  We introduce a new weakly-convex penalty function for signals with a group
behavior. The penalty promotes signals with a few number of active groups,
where within each group, only a few high magnitude coefficients are active. We
derive the threshold function associated with the proposed penalty and study
its properties. We discuss how the proposed penalty/threshold function can be
useful for signals with isolated non-zeros, such as audio with isolated
harmonics along the frequency axis, or reflection functions in exploration
seismology where the non-zeros occur on the boundaries of subsoil layers. We
demonstrate the use of the proposed penalty/threshold functions in a convex
denoising and a non-convex deconvolution formulation. We provide convergent
algorithms for both formulations and compare the performance with
state-of-the-art methods.
