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In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise…
The estimation of a sparse vector in the linear model is a fundamental problem in signal processing, statistics, and compressive sensing. This paper establishes a lower bound on the mean-squared error, which holds regardless of the…
One of the key challenges in sensor networks is the extraction of information by fusing data from a multitude of distinct, but possibly unreliable sensors. Recovering information from the maximum number of dependable sensors while…
A greedy algorithm is proposed for sparse-sensor selection in reduced-order sensing that contains correlated noise in measurement. The sensor selection is carried out by maximizing the determinant of the Fisher information matrix in a…
The problem of 1-bit compressive sampling is addressed in this paper. We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements. The model targets a solution that has the least l0-norm among all signals…
We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer…
This paper describes several improvements to a new method for signal decomposition that we recently formulated under the name of Differentiable Dictionary Search (DDS). The fundamental idea of DDS is to exploit a class of powerful deep…
This paper aims to propose and theoretically analyze a new distributed scheme for sparse linear regression and feature selection. The primary goal is to learn the few causal features of a high-dimensional dataset based on noisy observations…
In this paper, we study a class of nonconvex and nonsmooth structured difference-of-convex (DC) programs, which contain in the convex part the sum of a nonsmooth linearly composed convex function and a differentiable function, and in the…
Learning with noisy labels (LNL) has been extensively studied, with existing approaches typically following a framework that alternates between clean sample selection and semi-supervised learning (SSL). However, this approach has a…
In this paper, utilizing techniques in compressed sensing, parallel optimization and deep learning, we propose a model-driven approach to jointly design the common measurement matrix and GROUP LASSO-based jointly sparse signal recovery…
As technology grows, higher frequency signals are required to be processed in various applications. In order to digitize such signals, conventional analog to digital convertors are facing implementation challenges due to the higher sampling…
Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples.…
The signal demixing problem seeks to separate a superposition of multiple signals into its constituent components. This paper studies a two-stage approach that first decompresses and subsequently deconvolves the noisy and undersampled…
It is now well established that sparse signal models are well suited to restoration tasks and can effectively be learned from audio, image, and video data. Recent research has been aimed at learning discriminative sparse models instead of…
Compressive Sensing (CS) is a new paradigm for the efficient acquisition of signals that have sparse representation in a certain domain. Traditionally, CS has provided numerous methods for signal recovery over an orthonormal basis. However,…
A new algorithm is proposed for a) unsupervised learning of sparse representations from subsampled measurements and b) estimating the parameters required for linearly reconstructing signals from the sparse codes. We verify that the new…
Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…
In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…