Related papers: Sparse approximation based on a random overcomplet…
We discuss a method for sparse signal approximation, which is based on the correlation of the target signal with a pseudo-random signal, and uses a modification of the greedy matching pursuit algorithm. We show that this approach provides…
Various $\ell_1$-penalised estimation methods such as graphical lasso and CLIME are widely used for sparse precision matrix estimation. Many of these methods have been shown to be consistent under various quantitative assumptions about the…
Compressed sensing with sparse frame representations is seen to have much greater range of practical applications than that with orthonormal bases. In such settings, one approach to recover the signal is known as $\ell_1$-analysis. We…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
Two approximation algorithms are proposed for $\ell_1$-regularized sparse rank-1 approximation to higher-order tensors. The algorithms are based on multilinear relaxation and sparsification, which are easily implemented and well scalable.…
In this paper, based on a successively accuracy-increasing approximation of the $\ell_0$ norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class…
Sparse coding techniques for image processing traditionally rely on a processing of small overlapping patches separately followed by averaging. This has the disadvantage that the reconstructed image no longer obeys the sparsity prior used…
Finding the sparse solution of an underdetermined system of linear equations has many applications, especially, it is used in Compressed Sensing (CS), Sparse Component Analysis (SCA), and sparse decomposition of signals on overcomplete…
Sparse approximation is the problem to find the sparsest linear combination for a signal from a redundant dictionary, which is widely applied in signal processing and compressed sensing. In this project, I manage to implement the Orthogonal…
Subspace clustering methods based on $\ell_1$, $\ell_2$ or nuclear norm regularization have become very popular due to their simplicity, theoretical guarantees and empirical success. However, the choice of the regularizer can greatly impact…
An algorithmic framework, based on the difference of convex functions algorithm (DCA), is proposed for minimizing a class of concave sparse metrics for compressed sensing problems. The resulting algorithm iterates a sequence of $\ell_1$…
Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition. Unfortunately,…
A greedy pursuit strategy which finds a common basis for approximating a set of similar signals is proposed. The strategy extends the Optimized Orthogonal Matching Pursuit approach to selecting the subspace containing the approximation of…
In this paper we discuss the variable selection method from \ell0-norm constrained regression, which is equivalent to the problem of finding the best subset of a fixed size. Our study focuses on two aspects, consistency and computation. We…
Signals with sparse frame representations comprise a much more realistic model of nature than that with orthonomal bases. Studies about the signal recovery associated with such sparsity models have been one of major focuses in compressed…
Despite its nonconvex nature, $\ell_0$ sparse approximation is desirable in many theoretical and application cases. We study the $\ell_0$ sparse approximation problem with the tool of deep learning, by proposing Deep $\ell_0$ Encoders. Two…
Spare representation of signals has received significant attention in recent years. Based on these developments, a sparse representation-based classification (SRC) has been proposed for a variety of classification and related tasks,…
Feature selection and regularization are becoming increasingly prominent tools in the efforts of the reinforcement learning (RL) community to expand the reach and applicability of RL. One approach to the problem of feature selection is to…
We first propose a novel criterion that guarantees that an $s$-sparse signal is the local minimizer of the $\ell_1/\ell_2$ objective; our criterion is interpretable and useful in practice. We also give the first uniform recovery condition…
Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…