In this paper we consider the problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the `1-norm of the part of the solution vector which is known to be sparse. Such a problem is closely related to the classical problem in Compressed Sensing where the `1-norm of the whole solution vector is minimized. We introduce analogues of restricted...

We consider the problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the l1-norm of the part of the solution vector which is known to be sparse. Such a problem is closely related to a classical problem in Compressed Sensing where the l1-norm of the whole solution vector is minimized. We introduce analogues of restricted isometry and nu...

Sufficient number of linear and noisy measurements for exact and approximate sparsity pattern/support set recovery in the high dimensional setting is derived. Although this problem as been addressed in the recent literature, there is still considerable gaps between those results and the exact limits of the perfect support set recovery. To reduce this gap, in this paper, the sufficient con...

We consider the recovery of jointly sparse multichannel signals from incomplete measurements using convex relaxation methods. Worst case analysis is not able to provide insights into why joint sparse recovery is superior to applying standard sparse reconstruction methods to each channel individually. Therefore, we analyze an average case by imposing a probability model on the measured signals. ...

Orthogonal Frequency Division Multiplexing is a widely adopted multi carrier modulation in wireless communication systems due to its effective transmission and efficient bandwidth utilization ability. Wireless systems with coherent data detection require the estimation of channel at the receiver. Commonly employed pilot aided channel estimation probes the channel with known sequence called pilo...

The rapid developing area of compressed sensing suggests that a sparse vector lying in an arbitrary high dimensional space can be accurately recovered from only a small set of non-adaptive linear measurements. Under appropriate conditions on the measurement matrix, the entire information about the original sparse vector is captured in the measurements, and can be recovered using efficient polyn...

In this paper, we introduce a new detection algorithm for large-scale wireless systems, referred to as post sparse error detection (PSED) algorithm, that employs a sparse error recovery algorithm to refine the estimate of a symbol vector obtained by the conventional linear detector. The PSED algorithm operates in two steps: 1) sparse transformation converting the original non-sparse system into...

Orthogonal Matching Pursuit (OMP) is a simple, yet empirically competitive algorithm for sparse recovery. Recent developments have shown that OMP guarantees exact recovery of K-sparse signals with K or more than K iterations if the observation matrix satisfies the restricted isometry property (RIP) with some conditions. We develop RIP-based online guarantees for recovery of a K-sparse signal wi...