1. Chapter 05 2-Dim Multiresolution Analysis (MRA)

2. Haar Wavelet Transform - 1dim main

3. Haar Wavelet Transform - 1dim Result

4. Haar Wavelet Transform - 1dim printArray

5. Haar Wavelet Transform - 1dim Compute g-coefficients

6. Haar Wavelet Transform - 1dim Forward Transformation

7. Haar Wavelet Transform - 1dim Inverse Transformation

8. Standard Decomposition 1dimL H LL HL H
LLL
HLL HL H 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 2dimL H L H L H L H L H L H L H L H

13. Standard Decomposition 2dimLL 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 2dimLL HL LL
HLL HL H LL HL LL
HLL HL H LL HL LL
HLL HL H LL HL LL
HLL HL H LL HL LL
HLL HL H LL HL LL
HLL HL H LL HL LL
HLL HL H LL HL LL
HLL HL H

16. Standard Decomposition 2dim - V2L H LL HL H
LLL
LHL LH
Row
HLL
HHL HH
Col LL LL HL
HLL HL LL HL
HHH
HLL
HHL HH

17. Standard Decomposition 2dim - V2
Row
Column

18. Standard Decomposition 2dim - V3
Row
Column

19. 2-Dim Haar Base Functions Standard 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 V2 Standard constructiony + + - + - + - x + + - + - - + - - + - + + - + + - + - - + - - + - + + - + + - + + - - + + - - + - + + -

21. 2-Dim Haar Base Functions for V2 Standard constructiony x + - - + + - - +

22. NonStandard DecompositionL H
Row
Col LL HL
LLL
LLH HL
Row LH HH LH HH
Col 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
Column
Row
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)

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]) }

30. Use of class Wavelet - 1dim main

31. Use of class Wavelet - 1dim Result

32. Use of class Wavelet - 1dim printArray

33. Use of class Wavelet - 2dim main

34. Use of class Wavelet - 2dim Result

35. Use of class Wavelet - 1dim printArray

36. Use of class Wavelet - 2dim printArray

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

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

39. class Wavelet constructor - 1dim / 2dim

40. class Wavelet D2 - D4 - D6 - D8 - D10 - D12 - D14 - D16 - D18 - D20 - D30

41. class Wavelet compute g-coefficients

42. class Wavelet Forward 1dim

43. class Wavelet Inverse 1dim

44. class Wavelet Forward 2dim

45. class Wavelet Inverse 2dim

46. class Wavelet decomposition 1dim

47. class Wavelet reconstruction 1dim

48. class Wavelet decomposition_NonStandard 2dim

49. class Wavelet reconstruction_NonStandard 2dim

50. class Wavelet transpose

51. 2-Dim Haar Base Functions Nonstandard construction
The nonstandard construction of a two-dimensional wavelet basis
consists of a single coarse scaling function along with scales and translates
of three wavelet functions

52. 2-Dim Haar Base Functions for V2 Non-Standard constructiony + + - + - + - x + + - - - + + - + - + + + - + - - - - + - + + + + + - + + - - - - + - +

53. 2-Dim Haar Base Functions for V2 Non-Standard constructiony x + - + + - - +

54. End