Much research has been recently been devoted to sparse signal recovery and image reconstruction from multiple measurement vectors (MMV). The assumption that the underlying signals or images have some common features with sparse representation suggests that using a joint sparsity approach to recover each individual signal or image can be more effective than recovering each signal or image separately using standard sparse recovery techniques. Joint sparsity reconstruction is typically performed using $\ell_{2,1}$ minimization, and although the process often yields better results than separate recoveries, the inherent coupling makes the algorithm computationally intensive, since it is difficult to parallelize. It is also not robust to outliers or bad data. In this talk we introduce an algorithm based on the observation that the pixel-wise variance of the signals convey information about their shared support. This observation motivates the introduction of a weighted $\ell_{p}$, $p = 1,2$ joint sparsity algorithm, where the weights depend on information learned from the calculated variance. These spatially varying weights may also be determined by determining the magnitude of the features in the sparse domain. Specifically, the sparsity enforcing regularization term should be more heavily penalized in regions where it is likely that no signal is present. We demonstrate the accuracy, robustness, and cost efficiency of our new method. It can also be used where some of the measurement vectors may misrepresent the unknown signals or images of interest. Such "false data" problems appear in applications including state estimation of electrical power grids, large scale sensor network estimation, and synthetic aperture radar automated target recognition.

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