (MRA)

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  1. Chapter 052-Dim Multiresolution Analysis (MRA)

  2. Haar Wavelet Transform - 1dimmain

  3. Haar Wavelet Transform - 1dimResult

  4. Haar Wavelet Transform - 1dimprintArray

  5. Haar Wavelet Transform - 1dimCompute g-coefficients

  6. Haar Wavelet Transform - 1dimForward Transformation

  7. Haar Wavelet Transform - 1dimInverse Transformation

  8. Standard Decomposition 1dim L H LL HL H LLL HLL HL H LL LL HL LL HLL HL H

  9. fwd_DWT fwd_DWT (data) len_2 = data.length/2; for (k = 0; k < len_2; k++) { tdata[k] = 0; tdata[k+len_2] = 0; for (int m = 2k; m < (2k+h.length); m++) { tdata[k] = tdata[k] + h[m-2k] * data[m]; tdata[k+len_2] = tdata[k+len_2] + g[m-2k] * data[m]; } } data = tdata / sqrt(2);

  10. inv_DWT inv_DWT (data) len_2 = data.length/2; for (k = 0; k < len_2; k++) { tdata[2k] = 0; tdata[2k+1] = 0; for (every m) { tdata[2k] = tdata[k] + data[m] * h[k-2m]; tdata[2k+len_2] = tdata[k+len_2] + data[m] * g[k-2m]; } } data = tdata *sqrt(2);

  11. Standard Decomposition 2dim

  12. Standard Decomposition 2dim L H L H L H L H L H L H L H L H

  13. Standard Decomposition 2dim LL HL H LL HL H LL HL H LL HL H LL HL H LL HL H LL HL H LL HL H

  14. Standard Decomposition 2dim LLL HLL HL H LLL HLL HL H LLL HLL HL H LLL HLL HL H LLL HLL HL H LLL HLL HL H LLL HLL HL H LLL HLL HL H

  15. Standard Decomposition 2dim LL LL HL LL HLL HL H LL LL HL LL HLL HL H LL LL HL LL HLL HL H LL LL HL LL HLL HL H LL LL HL LL HLL HL H LL LL HL LL HLL HL H LL LL HL LL HLL HL H LL LL HL LL HLL HL H

  16. Standard Decomposition 2dim - V2 L H LL HL H LLL LHL LH Row HLL HHL HH Col LL LL LL HL HLL HL LL HL HL HHH HLL HHL HH

  17. Standard Decomposition 2dim - V2 Row Column

  18. Standard Decomposition 2dim - V3 Row Column

  19. 2-Dim Haar Base FunctionsStandard construction The standard construction of a two-dimensional wavelet basis consists of all possible tensor products of one-dimensional basis functions.

  20. 2-Dim Haar Base Functions for V2Standard construction y + + - + - + - x + + - + - - + - - + - + + - + + - + - - + - - + - + + - + + - + + - - + + - - + - - + +

  21. 2-Dim Haar Base Functions for V2Standard construction y x + - - + + - - +

  22. NonStandard Decomposition L H Row Col LL HL LLL LLH HL Row LH HH LH HH Col LL LL LL HL HL LL LH LL HH LH HH

  23. NonStandard Decomposition 2dim - V2 Row Column Row Column

  24. NonStandard Decomposition 2dim - V3 Row Row Column Column Row Column

  25. decomposition decomposition (data, jStart, jEnd) { for (j = jStart-1, j >= jEnd, j--) { fwd_DWT(data) } }

  26. decomposition_NonStandard decomposition_NonStandard (data, jStart, jEnd) { for (j = jStart-1, j >= jEnd, j--) { fwd_DWT_2D(data) } }

  27. fwd_DWT_2D fwd_DWT_2D (data) { for ( every row) fwd_DWT(data[row]) } transpose (data) for ( every row) fwd_DWT(data[row]) } transpose (data)

  28. reconstruction_NonStandard reconstruction_NonStandard (data, jStart, jEnd) { for (j = jStart+1, j <= jEnd, j--) { inv_DWT_2D(data) } }

  29. inv_DWT_2D inv_DWT_2D (data) { transpose (data) for ( every row) inv_DWT(data[row]) } transpose (data) for ( every row) inv_DWT(data[row]) }

  30. Use of class Wavelet - 1dimmain

  31. Use of class Wavelet - 1dimResult

  32. Use of class Wavelet - 1dimprintArray

  33. Use of class Wavelet - 2dimmain

  34. Use of class Wavelet - 2dimResult

  35. Use of class Wavelet - 1dimprintArray

  36. Use of class Wavelet - 2dimprintArray

  37. class Waveleth-coefficients D2-D4-D6-D8-D10-D12-D14-D16-D18-D20- D30

  38. class Waveletdouble[ ] data - double[ ] [ ] data_2D

  39. class Waveletconstructor - 1dim / 2dim

  40. class WaveletD2 - D4 - D6 - D8 - D10 - D12 - D14 - D16 - D18 - D20 - D30

  41. class Waveletcompute g-coefficients

  42. class WaveletForward 1dim

  43. class WaveletInverse 1dim

  44. class WaveletForward 2dim

  45. class WaveletInverse 2dim

  46. class Waveletdecomposition 1dim

  47. class Waveletreconstruction 1dim

  48. class Waveletdecomposition_NonStandard 2dim

  49. class Waveletreconstruction_NonStandard 2dim

  50. class Wavelettranspose

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