Spectral Radius of Biorthogonal Wavelets With Its Application

Abstract

Abstract. In this paper, a 2-circular matrix theory is developed, and a concept of spectral radius for biorthogonal wavelet is introduced. We propose a novel design method by minimizing the spectral radius and obtain a wavelet which has better performance than the famous 9-7 wavelet in terms of image compression coding.

Optimal model for 4-band biorthogonal wavelets bases for fast calculation

“…A so-called 4-circular matrix [8], which is generated by the filters h , , , , is denoted as . For , is as follows: …”

“…As a generalization of orthogonal wavelets, the biorthogonal wavelets have become a fundamental tool in many areas of applied mathematics, from signal processing to numerical analysis [1–8]. It is well known that 2-band orthogonal wavelets, suffering from severe constraint conditions, such as nontrivial symmetric 2-band orthogonal wavelets, do not exist [9].…”