Wavelet shrinkage using adaptive structured sparsity constraints

Wavelet shrinkage using adaptive structured sparsity constraints

Structured sparsity approaches have recently received much attention in the statistics, machine learning, and signal processing communities. A common strategy is to exploit or assume prior information about structural dependencies inherent in the data; the solution is encouraged to behave as such by the inclusion of an appropriate regularization term which enforces structured sparsity constrain...

Structured Sparsity: from Mixed Norms to Structured Shrinkage

Sparse and structured signal expansions on dictionaries can be obtained through explicit modeling in the coefficient domain. The originality of the present contribution lies in the construction and the study of generalized shrinkage operators, whose goal is to identify structured significance maps. These generalize Group LASSO and the previously introduced Elitist LASSO by introducing more flex...

Adaptive Sensing with Structured Sparsity

Adaptive sensing strategies have been proven to outperform traditional (non adaptive) compressed sensing, in terms of the signal to noise ratios that can be handled, and/or the number of measurements needed to accurately recover a signal of interest. Most existing adaptive sensing schemes for sparse signals, while work well in practice, do not take into account potential structure present in th...

Wavelet shrinkage: from sparsity and robust testing to smooth adaptation

Iterated Hard Shrinkage for Minimization Problems with Sparsity Constraints

A new iterative algorithm for the solution of minimization problems in infinitedimensional Hilbert spaces which involve sparsity constraints in form of `p-penalties is proposed. In contrast to the well-known algorithm considered by Daubechies, Defrise and De Mol, it uses hard instead of soft shrinkage. It is shown that the hard shrinkage algorithm is a special case of the generalized conditiona...