Related papers: Ranked Sparse Signal Support Detection
This paper provides a simple proof of the mutual incoherence condition $\mu < \frac{1}{2K-1}$ under which K-sparse signal can be accurately reconstructed from a small number of linear measurements using the orthogonal matching pursuit (OMP)…
The orthogonal matching pursuit (OMP) is one of the mainstream algorithms for sparse data reconstruction or approximation. It acts as a driving force for the development of several other greedy methods for sparse data reconstruction, and it…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…
Exact recovery of $K$-sparse signals $x \in \mathbb{R}^{n}$ from linear measurements $y=Ax$, where $A\in \mathbb{R}^{m\times n}$ is a sensing matrix, arises from many applications. The orthogonal matching pursuit (OMP) algorithm is widely…
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…
A reliable support detection is essential for a greedy algorithm to reconstruct a sparse signal accurately from compressed and noisy measurements. This paper proposes a novel support detection method for greedy algorithms, which is referred…
In this note, we investigate the theoretical properties of Orthogonal Matching Pursuit (OMP), a class of decoder to recover sparse signal in compressed sensing. In particular, we show that the OMP decoder can give $(p,q)$ instance…
The classical sparse parameter identification methods are usually based on the iterative basis selection such as greedy algorithms, or the numerical optimization of regularized cost functions such as LASSO and Bayesian posterior probability…
Orthogonal Matching Pursuit (OMP) has long been considered a powerful heuristic for attacking compressive sensing problems; however, its theoretical development is, unfortunately, somewhat lacking. This paper presents an improved Restricted…
Support estimation (SE) of a sparse signal refers to finding the location indices of the non-zero elements in a sparse representation. Most of the traditional approaches dealing with SE problem are iterative algorithms based on greedy…
Focusing on identification, this paper develops techniques to reconstruct zero and nonzero elements of a sparse parameter vector of a stochastic dynamic system under feedback control, for which the current input may depend on the past…
We propose extended coherence-based conditions for exact sparse support recovery using orthogonal matching pursuit (OMP) and orthogonal least squares (OLS). Unlike standard uniform guarantees, we embed some information about the decay of…
For compressive sensing of dynamic sparse signals, we develop an iterative pursuit algorithm. A dynamic sparse signal process is characterized by varying sparsity patterns over time/space. For such signals, the developed algorithm is able…
We consider the Orthogonal Least-Squares (OLS) algorithm for the recovery of a $m$-dimensional $k$-sparse signal from a low number of noisy linear measurements. The Exact Recovery Condition (ERC) in bounded noisy scenario is established for…
The role of sparse representations in the context of structured noise filtering is discussed. A strategy, especially conceived so as to address problems of an ill posed nature, is presented. The proposed approach revises and extends the…
In a bivariate setting, we consider the problem of detecting a sparse contamination or mixture component, where the effect manifests itself as a positive dependence between the variables, which are otherwise independent in the main…
This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a…
Matching pursuit, especially its orthogonal version (OMP) and variations, is a greedy algorithm widely used in signal processing, compressed sensing, and sparse modeling. Inspired by constrained sparse signal recovery, this paper proposes a…
In many practical settings one can sequentially and adaptively guide the collection of future data, based on information extracted from data collected previously. These sequential data collection procedures are known by different names,…