## Sparse Signal Recovery and Acquisition with Graphical Models -- A review of a broad set of sparse models, analysis tools, and recovery algorithms within the graphical models formalism (2010)

Citations: | 4 - 1 self |

### BibTeX

@MISC{Cevher10sparsesignal,

author = {Volkan Cevher and Piotr Indyk and Lawrence Carin and Richard G. Baraniuk},

title = { Sparse Signal Recovery and Acquisition with Graphical Models -- A review of a broad set of sparse models, analysis tools, and recovery algorithms within the graphical models formalism},

year = {2010}

}

### OpenURL

### Abstract

Many applications in digital signal processing, machine learning, and communications feature a linear regression problem in which unknown data points, hidden variables, or code words are projected into a lower dimensional space via y 5 Fx 1 n. (1) In the signal processing context, we refer to x [ R N as the signal, y [ R M as measurements with M, N, F[R M3N as the measurement matrix, and n [ R M as the noise. The measurement matrix F is a matrix with random entries in data streaming, an overcomplete dictionary of features in sparse Bayesian learning, or a code matrix in communications [1]–[3]. Extracting x from y in (1) is ill posed in general since M, N and the measurement matrix F hence has a nontrivial null space; given any vector v in this null space, x 1 v defines a solution that produces the same observations y. Additional information is therefore necessary to distinguish the true x among the infinitely many possible solutions [1], [2], [4], [5]. It is now well known that sparse