Noise suppression in complex-valued data is an important task for a wide class of applications, in particular concerning the phase retrieval in coherent imaging. The approaches based on BM3D techniques are ones of the most successful in the field. In this paper, we propose and develop a new class of BM3D-style algorithms, which use high order (3D and 4D) singular value decomposition (HOSVD) for transform design in complex domain. This set of the novel algorithms is implemented as a toolbox In Matlab. This development is produced for various types of the complex-domain sparsity: directly in complex domain, real/imaginary and phase/ amplitude parts of complexvalued variables. The group-wise transform design is combined with the different kinds of thresholding including multivariable Wiener filtering. The toolbox includes iterative and non-iterative novel complex-domain algorithms (filters). The efficiency of the developed algorithms is demonstrated on denoising problems with an additive Gaussian complex-valued noise. A special set of the complex-valued test-images was developed with spatially varying correlated phase and amplitudes imitating data typical for optical interferometry and holography. It is shown that for this class of the test-images the developed algorithms demonstrate the state-of-the-art performance.
Mykola Ponomarenko, Vladimir Katkovnik, Karen Egiazarian, "Methods and tools for denoising of complex-valued images based on block-matching and high order singular value decomposition" in Proc. IS&T Int’l. Symp. on Electronic Imaging: Image Processing: Algorithms and Systems XVI, 2018, pp 306-1 - 306-6, https://doi.org/10.2352/ISSN.2470-1173.2018.13.IPAS-306