Related papers: Frame-based Sparse Analysis and Synthesis Signal R…
Sparse representation leads to an efficient way to approximately recover a signal by the linear composition of a few bases from a learnt dictionary, based on which various successful applications have been achieved. However, in the scenario…
Compressive Sensing (CS) theory shows that a signal can be decoded from many fewer measurements than suggested by the Nyquist sampling theory, when the signal is sparse in some domain. Most of conventional CS recovery approaches, however,…
We propose a new approach to the problem of recovering signal from frame coefficients with erasures. Such problems arise naturally from applications where some of the coefficients could be corrupted or erased during the data transmission.…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
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…
Convolutional sparse representations are a form of sparse representation with a dictionary that has a structure that is equivalent to convolution with a set of linear filters. While effective algorithms have recently been developed for the…
A unified view of sparse signal processing is presented in tutorial form by bringing together various fields. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described…
Sparse representation-based classifiers have shown outstanding accuracy and robustness in image classification tasks even with the presence of intense noise and occlusion. However, it has been discovered that the performance degrades…
Sparse recovery is widely applied in many fields, since many signals or vectors can be sparsely represented under some frames or dictionaries. Most of fast algorithms at present are based on solving $l^0$ or $l^1$ minimization problems and…
We revisit the classical problem of Fourier-sparse signal reconstruction -- a variant of the \emph{Set Query} problem -- which asks to efficiently reconstruct (a subset of) a $d$-dimensional Fourier-sparse signal ($\|\hat{x}(t)\|_0 \leq…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…
Compressive Sensing (CS) is a new technique for the efficient acquisition of signals, images, and other data that have a sparse representation in some basis, frame, or dictionary. By sparse we mean that the N-dimensional basis…
This thesis consists of original contributions in the area of digital signal processing. The reconstruction of signals sparse (highly concentrated) in various transform domains is the primary problem analyzed in the thesis. The considered…
Sparsity regularization has garnered significant interest across multiple disciplines, including statistics, imaging, and signal processing. Standard techniques for addressing sparsity regularization include iterative soft thresholding…
In this paper we consider the problem of sparse signal recovery in Multiple Measurement Vectors (MMVs) case. Recently, ample researches have been conducted to solve this problem and diverse methods are proposed, one of which is deep neural…
In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is,…
With the objective of employing graphs toward a more generalized theory of signal processing, we present a novel sampling framework for (wavelet-)sparse signals defined on circulant graphs which extends basic properties of Finite Rate of…
The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…
The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In…
The past several years have witnessed a surge of research investigating various aspects of sparse representations and compressed sensing. Most of this work has focused on the finite-dimensional setting in which the goal is to decompose a…