Recall, If we have P non-zero elements in a sparse vector of length N, minimum required samples will be P*C*log (N/P). What if we have Q groups of known or unknown length instead? Do we have any advantage on the number of measurements by having group structure?
Jean-Luc Bouchot
If you already know that you have a particular (group or any other thing) structure, you should be able to reduce the lower bound of the minimum number of measurements. Some results have already been published; see the keywords "Model-based compressed sensing" for instance. Simon Foucart also published a paper on nonnegative sparse signal recovery. He also published (actually submitted) recently a paper on sparsity + separation between non-zeros very recently.
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