  We solve the problem of sparse signal deconvolution in the context of seismic
reflectivity inversion, which pertains to high-resolution recovery of the
subsurface reflection coefficients. Our formulation employs a nonuniform,
non-convex synthesis sparse model comprising a combination of convex and
non-convex regularizers, which results in accurate approximations of the l0
pseudo-norm. The resulting iterative algorithm requires the proximal average
strategy. When unfolded, the iterations give rise to a learnable proximal
average network architecture that can be optimized in a data-driven fashion. We
demonstrate the efficacy of the proposed approach through numerical experiments
on synthetic 1-D seismic traces and 2-D wedge models in comparison with the
benchmark techniques. We also present validations considering the simulated
Marmousi2 model as well as real 3-D seismic volume data acquired from the
Penobscot 3D survey off the coast of Nova Scotia, Canada.
