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.