Related papers: Fast L1-L2 minimization via a proximal operator
We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…
The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…
Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new…
The newly proposed $l_1$ norm constraint zero-point attraction Least Mean Square algorithm (ZA-LMS) demonstrates excellent performance on exact sparse system identification. However, ZA-LMS has less advantage against standard LMS when the…
We discuss two new methods of recovery of sparse signals from noisy observation based on $\ell_1$- minimization. They are closely related to the well-known techniques such as Lasso and Dantzig Selector. However, these estimators come with…
In this paper we look at a well known linear inverse problem that is one of the mathematical cornerstones of the compressed sensing field. In seminal works \cite{CRT,DOnoho06CS} $\ell_1$ optimization and its success when used for recovering…
We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…
Exact recovery of a sparse solution for an underdetermined system of linear equations implies full search among all possible subsets of the dictionary, which is computationally intractable, while l1 minimization will do the job when a…
We consider the problem of imaging sparse scenes from a few noisy data using an $l_1$-minimization approach. This problem can be cast as a linear system of the form $A \, \rho =b$, where $A$ is an $N\times K$ measurement matrix. We assume…
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.…
Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is…
This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary.…
An important observation in compressed sensing is that the $\ell_0$ minimizer of an underdetermined linear system is equal to the $\ell_1$ minimizer when there exists a sparse solution vector and a certain restricted isometry property…
The channel estimation is one of important techniques to ensure reliable broadband signal transmission. Broadband channels are often modeled as a sparse channel. Comparing with traditional dense-assumption based linear channel estimation…
Compressive sensing (CS) is a technique for estimating a sparse signal from the random measurements and the measurement matrix. Traditional sparse signal recovery methods have seriously degeneration with the measurement matrix uncertainty…
We propose a subspace-accelerated Bregman method for the linearly constrained minimization of functions of the form $f(\mathbf{u})+\tau_1 \|\mathbf{u}\|_1 + \tau_2 \|D\,\mathbf{u}\|_1$, where $f$ is a smooth convex function and $D$…
This paper presents an algorithm tailored for the efficient recovery of sparse probability measures incorporating $\ell_0$-sparse regularization within the probability simplex constraint. Employing the Bregman proximal gradient method, our…
Recovering a sparse signal from outlier-contaminated measurements is a fundamental challenge in many applications. While existing algorithms predominantly address scenarios with bounded noise or assume known signal sparsity, few methods…
Recent hardware advancements in AI Accelerators and GPUs allow to efficiently compute sparse matrix multiplications, especially when 2 out of 4 consecutive weights are set to zero. However, this so-called 2:4 sparsity usually comes at a…
Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…