Related papers: One-bit compressive sensing with norm estimation
We propose a new method, {\it robust binary fused compressive sensing} (RoBFCS), to recover sparse piece-wise smooth signals from 1-bit compressive measurements. The proposed method is a modification of our previous {\it binary fused…
Compressed Sensing decoding algorithms can efficiently recover an N dimensional real-valued vector x to within a factor of its best k-term approximation by taking m = 2klog(N/k) measurements y = Phi x. If the sparsity or approximate…
Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have…
Compressive sensing (CS) is a technique for estimating a sparse signal from the random measurements and the measurement matrix. Traditional sparse signal recovery methods have seriously degeneration with the measurement matrix uncertainty…
The fundamental principle underlying compressed sensing is that a signal, which is sparse under some basis representation, can be recovered from a small number of linear measurements. However, prior knowledge of the sparsity basis is…
In the theory of compressed sensing (CS), the sparsity $\|x\|_0$ of the unknown signal $\mathbf{x} \in \mathcal{R}^n$ is of prime importance and the focus of reconstruction algorithms has mainly been either $\|x\|_0$ or its convex…
The one-bit quantization is implemented by one single comparator that operates at low power and a high rate. Hence one-bit compressive sensing (1bit-CS) becomes attractive in signal processing. When measurements are corrupted by noise…
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…
This paper addresses the classical problem of one-bit compressed sensing using a deep learning-based reconstruction algorithm that leverages a trained generative model to enhance the signal reconstruction performance. The generator, a…
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…
Compressed sensing (sparse signal recovery) often encounters nonnegative data (e.g., images). Recently we developed the methodology of using (dense) Compressed Counting for recovering nonnegative K-sparse signals. In this paper, we adopt…
Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…
In this paper, we analyze the information theoretic lower bound on the necessary number of samples needed for recovering a sparse signal under different compressed sensing settings. We focus on the weighted graph model, a model-based…
Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information. Efficient recovery methods such as $\ell_1$-minimization find the sparsest solution to certain systems of equations. Random…
The theory of Compressed Sensing, the emerging sampling paradigm 'that goes against the common wisdom', asserts that 'one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some…
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…
In this paper we study the quantization stage that is implicit in any compressed sensing signal acquisition paradigm. We propose using Sigma-Delta quantization and a subsequent reconstruction scheme based on convex optimization. We prove…
Model-based compressed sensing refers to compressed sensing with extra structure about the underlying sparse signal known a priori. Recent work has demonstrated that both for deterministic and probabilistic models imposed on the signal,…
In compressive sensing, a small collection of linear projections of a sparse signal contains enough information to permit signal recovery. Distributed compressive sensing (DCS) extends this framework by defining ensemble sparsity models,…
We study the recovery of sparse signals from underdetermined linear measurements when a potentially erroneous support estimate is available. Our results are twofold. First, we derive necessary and sufficient conditions for signal recovery…