Related papers: Approximate message-passing with spatially coupled…

In this paper we show that inverses of well-conditioned, finite-time Gramians and impulse response matrices of large-scale interconnected systems described by sparse state-space models, can be approximated by sparse matrices. The…

For certain sensing matrices, the Approximate Message Passing (AMP) algorithm efficiently reconstructs undersampled signals. However, in Magnetic Resonance Imaging (MRI), where Fourier coefficients of a natural image are sampled with…

Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent…

This paper addresses the reconstruction of sparse signals from spatially coupled, linear, and noisy measurements. A unified framework of rigorous state evolution is established for developing long-memory message-passing (LM-MP) in spatially…

Recently, significant connections between compressed sensing problems and optimization of a particular class of functions relating to solutions of Hamilton-Jacobi equation was discovered. In this paper we introduce a fast approximate…

This paper considers the massive connectivity problem in an asynchronous grant-free random access system, where a huge number of devices sporadically transmit data to a base station (BS) with imperfect synchronization. The goal is to design…

We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g., block-banded), or be more highly structured (e.g., symmetric…

Compressed sensing (CS) deals with the problem of reconstructing a sparse vector from an under-determined set of observations. Approximate message passing (AMP) is a technique used in CS based on iterative thresholding and inspired by…

This paper provides a novel approach for finding sparse state-space realizations of linear systems (e.g., controllers). Sparse controllers are commonly used in distributed control, where a controller is synthesized with some sparsity…

In its most elementary form, compressed sensing studies the design of decoding algorithms to recover a sufficiently sparse vector or code from a lower dimensional linear measurement vector. Typically it is assumed that the decoder has…

We consider designing a robust structured sparse sensing matrix consisting of a sparse matrix with a few non-zero entries per row and a dense base matrix for capturing signals efficiently We design the robust structured sparse sensing…

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…

Coded compressed sensing is an algorithmic framework tailored to sparse recovery in very large dimensional spaces. This framework is originally envisioned for the unsourced multiple access channel, a wireless paradigm attuned to…

Sparse superposition codes were originally proposed as a capacity-achieving communication scheme over the gaussian channel, whose coding matrices were made of i.i.d. gaussian entries.We extend this coding scheme to more generic ensembles of…

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…

We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…

We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…

In this paper we consider Basis Pursuit De-Noising (BPDN) problems in which the sparse original signal is drawn from a finite alphabet. To solve this problem we propose an iterative message passing algorithm, which capitalises not only on…

Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…

It is known that certain structures of the signal in addition to the standard notion of sparsity (called structured sparsity) can improve the sample complexity in several compressive sensing applications. Recently, Hegde et al. proposed a…