Theory of regular M-band wavelet bases

Abstract

Orthonormal M-band wavelet bases have been constructed and applied by several authors. This paper makes three main contributions. First, it generalizes the minimal length Kregular 2-band wavelets of Daubechies to the M-band case by deriving explicit formulas for K-regular M-band scaling filters. Several equivalent characterizations of K-regularity are given and their significance explained. Second, two approaches to the construction of the (M-I) wavelet filters and associated wavelet bases are described; one relies on a state-space characterization with a novel technique to obtain the unitary wavelet filters; the other uses a factorization approach. Third, this paper gives a set of necessary and sufficient condition on the M-band scaling filter for it to generate an orthonormal wavelet basis. The conditions are very similar to those obtained by Cohen and Lawton for 2-band wavelets.

Symmetric tight frame wavelets with dilation factor M=4

“…Lowpass filter design based on Taylor series has been considered in [39] and later in [25]. The proposed method is also closely related to the complex orthogonal symmetric wavelet design method given recently by Han [40].…”

A Study of Ultrasonic Liver Images Classification With Artificial Neural Networks Based on Fractal Geometry and Multiresolution Analysis

“…To achieve M-band discrete wavelet transform, the explicit forms of <f> (t) and tp,(t) are not required but only depend on h 0 (k) and h,(k), which must meet several conditions [36][37][38][39][40][41][42][43][44][45]. Hence, an M-band wavelet basis can be completely specified by the choice of the scaling filter (i.e.…”

“…The most Multiresolution analysis in the 2-band case is popular measure is box counting [29][30][31][32][33]. Among the referenced in [36][37][38][39][40][41][42][43][44][45]: varieties of box-counting approaches, the Differential Using M-band wavelets [38], [40], [42][43][44][45], the Box Counting (DBC) method [29] that has a large general multiresolution analysis provides a more dynamic range and computational efficiency is adopted flexible tiling of the time-scale plane than that resulting herein. Hence, is calculated as follows [24][25], [29-from the two-band multiresolution analysis, which …”

“…with h 0 (k) denoting scaling filter and satisfying certain constraints [40], [42], [44]. 0,(t), /=1,2,... ,M-1, are called wavelet functions that satisfy the wavelet equations:…”

Characterization of regular linear-phase paraunitary filter banks using dyadic-based structures

“…. , K − 1 [3,4]. Regular filter banks are desirable to many applications such as signal interpolation and data compression [2, [5][6][7][8].…”