Characterization of Signals from Multiscale Edges
IEEE Transactions on Pattern Analysis and Machine Intelligence
Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
New POCS algorithms for regularization of inverse problems
Journal of Computational and Applied Mathematics
WCNA '92 Proceedings of the first world congress on World congress of nonlinear analysts '92, volume I
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
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In this paper, we consider a wavelet based singularity-preserving regularization scheme for use in signal deconvolution problems. The inverse problem of finding solutions with singularities to discrete Fredholm integral equations of the first kind arises in many applied fields, e.g. in Geophysics. This equation is usually an ill-posed problem when it is considered in a Hilbert space framework, requiring regularization techniques to control arbitrary error amplifications and to get adequate solutions. Thus, considering the joint detection-estimation character this kind of signal deconvolution problems have, we introduce two novel algorithms which involve two principal steps at each iteration: (a) detecting the positions of the singularities by a nonlinear projection selection operator based on the estimation of Lipschitz regularity using the discrete dyadic wavelet transform; and (b) estimating the amplitudes of these singularities by obtaining a regularized solution of the original equation using the a priori knowledge and the above approximation. Some simulation examples serve to appreciate the high performance of the proposed techniques in this kind of problems.