Fast communication: Basis selection for wavelet processing of sparse signals

Authors:
Ian C. Atkinson;Farzad Kamalabadi
Affiliations:
Department of Radiology, University of Illinois at Chicago, 1193 OCC (M/C 707), 1801 West Taylor, Chicago, IL 60612, USA and Department of Electrical and Computer Engineering, University of Illino ...;Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, USA and Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, USA
Venue:
Signal Processing
Year:
2008

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Abstract

The sparsity of a signal in a wavelet domain depends on both the wavelet basis and the exact form of the signal. We consider the selection of a wavelet basis that can efficiently represent a piecewise polynomial signal that is itself sparse in the signal domain. Accounting for the inherent sparsity of the signal allows for the maximum wavelet filter length and number of decomposition levels to be computed so as to guarantee that the resulting wavelet-domain representation is at least as sparse as the original signal, a desirable property for most wavelet processing techniques.