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Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements. Classical methods exploit the sparsity in one domain to formulate the L0 norm…
In the context of compressed sensing (CS), this paper considers the problem of reconstructing sparse signals with the aid of other given correlated sources as multiple side information. To address this problem, we theoretically study a…
We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…
This short note studies a variation of the Compressed Sensing paradigm introduced recently by Vaswani et al., i.e. the recovery of sparse signals from a certain number of linear measurements when the signal support is partially known. The…
Compressive Sensing (CS) stipulates that a sparse signal can be recovered from a small number of linear measurements, and that this recovery can be performed efficiently in polynomial time. The framework of model-based compressive sensing…
Sparsity and rank functions are important ways of regularizing under-determined linear systems. Optimization of the resulting formulations is made difficult since both these penalties are non-convex and discontinuous. The most common remedy…
The Orthogonal Matching Pursuit (OMP) for compressed sensing iterates over a scheme of support augmentation and signal estimation. We present two novel matching pursuit algorithms with intrinsic regularization of the signal estimation step…
A compressed sensing method consists of a rectangular measurement matrix, $M \in \mathbbm{R}^{m \times N}$ with $m \ll N$, together with an associated recovery algorithm, $\mathcal{A}: \mathbbm{R}^m \rightarrow \mathbbm{R}^N$. Compressed…
Detection of a signal under noise is a classical signal processing problem. When monitoring spatial phenomena under a fixed budget, i.e., either physical, economical or computational constraints, the selection of a subset of available…
Compressed sensing is a technique for recovering a high-dimensional signal from lower-dimensional data, whose components represent partial information about the signal, utilizing prior knowledge on the sparsity of the signal. For further…
Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…
This work addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction which employs the $\ell_1$-norm as the loss function for the residual error and…
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…
The recovery of approximately sparse or compressible coefficients in a Polynomial Chaos Expansion is a common goal in modern parametric uncertainty quantification (UQ). However, relatively little effort in UQ has been directed toward…
Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…
Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…
We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
Recently, the $\l_{p}$-norm regularization minimization problem $(P_{p}^{\lambda})$ has attracted great attention in compressed sensing. However, the $\l_{p}$-norm $\|x\|_{p}^{p}$ in problem $(P_{p}^{\lambda})$ is nonconvex and…