A reciprocity-aware, low-rank regularization for multidimensional deconvolution

Abstract

This paper presents a novel factorization-based, low-rank regularization method for solving multidimensional deconvolution problems in the frequency domain. In this approach, each frequency component of the unknown wavefield is represented as a complex-valued square matrix and approximated using the product of one rectangular matrix and its transpose. The benefit of such a parametrization is two-fold: first, the size of the unknown matrix is greatly reduced compared to that of the original wavefield of interest (and halved compared to conventional factorization-based, low-rank approximations); second, the retrieved wavefield is implicitly guaranteed to comply with the reciprocity principle, as expected from theory. We further show that the proposed objective function can be successfully optimized using the accelerated proximal gradient algorithm and discuss a robust strategy to define the initial guess of the solution. Numerical examples on synthetic and field data demonstrate the effectiveness of the proposed method in compressing the retrieved Green's function while preserving its accuracy.