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In this paper, we study a support set reconstruction problem in which thesignals of interest are jointly sparse with a common support set, and sampledby joint sparsity model-2 (JSM-2) in the presence of noise. Using mathematicaltools, we develop upper and lower bounds on the failure probability of supportset reconstruction in terms of the sparsity, the ambient dimension, the minimumsignal to noise ratio, the number of measurement vectors and the number ofmeasurements. These bounds can be used to provide a guideline to determine thesystem parameters in various applications of compressed sensing with noisyJSM-2. Based on the bounds, we develop necessary and sufficient conditions forreliable support set reconstruction. We interpret these conditions to givetheoretical explanations about the benefits enabled by joint sparsity structurein noisy JSM-2. We compare our sufficient condition with the existing result ofnoisy multiple measurement vectors model (MMV). As a result, we show that noisyJSM-2 may require less number of measurements than noisy MMV for reliablesupport set reconstruction.

An Information Theoretic Study for Noisy Compressed Sensing With Joint Sparsity Model-2