1 / 43

MRA 1dim / 2dim

MRA 1dim / 2dim. LL LL. LL HL. HL. LL LH. LL HH. +. +. -. LH. HH. -. +. 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.

brede
Télécharger la présentation

MRA 1dim / 2dim

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MRA 1dim / 2dim LL LL LL HL HL LL LH LL HH + + - LH HH - +

  2. 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.

  3. 2-Dim Haar Base Functions for V2Standard construction y + + - + - + - x + + - + - - + - - + - + + - + + - + - - + - - + - + + - + + - + + - - + + - - + - - + +

  4. 2-Dim Haar Base Functions for V2Standard construction y x + - - + + - - +

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

  6. Standard Decomposition 2dim

  7. Standard Decomposition 2dim L H L H L H L H L H L H L H L H

  8. 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

  9. 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

  10. 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

  11. 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

  12. Standard Decomposition 2dim - V2 Row Column

  13. Standard Decomposition 2dim - V3 Row Column

  14. Decomposition 1dim Decomposition ( c[1..2j] ) c := c/Sqrt(2j) // normalize g := 2j WHILE g >= 2 DecompositionStep( c[1..g] ) g := g/2 ENDWHILE END

  15. DecompositionStep 1dim DecompositionStep ( c[1..2j] ) FOR i := 1 TO 2j / 2 c’[i] := ( c[2i-1] + c[2i] ) / Sqrt(2) c’[2j/2 + i] := ( c[2i-1] - c[2i] ) / Sqrt(2) ENDFOR c := c’ END

  16. Reconstruction 1dim Reconstruction ( c[1..2j] ) g := 2 WHILE g <= 2j ReconstructionStep( c[1..g] ) g := 2 * g ENDWHILE c := c * Sqrt(2j) // undo normalization END

  17. ReconstructionStep 1dim ReconstructionStep ( c[1..2j] ) FOR i := 1 TO 2j / 2 c’[2i - 1] := ( c[i] + c[2j / 2 + i] ) / Sqrt(2) c’[2i] := ( c[i] - c[2j / 2 + i] ) / Sqrt(2) ENDFOR c := c’ END

  18. Standard Decomposition 2dim StandardDecomposition ( c[1..2j,1..2k] ) FOR row := 1 TO 2j Decomposition ( c[row,1..2k] ) ENDFOR FOR col := 1 TO 2k Decomposition ( c[1..2j,col] ) ENDFOR END

  19. Standard Reconstruction 2dim StandardReconstruction ( c[1..2j,1..2k] ) FOR col := 1 TO 2k Reconstruction ( c[1..2j,col] ) ENDFOR FOR row := 1 TO 2j Reconstruction ( c[row,1..2k] ) ENDFOR END

  20. 2-Dim Haar Base FunctionsNonstandard 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

  21. 2-Dim Haar Base Functions for V2Non-Standard construction y + + - + - + - x + + - - - + + - + - + + + - + - - - - + - + + + - + + - + + - - - - + +

  22. 2-Dim Haar Base Functions for V2Non-Standard construction y x + - + + - - +

  23. 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

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

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

  26. DecompositionStep 1dim DecompositionStep ( c[1..2j] ) FOR i := 1 TO 2j / 2 c’[i] := ( c[2i-1] + c[2i] ) / Sqrt(2) c’[2j/2 + i] := ( c[2i-1] - c[2i] ) / Sqrt(2) ENDFOR c := c’ END

  27. ReconstructionStep 1dim ReconstructionStep ( c[1..2j] ) FOR i := 1 TO 2j / 2 c’[2i - 1] := ( c[i] + c[2j / 2 + i] ) / Sqrt(2) c’[2i] := ( c[i] - c[2j / 2 + i] ) / Sqrt(2) ENDFOR c := c’ END

  28. NonStandard Decomposition 2dim NonStandardDecomposition ( c[1..2j,1..2j] ) c = c/2j g = 2j WHILE g >= 2 FOR row = 1 TO g DecompositionStep(c[row,1..g]) ENDFOR FOR col = 1 TO g DecompositionStep(c[1..g,col]) ENDFOR g = g / 2 ENDWHILE END

  29. NonStandard Reconstruction 2dim NonStandardReconstruction ( c[1..2j,1..2j] ) g = 2 WHILE g <= 2j FOR col = 1 TO g ReconstructionStep(c[1..g,col]) ENDFOR FOR row = 1 TO g ReconstructionStep(c[row,1..g]) ENDFOR g = 2g ENDWHILE c = 2jc END

  30. DWTJava Implementation - DWT

  31. DWTJava Implementation - class ImageDWT

  32. DWTJava Implementation - set_hCoefficient

  33. DWTJava Implementation - getGCoeff

  34. DWTJava Implementation - fwd_DWT

  35. DWTJava Implementation - inv_DWT

  36. DWTJava Implementation - fwd_DWT_2D

  37. DWTJava Implementation - inv_DWT_2D

  38. DWTJava Implementation - decomposition_NonStandard

  39. DWTJava Implementation - reconstruction_NonStandard

  40. DWTJava Implementation - transpose

  41. 2D Forward Wavelet Transform

  42. 2D Inverse Wavelet Transform

  43. End

More Related