Abstract—In this paper is presented one new approach for decorrelation of groups of color images (for example, multi-view, computer tomography, video sequences, etc.) in two directions: the color and the time domain. The correlation strength depends on the image kind (obtained by a video sensor with fixed or time-changing spatial position), and on their contents. To achieve correlation reduction, here is proposed new approach based on the sequential execution of two PCA-based algorithms: the Adaptive Color PCA for each color image in the group, and the Hierarchical Adaptive PCA - for each group or time-sequence, obtained after the execution of the first color space transform. Both algorithms were already presented in preceding publications of the authors, but their combined impact had not been analyzed yet. In the paper is given also the analysis of the information redundancy reduction as a result of the decorrelation got after the execution of both algorithms, and are indicated the future trends for their development. Keywords— Adaptive color PCA, Double PCA-based transform, Hierarchical adaptive PCA, Image decorrelation, Principal Component Analysis. I. INTRODUCTION As it is known, the non-compressed color image is represented through its primary color components - the matrices [R], [G] and [B], whose size is equal to that of the original image. In such case, a group of correlated images (for example, multi- view images, computer tomography, video sequences, etc.) could be represented by three groups which comprise the corresponding matrices [R р ], [G р ], [B р ], for р=1,2,3,... The source, which could be with fixed, or time-changing spatial position, defines the mutual correlation between the images in the groups and is much higher in the first case. The objective of this work is to propose new approach for image groups decorrelation both in time- and color domains. The main idea here is to apply sequentially two PCA-based transforms: 1) the Adaptive Color PCA (AС-PCA) for the RGB components of each image in the processed group, and 2) the Hierarchical АPCA (HА-PCA) for each group of principal color components (eigen images), got after the Prof. D. Sc. PhD. R. K. Kountchev is with the Technical University of Sofia, Department of Radio Communications and Video Technologies, Bul. Kl. Ohridsky 8, Sofia 1000, Bulgaria (corresponding author, phone: +899924284) e-mail: rkountch@ tu-sofia.bg). Dr. R. A. Kountcheva is with TK Engineering, Sofia, Bulgaria (e-mail: kountcheva_r@yahoo.com). execution of AС-PCA. Algorithms AС-PCA and HА-PCA are presented in detail in earlier publications of the authors and here is investigated their combined impact. The choice of these two algorithms for decorrelation of the three groups of RGB components in the color and time domains is determined by their lower computational complexity compared to iterative PCA algorithms, retaining their most important properties (minimum mean square error of the restored images got after the reduction of their information redundancy, and maximum energy concentration in the first decomposition components). II. RELATED WORKS Various orthogonal transforms for image decorrelation in the pixel space are already investigated and used in practice: the Рrincipal Сomponent Аnalysis (PCA) or Karhunen-Loeve Transform (KLT) [1-6], and the related Independent Component Analysis (ICA) [7,8] and the Singular Value Decomposition (SVD) [9,10]. The image representation through ICA in whitened space is obtained by left multiplication with the matrix square root of the inverse covariance matrix [7]. There are also transforms used for processing of multi-channel images, based on the quaternion DFT [11], the KLT in the time domain [1], and the Hierarchical KLT (HKLT) [12] - in the spectrum domain. In [13] the algorithm ICA is used for feature extraction from color and stereo images. The approach for processing of groups of correlated images in their color and spatial domains, presented here, corresponds to some degree to the method offered in [13], but instead of processing one stereo couple only, it is developed for processing a sequence (group) of 2 n color images. Besides, for the processing are used new PCA-based algorithms with low computational complexity. The paper comprises the following sections: Section 3: Adaptive Color PCA algorithm for decorrelation of the color image components; Section 4: Algorithm АPCA for decorrelation of a couple of images; Section 5: Hierarchical Adaptive PCA (HA-PCA) for decorrelation of a group of 2 n images; Section 6: Evaluation of the decorrelation got after the HA-PCA execution; Section 7: Decorrelation of a group of color images through double transform: AC-PCA and HA- PCA; Section 8: Evaluation of the decorrelation efficiency; Section 9: Conclusions. Processing of Correlated Images through Double PCA-based Transform in Color and Time Domains Roumen Kountchev and Roumiana Kountcheva INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTERS IN SIMULATION Volume 11, 2017 ISSN: 1998-0159 135