相关论文: Sparse recovery guarantees for block orthogonal bi…

Sparse support recovery arises in many applications in communications and signal processing. Existing methods tackle sparse support recovery problems for a given measurement matrix, and cannot flexibly exploit the properties of sparsity…

In this paper, we propose a novel sparse recovery method based on the generalized error function. The penalty function introduced involves both the shape and the scale parameters, making it very flexible. The theoretical analysis results in…

The focus of this paper is on linear, binary codes with locality having locality parameter $r$, that are capable of recovering from $t\geq 2$ erasures and that moreover, have short block length. Both sequential and parallel (through…

Block coherence of matrices plays an important role in analyzing the performance of block compressed sensing recovery algorithms (Bajwa and Mixon, 2012). In this paper, we characterize two block coherence metrics: worst-case and average…

Unit norm finite frames are generalizations of orthonormal bases with many applications in signal processing. An important property of a frame is its coherence, a measure of how close any two vectors of the frame are to each other. Low…

Advances in sensing technology have made it possible to collect large volumes of high-dimensional time-series data. In fields like genetics and neuroscience, key questions concern whether directed relationships between variables can be…

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…

The generalized phase retrieval problem over compact groups aims to recover a set of matrices -- representing an unknown signal -- from their associated Gram matrices. This framework generalizes the classical phase retrieval problem, which…

We propose an iterative algorithm for the minimization of a $\ell_1$-norm penalized least squares functional, under additional linear constraints. The algorithm is fully explicit: it uses only matrix multiplications with the three matrices…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general…

An attempt is made to describe random matrix ensembles with unitary invariance of measure (UE) in a unified way, using a combination of Tracy-Widom (TW) and Adler-Shiota-Van Moerbeke (ASvM) approaches to derivation of partial differential…

Compressed sensing (CS) techniques demand significant storage and computational resources, when recovering high-dimensional sparse signals. Block CS (BCS), a special class of CS, addresses both the storage and complexity issues by…

Partitioning sparse matrices and graphs is a common and important problem in many scientific and graph analytics applications. In this work, we are concerned with a spatial partitioning called rectilinear partitioning (also known as…

In phase-only compressive sensing (PO-CS), our goal is to recover low-complexity signals (e.g., sparse signals, low-rank matrices) from the phase of complex linear measurements. While perfect recovery of signal direction in PO-CS was…

Identifying damage of structural systems is typically characterized as an inverse problem which might be ill-conditioned due to aleatory and epistemic uncertainties induced by measurement noise and modeling error. Sparse representation can…

Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse…

Many inverse problems in signal processing deal with the robust estimation of unknown data from underdetermined linear observations. Low dimensional models, when combined with appropriate regularizers, have been shown to be efficient at…

This paper aims at showing the stability of the recovery of a smooth planar domain with a real algebraic boundary from a finite number of its generalized polarization tensors. It is a follow-up of the work [H. Ammari et al., Math. Annalen,…

We present a fast algorithm for linear least squares problems governed by hierarchically block separable (HBS) matrices. Such matrices are generally dense but data-sparse and can describe many important operators including those derived…