Hadamard-based image decomposition and compression

We develop a general algorithm for decomposition and compression of grayscale images. The decomposition can be expressed as a functional relation between the original image and the Hadamard waveforms. The dynamic adaptive clustering procedure incorporates potential functions as a similarity measure for clustering as well as a reclustering phase. The latter is a multi-iteration, convergent procedure which divides the inputs into nonoverlapping clusters. These two techniques allow us to efficiently store and transmit a class of half-tone medical images such as magnetic resonance imaging (MRI) of the human brain. Due to the redundant image structure of MRI, obtained after the decomposition and clustering, almost half of the image can be omitted all together. Naturally, the compression rates for this specific type of grayscale image are increased greatly. A run-length coding is performed in order to compress further the retained information from the first two steps. Although all the techniques applied are simple, they represent an efficient way to compress grayscale images. The algorithm exhibits a performance which is competitive and often outperforming some of the methods reported in the literature.