Sliding Recursive Hierarchical Adaptive PCA for 3D image processing

Principal Components Analysis (PCA) is the basic approach for processing of 3D tensor images (for example, multi- and hyper-spectral, multi-view, computer tomography, video, etc.). As a result of their processing, the information redundancy is significantly reduced. This is of high importance for their efficient compression and for the reduction of the features space needed, when object recognition is performed. The basic obstacle for the wide application of PCA, is the high computational complexity. One of the approaches, used to overcome the problem, is to use algorithms, based on the recursive PCA. The well-known methods for recursive PCA are aimed at the processing of sequences of images, represented as non-overlapping groups of vectors. In the last several years, the interest towards the recursive PCA for 3D tensor images executed in sliding temporal window, was significantly increased. Such analysis is needed, for example for the convolution tensor decomposition in multi-layer neural networks, in the systems for 3D noise filtration, video compression, etc. In this work is proposed new method, called Sliding Recursive Hierarchical Adaptive PCA (SR-HAPCA), based on the HAPCA algorithm. The method SR-HAPCA retains all advantages of HAPCA towards the PCA: it decreases the number of calculations needed, and permits parallel implementation. Besides, the lower computational complexity of SR-HAPCA makes easier its application in real-time processing of 3D tensor images.