Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics applications: While the ambient dimension is vast in modern data analysis problems, the relevant information therein typically resides in a much lower dimensional s...

We consider the problem of recovering a signal x∗ ∈ R, from magnitude-only measurements, yi = |〈ai,x∗〉| for i = {1, 2, . . . ,m}. Also known as the phase retrieval problem, it is a fundamental challenge in nano-, bioand astronomical imaging systems, and speech processing. The problem is ill-posed, and therefore additional assumptions on the signal and/or the measurements are necessary. In this ...

Sparsity helps reduce the computational complexity of deep neural networks by skipping zeros. Taking advantage of sparsity is listed as a high priority in the next generation DNN accelerators such as TPU[1]. The structure of sparsity, i.e., the granularity of pruning, affects the efficiency of hardware accelerator design as well as the prediction accuracy. Coarse-grained pruning brings more reg...

Support recovery of sparse signals from compressed linear measurements is a fundamental problem in compressed sensing (CS). In this paper, we study the orthogonal matching pursuit (OMP) algorithm for the recovery of support under noise. We consider two signal-to-noise ratio (SNR) settings: i) the SNR depends on the sparsity level K of input signals, and ii) the SNR is an absolute constant indep...

The study of sparsity has recently garnered significant attention in the signal processing and statistics communities. Generally speaking, sparsity describes the phenomenon where a large data set may be succinctly represented or approximated using only a small number of summary values or coefficients. The implications are clear—the presence of sparsity suggests the potential for efficient metho...

We consider a class of `0-regularized linearquadratic (LQ) optimal control problems. This class of problems is obtained by augmenting a penalizing sparsity measure to the cost objective of the standard linear-quadratic regulator (LQR) problem in order to promote sparsity pattern of the state feedback controller. This class of problems is generally NP hard and computationally intractable. First,...