Discrete-Time Wavelet Extrema Representation - Design and Consistent Reconstruction

The paper studies wavelet transform extrema and zero-crossings representations within the framework of convex representations in L(Z). Wavelet zero-crossings representation of two-dimensional signals is introduced as a convex multiscale edge representation as well. One appealing property of convex representations is that the reconstruction problem can be solved, at least theoretically, using the method of alternating projections onto convex sets. It turns out that in the case of the wavelet extrema and wavelet zero-crossings representations this method yields simple and practical reconstruction algorithms. Nonsubsampled filter banks that implement the wavelet transform for the two representations are also studied in the paper. Relevant classes of nonsubsampled perfect reconstruction FIR filter banks are characterized. This characterization gives a broad class of wavelets for the representations which are derived from those of the filter banks which satisfy a regularity condition.


Published in:
IEEE Transactions on Signal Processing, 43, 3, 681-694
Year:
1995
Laboratories:




 Record created 2005-04-18, last modified 2018-03-17

n/a:
Download fulltext
PDF

Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)