Related papers: Sparse Representation in Fourier and Local Bases U…
We consider the recovery of sparse signals subject to sparse interference, as introduced in Studer et al., IEEE Trans. IT, 2012. We present novel probabilistic recovery guarantees for this framework, covering varying degrees of knowledge of…
It is well known that sparse approximation problem is \textsf{NP}-hard under general dictionaries. Several algorithms have been devised and analyzed in the past decade under various assumptions on the \emph{coherence} $\mu$ of the…
Recently, great attention was intended toward overcomplete dictionaries and the sparse representations they can provide. In a wide variety of signal processing problems, sparsity serves a crucial property leading to high performance.…
In ill-posed dynamic inverse problems expected spatial features and temporal correlation between frames can be leveraged to improve the quality of the computed solution, in particular when the available data are limited and the…
A compressive sensing (CS) reconstruction method for polynomial phase signals is proposed in this paper. It relies on the Polynomial Fourier transform, which is used to establish a relationship between the observation and sparsity domain.…
Matching pursuits are a class of greedy algorithms commonly used in signal processing, for solving the sparse approximation problem. They rely on an atom selection step that requires the calculation of numerous projections, which can be…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
Conventional compressed sensing theory assumes signals have sparse representations in a known, finite dictionary. Nevertheless, in many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the…
We take an information theoretic perspective on a classical sparse-sampling noisy linear model and present an analytical expression for the mutual information, which plays central role in a variety of communications/processing problems.…
The linear representation hypothesis states that neural network activations encode high-level concepts as linear mixtures. However, under superposition, this encoding is a projection from a higher-dimensional concept space into a…
Sparse representations using learned dictionaries are being increasingly used with success in several data processing and machine learning applications. The availability of abundant training data necessitates the development of efficient,…
Convolutional Sparse Coding (CSC) is an increasingly popular model in the signal and image processing communities, tackling some of the limitations of traditional patch-based sparse representations. Although several works have addressed the…
Sparse representation-based classification (SRC) has been shown to achieve a high level of accuracy in face recognition (FR). However, matching faces captured in unconstrained video against a gallery with a single reference facial still per…
Classical results in sparse recovery guarantee the exact reconstruction of $s$-sparse signals under assumptions on the dictionary that are either too strong or NP-hard to check. Moreover, such results may be pessimistic in practice since…
Sparsity priors are commonly used in denoising and image reconstruction. For analysis-type priors, a dictionary defines a representation of signals that is likely to be sparse. In most situations, this dictionary is not known, and is to be…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
We consider the problem of sparse atomic optimization, where the notion of "sparsity" is generalized to meaning some linear combination of few atoms. The definition of atomic set is very broad; popular examples include the standard basis,…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
We propose a compressed sensing algorithm termed variance state propagation (VSP) for block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. The VSP algorithm is developed under the Bayesian…
In this paper, we introduce a wideband dictionary framework for estimating sparse signals. By formulating integrated dictionary elements spanning bands of the considered parameter space, one may efficiently find and discard large parts of…