In multivariate regression, a K-dimensional response vector is regressed upon a common set of p covariates, with a matrix B∗ ∈ Rp×K of regression coefficients. We study the behavior of the multivariate group Lasso, in which block regularization based on the `1/`2 norm is used for support union recovery, or recovery of the set of s rows for which B∗ is non-zero. Under high-dimensional scaling, w...

Sparse recovery aims to reconstruct signals that are sparse in a linear transform domain from a heavily underdetermined set of measurements. The success of sparse recovery relies critically on the knowledge of transform domains that give compressible representations of the signal of interest. Here we consider twoand three-dimensional images, and investigate various multi-dimensional transforms ...

This thesis takes place in the context of multi-microphone distant speech recognition in multiparty meetings. It addresses the fundamental problem of overlapping speech recognition in reverberant rooms. Motivated from the excellent human hearing performance on such problem, possibly resulting of sparsity of the auditory representation, our work aims at exploiting sparse component analysis in sp...

Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming probability when incoming data can be sparsely represented with a fixed number of components, which is one of the drawbacks of CS frameworks because the signal sparsit...

In this paper, we present a new discrete undersampling scheme designed to favor wavefield reconstruction by sparsity-promoting inversion with transform elements that are localized in the Fourier domain. Our work is motivated by empirical observations in the seismic community, corroborated by recent results from compressive sampling, which indicate favorable (wavefield) reconstructions from rand...

High-resolution imaging of densely connected samples such as pathology slides using digital in-line holographic microscopy requires the acquisition of several holograms, e.g., at >6-8 different sample-to-sensor distances, to achieve robust phase recovery and coherent imaging of specimen. Reducing the number of these holographic measurements would normally result in reconstruction artifacts and ...

The hippocampus plays a key role in pattern separation, the process of transforming similar incoming information to highly dissimilar, nonverlapping representations. Sparse firing granule cells (GCs) in the dentate gyrus (DG) have been proposed to undertake this computation, but little is known about which of their properties influence pattern separation. Dendritic atrophy has been reported in ...

A nonlinear singularity-preserving solution to seismic image recovery with sparseness and continuity constraints is proposed. We observe that curvelets, as a directional frame expansion, lead to sparsity of seismic images and exhibit invariance under the normal operator of the linearized imaging problem. Based on this observation we derive a method for stable recovery of the migration amplitude...

A trend in compressed sensing (CS) is to exploit structure for improved reconstruction performance. In the basic CS model (i.e. the single measurement vector model), exploiting the clustering structure among nonzero elements in the solution vector has drawn much attention, and many algorithms have been proposed such as group Lasso (Yuan & Lin, 2006). However, few algorithms explicitly consider ...