Estimation Under Model-Based Sparsity

Abstract

Beyond the ordinary, extensively studied, plain sparsity model, a variety of structured sparsity models have been proposed in the literature Bach (2008); Roth and Fischer (2008); Jacob et al. (2009); Baraniuk et al. (2010); Bach (2010); Bach et al. (2012); Chandrasekaran et al. (2012); Kyrillidis and Cevher (2012a). These sparsity models are designed to capture the interdependence of the locations of the non-zero components that is known a priori in certain applications. For instance, the wavelet transform of natural images are often (nearly) sparse and the dependence among the dominant wavelet coefficients can be represented by a rooted and connected tree. Furthermore, in applications such as array processing or sensor networks, while different sensors may take different measurements, the support set of the observed signal is identical across the sensors. Therefore, to model this property of the system, we can compose an enlarged signal with jointly-sparse or block-sparse support set, whose non-zero coefficients occur as contiguous blocks.