Construction of Biorthogonal Multiwavelets Using the Lifting Scheme

Abstract

Abstract-The lifting scheme has been found to be a flexible method for constructing scalar wavelets with desirable properties. Here it is extended to the construction of multiwavelets. It is shown that any set of compactly supported biorthogonal multiwavelets can be obtained from the Lazy matrix filters with a finite number of lifting steps. As an illustration of the general theory, compactly supported biorthogonal multiwavelets with optimum time-frequency resolution are constructed. In addition, experimental results of applying these multiwavelets to image compression are presented.

Nonnegative Scaling Vectors on the Interval

“…The construction of scaling vectors on the interval has been addressed in [1][2][3]. In these cases, the authors constructed scaling vectors on the interval from scratch.…”

“…Scaling vectors for the interval have been constructed in [1][2][3]. The approach here is different in that the we start with an existing scaling vector Φ that generates a multi-resolution analysis for L 2 (R) to create a scaling vector for the interval.…”

On interpolatory divergence-free wavelets

“…in [11,18]. In [2,19,20], the lifting scheme has been applied for biorthogonal multiwavelets generated from Hermite splines also yielding wavelets with arbitrary order of vanishing moments.…”

An Efficient and Effective Wavelet Transform Methods for OCT, SD-OCT and Secondary Image Compression

“…The objective of image compression is to reduce the redundancy of the image and to store or transmit data in an efficient form. Image processing usually refers to digital image processing, but optical and analog image processing also are possible [1]. Image processing is a rapidly growing area of computer science.…”