Study On Selection And Design Of Local Cosine Bases

The Discrete Cosine Transform (DCT) is adopted in the standard of JEPG. The Discrete Cosine Transform has rapid arithmetic and the transformed coefficients are mostly concentrated in the lower frequency region. According to these advantages, DCT has been widely applied in image and voice processing. However, the data processed for DCT need to divide into some small segments, which will cause"mosaic effect"or"block effect". In order to eliminate the"block effect", the concept of the Local Cosine Transform (LCT) was proposed by Coifman and Meyer in early 1990s.Firstly, the construction theory of local cosine bases is introduced in detail in this paper. We also deduce the condition that an orthogonal bell function must satisfy, and popose two kinds of bell functions which can be commonly used. An improved orthogonal bell function is proposed according to Coifman and Meyer theory. Comparing the compression performance of the improved orthogonal bell function with the Donoho's bell function, the experimental results show that the more transformation coefficients via the improved orthogonal bell function are concentrated in the lower frequency region, which can achieve more coding gain. For some lower compression distortion applications, the improved orthogonal bell function is better than the Donoho's orthogonal bell function.The construction method of biorthogonal local cosine bases is also discussed in this paper. This biorthogonal local cosine bases can overcome the disadvantages of the general local cosine bases. Since the biorthogonal local cosine bases have more freedom in the design of bell function. We can design a biorthogonal bases which ensure either satisfy the condition or the first coefficient via local cosine transform is the DC component of the signal. Some examples regarding biorthogonal local cosine bases are presented in the paper. Finally, the energy concentrate degree of the Bittner's bell funcyion is compared with the Donho's bell function.