Related papers: Signal Recovery under Cumulative Coherence
Most of compressed sensing (CS) theory to date is focused on incoherent sensing, that is, columns from the sensing matrix are highly uncorrelated. However, sensing systems with naturally occurring correlations arise in many applications,…
In this paper, we consider the problem of recovering a sparse signal from noisy linear measurements using the so called LASSO formulation. We assume a correlated Gaussian design matrix with additive Gaussian noise. We precisely analyze the…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
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…
In this paper, utilizing techniques in compressed sensing, parallel optimization and deep learning, we propose a model-driven approach to jointly design the common measurement matrix and GROUP LASSO-based jointly sparse signal recovery…
We investigate the recovery of signals exhibiting a sparse representation in a general (i.e., possibly redundant or incomplete) dictionary that are corrupted by additive noise admitting a sparse representation in another general dictionary.…
We present a general architecture for the acquisition of ensembles of correlated signals. The signals are multiplexed onto a single line by mixing each one against a different code and then adding them together, and the resulting signal is…
This paper studies the problem of recovering a structured signal from a relatively small number of corrupted non-linear measurements. Assuming that signal and corruption are contained in some structure-promoted set, we suggest an extended…
In this paper, {the goal is to design deterministic sampling patterns on the sphere and the rotation group} and, thereby, construct sensing matrices for sparse recovery of band-limited functions. It is first shown that random sensing…
In this paper, we investigate the theoretical guarantees of penalized $\lun$ minimization (also called Basis Pursuit Denoising or Lasso) in terms of sparsity pattern recovery (support and sign consistency) from noisy measurements with…
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…
Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…
A combinatorial approach to compressive sensing based on a deterministic column replacement technique is proposed. Informally, it takes as input a pattern matrix and ingredient measurement matrices, and results in a larger measurement…
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of…
Given an overcomplete dictionary $A$ and a signal $b = Ac^*$ for some sparse vector $c^*$ whose nonzero entries correspond to linearly independent columns of $A$, classical sparse signal recovery theory considers the problem of whether…
This paper provides novel results for the recovery of signals from undersampled measurements based on analysis $\ell_1$-minimization, when the analysis operator is given by a frame. We both provide so-called uniform and nonuniform recovery…
We give some new results on sparse signal recovery in the presence of noise, for weighted spaces. Traditionally, were used dictionaries that have the norm equal to 1, but, for random dictionaries this condition is rarely satisfied.…
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…
The recovery of structured signals from a few linear measurements is a central point in both compressed sensing (CS) and discrete tomography. In CS the signal structure is described by means of a low complexity model e.g. co-/sparsity. The…