Related papers: Sparse Solutions of an Undetermined Linear System
Motivated by the question of optimal functional approximation via compressed sensing, we propose generalizations of the Iterative Hard Thresholding and the Compressive Sampling Matching Pursuit algorithms able to promote sparse in levels…
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…
This paper introduces a novel approach for recovering sparse signals using sorted L1/L2 minimization. The proposed method assigns higher weights to indices with smaller absolute values and lower weights to larger values, effectively…
Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…
A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading…
In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…
We consider the problem of finding sparse solutions to a system of underdetermined nonlinear system of equations. The methods are based on a Gauss-Newton approach with line search where the search direction is found by solving a linearized…
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…
Recently, the worse-case analysis, probabilistic analysis and empirical justification have been employed to address the fundamental question: When does $\ell_1$-minimization find the sparsest solution to an underdetermined linear system? In…
A common task in inverse problems and imaging is finding a solution that is sparse, in the sense that most of its components vanish. In the framework of compressed sensing, general results guaranteeing exact recovery have been proven. In…
Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…
In sparse recovery, the unique sparsest solution to an under-determined system of linear equations is of main interest. This scheme is commonly proposed to be applied to signal acquisition. In most cases, the signals are not sparse…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
We take an information theoretic perspective on a classical sparse-sampling noisy linear model and present an analytical expression for the mutual information, which plays central role in a variety of communications/processing problems.…
In this work, we formulate the fixed-length distribution matching as a Bayesian inference problem. Our proposed solution is inspired from the compressed sensing paradigm and the sparse superposition (SS) codes. First, we introduce sparsity…
Compressive sensing aims to recover a high-dimensional sparse signal from a relatively small number of measurements. In this paper, a novel design of the measurement matrix is proposed. The design is inspired by the construction of…
We present a novel sparse modeling approach to non-rigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so…
Intensively growing approach in signal processing and acquisition, the Compressive Sensing approach, allows sparse signals to be recovered from small number of randomly acquired signal coefficients. This paper analyses some of the commonly…
In this short paper, we aim at developing algorithms for sparse Volterra system identification when the system to be identified has infinite impulse response. Assuming that the impulse response is represented as a sum of exponentials and…
We propose a new technique for adaptive identification of sparse systems based on the compressed sensing (CS) theory. We manipulate the transmitted pilot (input signal) and the received signal such that the weights of adaptive filter…