Related papers: Mixed Compressed Sensing Based on Random Graphs
Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming…
This paper introduces a simple and very general theory of compressive sensing. In this theory, the sensing mechanism simply selects sensing vectors independently at random from a probability distribution F; it includes all models - e.g.…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
We consider the recovery of a nonnegative vector x from measurements y = Ax, where A is an m-by-n matrix whos entries are in {0, 1}. We establish that when A corresponds to the adjacency matrix of a bipartite graph with sufficient…
The problem of recovering a structured signal $\mathbf{x} \in \mathbb{C}^p$ from a set of dimensionality-reduced linear measurements $\mathbf{b} = \mathbf {A}\mathbf {x}$ arises in a variety of applications, such as medical imaging,…
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…
In the problem of matrix compressed sensing we aim to recover a low-rank matrix from few of its element-wise linear projections. In this contribution we analyze the asymptotic performance of a Bayes-optimal inference procedure for a model…
Can compression algorithms be employed for recovering signals from their underdetermined set of linear measurements? Addressing this question is the first step towards applying compression algorithms for compressed sensing (CS). In this…
Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…
Compressed sensing is a theory which guarantees the exact recovery of sparse signals from a small number of linear projections. The sampling schemes suggested by current compressed sensing theories are often of little practical relevance…
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…
A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in a…
In this paper, we exploit the theory of compressive sensing to perform detection of a random source in a dense sensor network. When the sensors are densely deployed, observations at adjacent sensors are highly correlated while those…
Compressed sensing is the art of reconstructing a sparse vector from its inner products with respect to a small set of randomly chosen measurement vectors. It is usually assumed that the ensemble of measurement vectors is in isotropic…
Recent development in compressed sensing (CS) has revealed that the use of a special design of measurement matrix, namely the spatially-coupled matrix, can achieve the information-theoretic limit of CS. In this paper, we consider the…
The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach…
In colocated multiple-input multiple-output (MIMO) radar using compressive sensing (CS), a receive node compresses its received signal via a linear transformation, referred to as measurement matrix. The samples are subsequently forwarded to…
Consider the problem of recovering an unknown signal from undersampled measurements, given the knowledge that the signal has a sparse representation in a specified dictionary $D$. This problem is now understood to be well-posed and…
Practical applications of compressed sensing often restrict the choice of its two main ingredients. They may (i) prescribe using particular redundant dictionaries for certain classes of signals to become sparsely represented, or (ii)…
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The…