  We propose a novel regularization method for compressive imaging in the
context of the compressed sensing (CS) theory with coherent and redundant
dictionaries. Natural images are often complicated and several types of
structures can be present at once. It is well known that piecewise smooth
images exhibit gradient sparsity, and that images with extended structures are
better encapsulated in wavelet frames. Therefore, we here conjecture that
promoting average sparsity or compressibility over multiple frames rather than
single frames is an extremely powerful regularization prior.
