Related papers: Re-Weighted $\ell_1$ Algorithms within the Lagrang…

Deep neural networks have been shown to be very powerful modeling tools for many supervised learning tasks involving complex input patterns. However, they can also easily overfit to training set biases and label noises. In addition to…

Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an…

We propose and analyze an efficient algorithm for solving the joint sparse recovery problem using a new regularization-based method, named orthogonally weighted $\ell_{2,1}$ ($\mathit{ow}\ell_{2,1}$), which is specifically designed to take…

Efficient algorithms for the sparse solution of under-determined linear systems $Ax = b$ are known for matrices $A$ satisfying suitable assumptions like the restricted isometry property (RIP). Without such assumptions little is known and…

Despite the growing availability of high-capacity computational platforms, implementation complexity still has been a great concern for the real-world deployment of neural networks. This concern is not exclusively due to the huge costs of…

Modern statistical learning algorithms are capable of amazing flexibility, but struggle with interpretability. One possible solution is sparsity: making inference such that many of the parameters are estimated as being identically 0, which…

This paper is intended to solve the nonconvex $\ell_{p}$-ball constrained nonlinear optimization problems. An iteratively reweighted method is proposed, which solves a sequence of weighted $\ell_{1}$-ball projection subproblems. At each…

This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear…

The $\ell^0$ minimization of compressed sensing is often relaxed to $\ell^1$, which yields easy computation using the shrinkage mapping known as soft thresholding, and can be shown to recover the original solution under certain hypotheses.…

Sparse manifold learning algorithms combine techniques in manifold learning and sparse optimization to learn features that could be utilized for downstream tasks. The standard setting of compressive sensing can not be immediately applied to…

Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…

In this paper we introduce and analyze an iteratively re-weighted algorithm, that allows to approximate the weak solution of the $p$-Poisson problem for $1 < p \leq 2$ by iteratively solving a sequence of linear elliptic problems. The…

Compressive sensing claims that the sparse signals can be reconstructed exactly from many fewer measurements than traditionally believed necessary. One of issues ensuring the successful compressive sensing is to deal with the…

This work considers reconstructing a target signal in a context of distributed sparse sources. We propose an efficient reconstruction algorithm with the aid of other given sources as multiple side information (SI). The proposed algorithm…

In this article, we present a method for increasing adaptivity of an existing robust estimation algorithm by learning two parameters to better fit the residual distribution. The analyzed method uses these two parameters to calculate weights…

Recurrent neural networks (RNNs) have recently achieved remarkable successes in a number of applications. However, the huge sizes and computational burden of these models make it difficult for their deployment on edge devices. A practically…

Noiseless compressive sensing is a protocol that enables undersampling and later recovery of a signal without loss of information. This compression is possible because the signal is usually sufficiently sparse in a given basis. Currently,…

We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the…

The iteratively reweighted l1 algorithm is a widely used method for solving various regularization problems, which generally minimize a differentiable loss function combined with a nonconvex regularizer to induce sparsity in the solution.…

We address the problem of sparse recovery in an online setting, where random linear measurements of a sparse signal are revealed sequentially and the objective is to recover the underlying signal. We propose a reweighted least squares (RLS)…