Abstract
Abstract. In this paper, a 2-circular matrix theory is developed, anda concept of spectral radius for biorthogonal wavelet is introduced. Wepropose a novel design method by minimizing the spectral radius and ob-tain a wavelet which has better performance than the famous 9-7 waveletin terms of image compression coding. 1. IntroductionOver the last two decades, wavelets have become a fundamental tool in manyareas of applied mathematics and engineering ranging from signal and imageprocessing to numerical analysis. In her celebrated paper [2], Daubechies in-troduced a general method to construct compactly supported wavelets. It iswell known that 2-band orthogonal wavelet suffers from severe constraint con-ditions. For instance, nontrivial symmetric 2-band orthogonal wavelet doesnot exist except the Haar wavelet [3]. Biorthogonal wavelet enjoy two im-portant properties of linear phase and higher vanishing moments, was studied[4, 8, 11, 12]. Vetterli and Herley studied theory and design for biorthogonalwavelet [9] and Cohen gave another biorthogonal wavelet family [6]. GuoqiuWang constructed wavelet filters with free paraments based on 2-circular ma-trix method [1]. Even though the research on biorthogonal wavelet is relativelymature, further study is still valuable.Let (ψ, ψe) be a pair of dual wavelet functions,(1.1) ψ
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