Coshar transform

Abstract

This paper defines and develops a new transform called the COSHAR. The wide utility of the discrete cosine transform (DCT) is primarily due to its near-optimal performance. A transform which possesses both global and local characteristics is the Haar transform (HT), and the governing factor in its wide-range successful application has been its ease of implementation. The newly defined transform compromises between the DCT and HT in terms of implementation, properties, and applications. It results, as a hybrid version, from the Kronecker product of the DCT and HT. Fast algorithms for efficient implementation of the COSHAR transform and its inverses, based on sparse-matrix factorization, are developed. The performance of the COSHAR transform is investigated in terms of some standard quantitative performance measures such as variance distribution, Wiener filtering, decorrelation property, and transform image coding.