Wavelet Analysis: Three or two-D discrete wavelet transform

Four or two-D discrete wavelet transform

Statement: This article is my understanding of the wavelet, not guarantee correctness and rigor.

Reference: "Digital Image processing" Gonzalez P317

1. Overview

A two-dimensional scale function and three two-dimensional wavelet functions can be combined with a given scale function and a wavelet function:

The f (x, Y) discrete function can be decomposed into a linear combination of the different scales and positions of these four functions (2DIDWT):

The approximate coefficients and the detail coefficients are as follows (2DDWT):

2. Description of other symbols

scale functions and wavelet functions of different scales and positions, respectively, are defined as follows:

3. Understanding

The higher the order of detail, the smaller the scale, the more meticulous it is, the equivalent of the high-frequency part of Fourier.

Generally do two-dimensional wavelet transform, are directly drawn into a multi-scale WDT graph analysis, the outermost layer is the highest order of detail, that is, the smallest detail of the scale, is the most detailed.

The higher the order of the detail part, the higher the frequency. Examples of applications are shown in p320 of reference books, examples 7.12 and 7.13.

Wavelet Analysis: Three or two-D discrete wavelet transform