Related papers: On the Doubly Sparse Compressed Sensing Problem
We consider a generalization of the multiple measurement vector (MMV) problem, where the measurement matrices are allowed to differ across measurements. This problem arises naturally when multiple measurements are taken over time, e.g., and…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…
Our aim of this article is to reconstruct a signal from undersampled data in the situation that the signal is sparse in terms of a tight frame. We present a condition, which is independent of the coherence of the tight frame, to guarantee…
We consider the problem of reconstructing time sequences of spatially sparse signals (with unknown and time-varying sparsity patterns) from a limited number of linear "incoherent" measurements, in real-time. The signals are sparse in some…
This paper studies the problem of recovering a non-negative sparse signal $\x \in \Re^n$ from highly corrupted linear measurements $\y = A\x + \e \in \Re^m$, where $\e$ is an unknown error vector whose nonzero entries may be unbounded.…
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…
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…
In this paper we present two new approaches to efficiently solve large-scale compressed sensing problems. These two ideas are independent of each other and can therefore be used either separately or together. We consider all possibilities.…
Since compressive sensing deals with a signal reconstruction using a reduced set of measurements, the existence of a unique solution is of crucial importance. The most important approach to this problem is based on the restricted isometry…
Unlike compressive sensing where the measurement outputs are assumed to be real-valued and have infinite precision, in "one-bit compressive sensing", measurements are quantized to one bit, their signs. In this work, we show how to recover…
In this paper we develop a general theory of compressed sensing for analog signals, in close similarity to prior results for vectors in finite dimensional spaces that are sparse in a given orthonormal basis. The signals are modeled by…
In this work, we consider the problem of recovering analysis-sparse signals from under-sampled measurements when some prior information about the support is available. We incorporate such information in the recovery stage by suitably tuning…
We consider the problem of exact support recovery of sparse signals via noisy measurements. The main focus is the sufficient and necessary conditions on the number of measurements for support recovery to be reliable. By drawing an analogy…
The recently proposed modified-compressive sensing (modified-CS), which utilizes the partially known support as prior knowledge, significantly improves the performance of recovering sparse signals. However, modified-CS depends heavily on…
In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
Recent research has shown that performance in signal processing tasks can often be significantly improved by using signal models based on sparse representations, where a signal is approximated using a small number of elements from a fixed…
The problem of identifying sparse solutions for the link structure and dynamics of an unknown linear, time-invariant network is posed as finding sparse solutions x to Ax=b. If the sensing matrix A satisfies a rank condition, this problem…
Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as Compressed Sensing (CS). Fusion frames are very rich new signal…