Solving multi-dimensional deconvolution via a nuclear-norm regularized least-squares approach

Multi-dimensional deconvolution (MDD), a data processing technique stemming from the Green’s function representation theorem, is commonly solved as a linear least-squares inverse problem. When the wavefields to be deconvolved contain random or coherent noise, MDD may produce severe artifacts. We suggest regularizing the unknown parameters of MDD in the frequency domain by the nuclear norm, the sum of singular values of a matrix such that the solution to MDD lies in low-dimensional subspaces. The proposed nuclear-norm regularized MDD can be efficiently solved using the accelerated proximal gradient method. The numerical examples demonstrate that the suggested regularization scheme can reduce the artifacts of MDD in such a circumstance.