PCA-based Adaptive Hierarchical Transform for correlated image groups

In this work one new algorithm is proposed, for Adaptive Hierarchical Transform (AHT) of groups (sequences) of correlated images, based on the famous method Principal Component Analysis (PCA). The groups of correlated images exist in many practical cases. These are, for example, the components (spectrum bands) of the multispectral images, the sequences of the computer tomography images, video sequences from surveillance TV cameras with fixed spatial position, video information from TV microscopes, etc. The new Hierarchical Transform is reversible. It results in high decorrelation of the processed groups of images and ensures high power concentration in the former in the group, called “eigen”. The decorrelation, achieved through the AHT is close in efficiency to the “classic” PCA, but has lower computational complexity. Besides, the structure of the AHT algorithm is extremely suitable for parallel processing. In the paper are also given some experimental results for the algorithm modeling, applied on sequences of CT images. The computational complexity of the AHT algorithm is compared with this of the classic PCA.