DISCRETE-TIME WAVELET EXTREMA REPRESENTATION - DESIGN AND CONSISTENT RECONSTRUCTION

TY - JOUR

T1 - DISCRETE-TIME WAVELET EXTREMA REPRESENTATION - DESIGN AND CONSISTENT RECONSTRUCTION

AU - CVETKOVIC, Z

AU - VETTERLI, M

PY - 1995/3

Y1 - 1995/3

N2 - This paper studies wavelet transform extrema and zero-crossings representations within the framework of convex representations in l(2)(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 this 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.

AB - This paper studies wavelet transform extrema and zero-crossings representations within the framework of convex representations in l(2)(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 this 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.

KW - TRANSFORM

U2 - 10.1109/78.370622

DO - 10.1109/78.370622

M3 - Article

SN - 1053-587X

VL - 43

SP - 681

EP - 693

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

IS - 3

ER -