In this work is presented one new method and algorithm for block two-dimensional (2D) Karhunen-Loeve transform of grayscale images, based on transform matrices of size 2×2. In correspondence with the method, the couples of neighbor elements for each block of size 2n×2n are transformed and rearranged n times: first in horizontal, and after that - in vertical direction. In result is obtained full decorrelation of the transformed block elements. Here is also offered an algorithm for parallel and recursive calculation of the transform and its computational complexity is compared to that of the separable 2D Karhunen-Loeve transform for a block of same size. The evaluation of the basic characteristics of the new method outlines its advantages in respect to the well-known 2D Karhunen-Loeve transform, applied for grayscale images.
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