Related papers: Adaptive Block Sparse Regularization under Arbitra…
We propose a unified fractional regularization framework for sparse signal recovery based on the $\ell_1/\ell_p^q$ model. This model generalizes several widely used sparsity-promoting regularizers and provides additional flexibility through…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…
Deep neural networks have become very popular in modeling complex nonlinear processes due to their extraordinary ability to fit arbitrary nonlinear functions from data with minimal expert intervention. However, they are almost always…
An l0-regularized linear regression for a sparse signal reconstruction is implemented based on the quadratic unconstrained binary optimization (QUBO) formulation. In this method, the signal values are quantized and expressed as bit…
The recovery of block-sparse signals with unknown structural patterns remains a fundamental challenge in structured sparse signal reconstruction. By proposing a variance transformation framework, this paper unifies existing pattern-based…
Non-stationary blind super-resolution is an extension of the traditional super-resolution problem, which deals with the problem of recovering fine details from coarse measurements. The non-stationary blind super-resolution problem appears…
Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…
We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…
The 1-norm was proven to be a good convex regularizer for the recovery of sparse vectors from under-determined linear measurements. It has been shown that with an appropriate measurement operator, a number of measurements of the order of…
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…
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…
Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the…
In this paper, we propose a double iteratively reweighted algorithm to solve nonconvex and nonsmooth optimization problems, where both the objectives and constraint functions are formulated by concave compositions to promote group-sparse…
We solve the problem of sparse signal deconvolution in the context of seismic reflectivity inversion, which pertains to high-resolution recovery of the subsurface reflection coefficients. Our formulation employs a nonuniform, non-convex…
The mathematical theory of super-resolution developed recently by Cand\`{e}s and Fernandes-Granda states that a continuous, sparse frequency spectrum can be recovered with infinite precision via a (convex) atomic norm technique given a set…
Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine…
This paper considers the problem of reconstructing sparse or compressible signals from one-bit quantized measurements. We study a new method that uses a log-sum penalty function, also referred to as the Gaussian entropy, for sparse signal…
We study the problem of recovering a block-sparse signal from under-sampled observations. The non-zero values of such signals appear in few blocks, and their recovery is often accomplished using a $\ell_{1,2}$ optimization problem. In…
In this paper, we consider the problem of recovering a sparse signal based on penalized least squares formulations. We develop a novel algorithm of primal-dual active set type for a class of nonconvex sparsity-promoting penalties, including…
It is now well understood that convex programming can be used to estimate the frequency components of a spectrally sparse signal from $2m+1$ uniform temporal measurements. It is conjectured that a phase transition on the success of the…