Theoretical performance limits for jointly sparse signals via graphical models

The compressed sensing (CS) framework has been proposed for efficient acquisition of sparse and compressible signals through incoherent measurements. In our recent work, we introduced a new concept of joint sparsity of a signal ensemble. For several specific joint sparsity models, we demonstrated distributed CS schemes. This paper considers joint sparsity via graphical models that link the sparse underlying coefficient vector, signal entries, and measurements. Our converse and achievable bounds establish that the number of measurements required in the noiseless measurement setting is closely related to the dimensionality of the sparse coefficient vector. Single signal and joint (single-encoder) CS are special cases of joint sparsity, and their performance limits fit into our graphical model framework for distributed (multi-encoder) CS.