  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.
