Block-sparse compressed sensing with partially known signal support via non-convex minimisation

The mixed l(2)/l(p) (0 < p 1) norm minimisation method with partially known support for recovering block-sparse signals is studied. The authors mainly extend this work on block-sparse compressed sensing by incorporating some known part of the block support information as a priori and establish sufficient restricted p-isometry property (p-RIP) conditions for exact and robust recovery. The authors' theoretical results show it is possible to recover the block-sparse signals via l(2)/l(p) minimisation from reduced number of measurements by applying the partially known support. The authors also derive a lower bound on necessary random Gaussian measurements for the p-RIP conditions to hold with high possibility. Finally, a series of numerical experiments are carried out to illustrate that fewer measurements with smaller p are needed to reconstruct the signal.