Image Compression Via Orthogonal Space Decomposition

In this paper, an algorithm is devised to construct a set of M orthogonal bases along which images can be optimally decomposed. It is shown that these bases are closely related to the roots of an M order forward linear prediction polynomial, satisfying the system. Image compression is achieved through keeping only the coefficients of the linear prediction polynomials, as well as the weights of the decomposing bases, that optimally represent each block of the image. Alternatively, one can keep the bases and weights of the singular vectors of the dominant singular values of the image´s singular value decomposition. These bases and weights are subsequently used in image reconstruction. Computer simulations have shown that, due to the orthogonality features of the proposed algorithm, the weights of the decomposing bases are less sensitive to finite word length effects. This feature suggests further compression by applying schemes like EZW or SPIHT coders to the coefficients of the decomposing bases. Simulation results have revealed that the proposed compression scheme, competes very well with compression schemes like JPEG or SPIHT coders. In fact, over a wide range of bit rate reduction, the proposed algorithm is more superior than the JPEG or SPIHT coder compression scheme