Wavelet Reconstruction of Nonuniformly Sampled Signals

Leming Qu, Boise State University
Partha S. Routh, Seismic Technology Development, ConocoPhillips, Houston, TX
Phil D. Anno, Seismic Technology Development, ConocoPhillips, Houston, TX

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This document was originally published by IEEE in IEEE Signal Processing Letters. Copyright restrictions may apply. DOI: 10.1109/LSP.2008.2008939

Abstract

For the reconstruction of a nonuniformly sampled signal based on its noisy observations, we propose a level dependent l₁ penalized wavelet reconstruction method. The LARS/Lasso algorithm is applied to solve the Lasso problem. The data adaptive choice of the regularization parameters is based on the AIC and the degrees of freedom is estimated by the number of nonzero elements in the Lasso solution. Simulation results conducted on some commonly used 1_D test signals illustrate that the proposed method possesses good empirical properties.