  Signal recovery is one of the key techniques of Compressive sensing (CS). It
reconstructs the original signal from the linear sub-Nyquist measurements.
Classical methods exploit the sparsity in one domain to formulate the L0 norm
optimization. Recent investigation shows that some signals are sparse in
multiple domains. To further improve the signal reconstruction performance, we
can exploit this multi-sparsity to generate a new convex programming model. The
latter is formulated with multiple sparsity constraints in multiple domains and
the linear measurement fitting constraint. It improves signal recovery
performance by additional a priori information. Since some EMG signals exhibit
sparsity both in time and frequency domains, we take them as example in
numerical experiments. Results show that the newly proposed method achieves
better performance for multi-sparse signals.
