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Signal reconstruction from multiscale edges. A wavelet based algorithm. Algorithm. Decomposition. Input. Discrete Wavelet Transform. Save edges e.g. local extrema. Reconstruction. local extrema. Find approximation. Inverse Wavelet Transform. Output. contained two bugs.
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Signal reconstruction from multiscale edges A wavelet based algorithm
Decomposition Input Discrete Wavelet Transform Save edges e.g. local extrema
Reconstruction local extrema Find approximation Inverse Wavelet Transform Output contained two bugs
Discrete Wavelet Transform (1 level) Detail Coefficients input Approximation Coefficients
input Detail Level 1 Detail Level 2 Detail Level 3 Approximation Level 3
DWT + IDWT input Detail Coefficients + Approximation Coefficients output
Perfect Reconstruction Property = + X X
Perfect Reconstruction Property Bug: Incorrect coefficient given in paper = + X X
Perfect Reconstruction Property = + X X Given 0.054685 Correct 0.0546875
input Detail Coefficients = + + X X Approximation Coefficients output
output Detail (L1) Detail (L2) Detail (L3) + + + Approx. (L3)
Bug: cascade not implemented correctly output Detail (L1) Detail (L2) Detail (L3) + + + Approx. (L3)
Interpolation Space check for interpolation DWT Space check for perfect reconstruction DWT -> IDWT = identity
Approximation (5 levels) All coefficients discarded since last level zero
output Detail (L1) Detail (L2) Detail (L3) + + + Approx. (L3)
Find approximation (iterative) Alternate projections between two spaces
Source: Zoolander (2001)