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.
Face recognition in real world environments is mainly affected by critical factors such as illumination variation, occlusion and small sample size. This paper proposes a robust preprocessing chain and robust feature extraction in order to handle these issues simultaneously. The proposed preprocessing chain exploits Difference of Gaussian (DoG) filtering as a bandpass filter to reduce the effects of aliasing, noise and shadows, and then exploits the gradient domain as an illumination insensitive measure. On the other hand, Linear Discriminant Analysis (LDA) is one of the most successful facial feature extraction techniques, but the recognition performance of LDA is dramatically decreased by the presence of occlusion and small sample size (SSS) problem. Therefore, it is necessary to develop a robust LDA algorithm in order to handle these cases. At this point, we propose to combine Robust Sparse Principal Component Analysis (RSPCA) and LDA (RSPCA+LDA). The RSPCA is performed first in order to reduce the dimension and to deal with outliers typically affecting sample images due to pixels that are corrupted by noise or occlusion. Then, LDA in low-dimensional subspaces can operate more effectively. Experimental results on three standard databases, namely, Extended Yale-B, AR and JAFFE confirm the effectiveness of the proposed method and the results are superior to well-known methods in the literature.