We address the problem of finding a set of sparse signals that have nonzero coefficients in the same locations from a set of their compressed measurements. A mixed 2 0 norm optimization approach is considered. A cost function appropriate to the joint-sparse problem is developed, and an algorithm is derived. Compared to other convex relaxation based techniques, the results obtained by the proposed method show a clear improvement in both noiseless and noisy environments.

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0 norm based signal recovery is attractive in compressed sensing as it can facilitate exact recovery of sparse signal with very high probability. Unfortunately, direct 0 norm minimization problem is NP-hard. This paper describes an approximate 0 norm algorithm for sparse representation which preserves most of the advantages of 0 norm. The algorithm shows attractive convergence properties, and provides remarkable performance improvement in noisy environment compared to other popular algorithms. The sparse representation algorithm presented is capable of very fast signal recovery, thereby reducing retrieval latency when handling high dimensional signal.

We present a grid-less version of the L1-SVD algorithm for direction of arrival estimation. The resulting semidefinite programming approach is a globally convergent, fully parametric method capable of working with two dimensional arrays with any arbitrary sensor configurations. It is computationally efficient, and shows improved performance when compared with other popular alternatives. The analysis also allows us to formulate the SPICE algorithm in gridless manner.

We pose the range-Doppler imaging problem as a two-dimensional sparse signal recovery problem with an overcomplete basis. The resulting optimization problem can be solved using both ℓ0 and ℓ1 norm minimization algorithms. Algorithm performance and estimation quality are illustrated using artificial data set, where targets are close to each other and target SNR is low. We show that accurate target location is achieved with high resolution. In particular, compared to other state-of-art algorithms, the proposed approach is shown to achieve more robustness in noisy environment with limited data.