Complex domain nonlocal block-matching denoising based on high-order singular value decomposition (HOSVD)

Block matching 3D collaborative filtering (BM3D) is one of the most popular denoising technique based on data sparsity concept applied to specially structured data. In this paper we develop this technique for complex domain, i.e. for application to complex-valued data. Sparsity as an approximation technique can be addressed directly to complex-valued variables or to real-valued pairs phase/amplitude and real/imaginary parts of complex-valued variables. As a result we arrive to various ways of development and obtain a set of quite different algorithms. The algorithms proposed in this paper are composed from two components: nonlocal patch-wise grouping and high-order singular value decomposition (HOSVD) for grouped data processing. The latter gives data adaptive complex-valued bases for complex-valued data or real-valued bases for joint processing of the pairs phase/amplitude, real/imaginary parts of complex-valued variables. Comparative study of the developed algorithms is produced in order to select the most efficient ones.