The joint sparse recovery problem is a generalization of the single measurement vector problem which is widely studied in Compressed Sensing and it aims to recovery a set of jointly sparse vectors. i.e. have nonzero entries concentrated at common location. Meanwhile lp-minimization subject to matrices is widely used in a large number of algorithms designed for this problem. Therefore the main c...

One of the main challenges in block-sparse signal recovery, as encountered in, e.g., multi-antenna mmWave channel models, is block-patterned estimation without knowledge block sizes and boundaries. We propose a novel Sparse Bayesian Learning (SBL) method for recovery under unknown patterns. Contrary to conventional approaches that impose block-promoting regularization on components, we a...

We address the problem of robustly recovering the support of high-dimensional sparse signals1 from linear measurements in a low-dimensional subspace. We introduce a new family of sparse measurement matrices associated with low-complexity recovery algorithms. Our measurement system is designed to capture observations of the signal through sparse-graph codes, and to recover the signal by using a ...

Traditional Compressive Sensing (CS) recovery techniques resorts a dictionary matrix to recover a signal. The success of recovery heavily relies on finding a dictionary matrix in which the signal representation is sparse. Achieving a sparse representation does not only depend on the dictionary matrix, but also depends on the data. It is a challenging issue to find an optimal dictionary to recov...

Compressed sensing (CS) demonstrates that sparse signals can be recovered from underdetermined linear measurements. We focus on the joint sparse recovery problem where multiple signals share the same common sparse support sets, and they are measured through the same sensing matrix. Leveraging a recent information theoretic characterization of single signal CS, we formulate the optimal minimum m...

Sparse signal recovery algorithms can be used to improve radar imaging quality by using the sparse property of strong scatterers. Traditional sparse inverse synthetic aperture radar (ISAR) imaging algorithms mainly consider the recovery of sparse scatterers. However, the scatterers of an ISAR target usually exhibit block or group sparse structure. By utilizing the inherent block sparse structur...

The aim of this paper is to build up the theoretical framework for the recovery of sparse signals from the magnitude of the measurement. We first investigate the minimal number of measurements for the success of the recovery of sparse signals without the phase information. We completely settle the minimality question for the real case and give a lower bound for the complex case. We then study t...

A noisy underdetermined system of linear equations is considered in which a sparse vector (a vector with a few nonzero elements) is subject to measurement. The measurement matrix elements are drawn from a Gaussian distribution. We study the information-theoretic constraints on exact support recovery of a sparse vector from the measurement vector and matrix. We compute a tight, sufficient condit...

It is well known that the performance of sparse vector recovery algorithms from compressive measurements can depend on the distribution underlying the non-zero elements of a sparse vector. However, the extent of these effects has yet to be explored, and formally presented. In this paper, I empirically investigate this dependence for seven distributions and fifteen recovery algorithms. The two m...