Related papers: Estimating Sparse Signals with Smooth Support via …
Sparse signal recovery based on nonconvex and nonsmooth optimization problems has significant applications and demonstrates superior performance in signal processing and machine learning. This work deals with a scale-invariant…
In a recent article series, the authors have promoted convex optimization algorithms for radio-interferometric imaging in the framework of compressed sensing, which leverages sparsity regularization priors for the associated inverse problem…
The problem of finding sparse solutions to underdetermined systems of linear equations arises in several applications (e.g. signal and image processing, compressive sensing, statistical inference). A standard tool for dealing with sparse…
Motivated by the observation that a given signal $\boldsymbol{x}$ admits sparse representations in multiple dictionaries $\boldsymbol{\Psi}_d$ but with varying levels of sparsity across dictionaries, we propose two new algorithms for the…
Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by…
Images acquired with a telescope are blurred and corrupted by noise. The blurring is usually modeled by a convolution with the Point Spread Function and the noise by Additive Gaussian Noise. Recovering the observed image is an ill-posed…
We study the problem of recovering the underlining sparse signals from clean or noisy phaseless measurements. Due to the sparse prior of signals, we adopt an L0regularized variational model to ensure only a small number of nonzero elements…
Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal/image processing. A standard approach to deal with ILIP uses a constrained optimization problem, where a regularization function is…
The recovery of unknown signals from quadratic measurements finds extensive applications in fields such as phase retrieval, power system state estimation, and unlabeled distance geometry. This paper investigates the finite sample properties…
Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…
We propose two nonconvex regularization methods, LogLOP-l2/l1 and AdaLOP-l2/l1, for recovering block-sparse signals with unknown block partitions. These methods address the underestimation bias of existing convex approaches by extending…
Sparse modeling is one of the efficient techniques for imaging that allows recovering lost information. In this paper, we present a novel iterative phase-retrieval algorithm using a sparse representation of the object amplitude and phase.…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…
This article aims to provide a comprehensive overview of sparse optimization, with a focus on both sparse signal recovery and sparse regularization techniques. We will begin by exploring the foundations of sparse optimization, delving into…
We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key…
We investigate conditions for the unique recoverability of sparse integer-valued signals from a small number of linear measurements. Both the objective of minimizing the number of nonzero components, the so-called $\ell_0$-norm, as well as…
Compared with digital methods, sparse recovery based on spiking neural networks has great advantages like high computational efficiency and low power-consumption. However, current spiking algorithms cannot guarantee more accurate estimates…
Block-sparse regularization is already well-known in active thermal imaging and is used for multiple measurement based inverse problems. The main bottleneck of this method is the choice of regularization parameters which differs for each…
Sparsity and rank functions are important ways of regularizing under-determined linear systems. Optimization of the resulting formulations is made difficult since both these penalties are non-convex and discontinuous. The most common remedy…
In this paper, we consider a squared $L_1/L_2$ regularized model for sparse signal recovery from noisy measurements. We first establish the existence of optimal solutions to the model under mild conditions. Next, we propose a proximal…