Related papers: Compressed Sensing under Matrix Uncertainty: Optim…
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…
Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse signal at low rate and later using computational power for its exact reconstruction, so that only the necessary information is…
This paper proposes a verification-based decoding approach for reconstruction of a sparse signal with incremental sparse measurements. In its first step, the verification-based decoding algorithm is employed to reconstruct the signal with a…
Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy this…
Compressed sensing (CS) is a concept that allows to acquire compressible signals with a small number of measurements. As such it is very attractive for hardware implementations. Therefore, correct calibration of the hardware is a central…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…
Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a…
Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy the…
Many practical sensing applications involve multiple sensors simultaneously acquiring measurements of a single object. Conversely, most existing sparse recovery guarantees in compressed sensing concern only single-sensor acquisition…
This paper describes performance bounds for compressed sensing in the presence of Poisson noise when the underlying signal, a vector of Poisson intensities, is sparse or compressible (admits a sparse approximation). The signal-independent…
The central idea of compressed sensing is to exploit the fact that most signals of interest are sparse in some domain and use this to reduce the number of measurements to encode. However, if the sparsity of the input signal is not precisely…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this paper, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via multiplicative…
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…
Bayesian approximate message passing (BAMP) is an efficient method in compressed sensing that is nearly optimal in the minimum mean squared error (MMSE) sense. Bayesian approximate message passing (BAMP) performs joint recovery of multiple…
Compressed sensing investigates the recovery of sparse signals from linear measurements. But often, in a wide range of applications, one is given only the absolute values (squared) of the linear measurements. Recovering such signals (not…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
We present a novel compressed sensing recovery algorithm - termed Bayesian Optimal Structured Signal Approximate Message Passing (BOSSAMP) - that jointly exploits the prior distribution and the structured sparsity of a signal that shall be…
Compressive sensing is a technique to sample signals well below the Nyquist rate using linear measurement operators. In this paper we present an algorithm for signal reconstruction given such a set of measurements. This algorithm…
Compressed sensing deals with efficient recovery of analog signals from linear encodings. This paper presents a statistical study of compressed sensing by modeling the input signal as an i.i.d. process with known distribution. Three classes…
We consider the problems of compressed sensing and optimal denoising for signals $\mathbf{x_0}\in\mathbb{R}^N$ that are monotone, i.e., $\mathbf{x_0}(i+1) \geq \mathbf{x_0}(i)$, and sparsely varying, i.e., $\mathbf{x_0}(i+1) >…