﻿ 基于双密度双树复小波变换的图像压缩 Image Compression Based on Dual Density Dual Tree Complex Wavelet Transform

Journal of Image and Signal Processing
Vol. 08  No. 01 ( 2019 ), Article ID: 28107 , 6 pages
10.12677/JISP.2019.81002

Image Compression Based on Dual Density Dual Tree Complex Wavelet Transform

Wanshe Li, Ruizhi Zhu

School of Mathematics and Information Science, Shaanxi Normal University, Xi’an Shaanxi

Received: Nov. 27th, 2018; accepted: Dec. 13th, 2018; published: Dec. 20th, 2018

ABSTRACT

With the rapid development of multimedia information technology, the extremely large image data is produced. When these massive image data are stored and transmitted, it is necessary to use image compression coding technology to reduce the amount of data. The purpose of this study is to find a method of a better quality of compressed image. The paper is based on the theory of wavelet transform and image compression, and an image compression method based on dual-density dual-tree complex wavelet transform is proposed. According to MATLAB simulation, experimental results are given. Finally, it is confirmed that this method has obvious optimization compared with the traditional image compression method for image compression quality.

Keywords:Wavelet Transform, Image Compression, Double-Density Dual-Tree Complex Wavelet Transform

1. 引言

2. 双密度双树复小波变换

2.1. 双树复小波变换

$\psi \left(t\right)={\psi }_{h}\left(t\right)+j{\psi }_{g}\left(t\right)$ (2-1)

${\psi }_{h}\left(t\right)\approx H\left\{{\psi }_{g}\left(t\right)\right\}$ (2-2)

$\psi \left(x,y\right)=\psi \left(x\right)\psi \left(y\right)$ ，由(2-1)代入可得

$\begin{array}{c}\psi \left(x,y\right)=\left[\left({\psi }_{h}\left(x\right)+j{\psi }_{g}\left(x\right)\right)\right]\left[\left({\psi }_{h}\left(y\right)+j{\psi }_{g}\left(y\right)\right)\right]\\ ={\psi }_{h}\left(x\right){\psi }_{h}\left(y\right)-{\psi }_{g}\left(x\right){\psi }_{g}\left(y\right)+j\left[{\psi }_{g}\left(x\right){\psi }_{h}\left(y\right)+{\psi }_{h}\left(x\right){\psi }_{g}\left(y\right)\right]\end{array}$

2.2. 双密度小波变换

$\left\{\begin{array}{l}\phi \left(t\right)=\sqrt{2}\underset{n}{\sum }{h}_{0}\left(n\right)\phi \left(2t-n\right)\\ {\psi }_{1}\left(t\right)=\sqrt{2}\underset{n}{\sum }{h}_{1}\left(n\right)\phi \left(2t-n\right)\\ {\psi }_{2}\left(t\right)=\sqrt{2}\underset{n}{\sum }{h}_{2}\left(n\right)\phi \left(2t-n\right)\end{array}$ (2-3)

2.3. 双密度双树复小波变换的获取

$\left\{\begin{array}{c}{\psi }_{h,1}\left(t\right)={\psi }_{h,2}\left(t-0.5\right)\\ {\psi }_{g,1}\left(t\right)={\psi }_{g,2}\left(t-0.5\right)\end{array}$ (2-4)

$\left\{\begin{array}{c}{\psi }_{g,1}\left(t\right)=H\left({\psi }_{h,1}\left(t\right)\right)\\ {\psi }_{g,2}\left(t\right)=H\left({\psi }_{h,2}\left(t\right)\right)\end{array}$ (2-5)

$\varphi \left(t\right)={\varphi }_{h}\left(t\right)+j{\varphi }_{g}\left(t\right)$ (2-6)

$\left\{\begin{array}{c}{\psi }_{1}\left(t\right)={\psi }_{h,1}\left(t\right)+j{\psi }_{g,1}\left(t\right)\\ {\psi }_{2}\left(t\right)={\psi }_{h,2}\left(t\right)+j{\psi }_{g,2}\left(t\right)\end{array}$ (2-7)

3. 基于双密度双树复小波变换的图像压缩

3.1. 图像质量评价标准

$\text{PSNR}=10\mathrm{log}\left(\frac{{255}^{2}}{MSE}\right)$ (3-1)

$MSE=\frac{1}{w×h}\underset{i=0}{\overset{w-1}{\sum }}\underset{i=0}{\overset{h-1}{\sum }}{\left(a\left[i\right]\left[j\right]-b\left[i\right]\left[j\right]\right)}^{2}$ (3-2)

3.2. 实验结果比较和分析

Figure 1. PSNR value comparison diagram of the two compression methods

Figure 2. Compression Lena graph based on dual density dual tree complex wavelet transform

Figure 3. JPEG standard compressed Lena

4. 总结

Image Compression Based on Dual Density Dual Tree Complex Wavelet Transform[J]. 图像与信号处理, 2019, 08(01): 9-14. https://doi.org/10.12677/JISP.2019.81002

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