Hierarchical principal component analysis-based transformation of multispectral images

In this paper we present a new approach for the transformation of multispectral (MS) images based on the principal component analysis (PCA). The objective is to obtain high decorrelation of the MS image set as well as predictability of the power distribution at the end of the transform. The typical PCA depends on the vector size i.e., for N image vectors we need N × N covariance matrix after which should be solved a system of N equations, which is computationally intensive. This algorithm however uses transform matrices of size 2 × 2 or 3 × 3 for each sub–group of images. The algorithm is designed to allow parallel processing of each image sub–group in the set, which significantly enhances the performance. The algorithm is not limited by the size of the image sets so it can transform multi– and hyper–spectral images. In the same time it is reversible and gives good quality of the restored images.

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