Adaptive structured sparsity for wavelet-based signal denoising

TOMASSI, DIEGO

Rosario

Simposio; Simposio argentino de Inteligencia Artificial, ASAI 2015; 2015

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. By introducing an appropriate regularization term which enforces structured sparsity constraints over sub-groups of data, the estimate is encouraged to present such patterns or dependencies. Under this apporach, the common strategy is to set a mixed-norm regularizer with its constituent groups and associated weights defined a priori. In this talk we build upon these ideas to present an adaptive wavelet denoising framework whereby a sparsity-inducing regularizer, designed to capture the tree-like dependency structure often apparent in wavelet decompositions, is modified based on information extracted from the signal itself. In particular, we use the same wavelet decomposition to detect the location of salient features in the signal, such as jumps or sharp bumps. Given these locations, some weights in the regularizer are modified in order to favor retention of the coefficients related to such important locations. Denoising experiments show that, not only does the adaptive method preserve the salient features better than the non-adaptive constraints, but it also delivers significantly better shrinkage over the signal as a whole.Beyond the contributed method, which represents an application of machine learning approaches to signal processing, we will discuss relevant recent articles from machine learning and statistics involving structured-sparsity-inducing regularization, decomposable regularizers and tree-structured estimators.