平稳小波变换在红外图像去噪增强中的应用

Infrared Image Enhancement by Denoising Using Stationary Wavelet Transform* Wu Panlong, Zhang Ke, Li Yanjun (College of Astronautics, Northwentern Polytechnical University, Xi’an 710072) Abstract: In the infrared image guidance system, the main factor that affects the guidance accuracy is the noise during the image processing. Therefore, how to eliminate the noise effectively becomes very important to guarantee the guidance accuracy. Traditionally, as wavelets have preferable time-frequency resolving characteristics, they are applied to the denoising of image and better results are obtained. In this paper, a new kind of infrared image threshold denoising method based on discrete stationary wavelet transform (SWT) is presented. That is after making SWT to an infrared image, an adaptive soft threshold denoising is done in the high frequency subbands of each decomposition level respectively. The denoising results show that it has a superior performance than conventional discrete wavelet transform. Key words: stationary wavelet transform, infrared images, threshold de-noising I. INTRODUCTION With the development of infrared detector technology, infrared imaging system tends to become mature and be used in many fields, such as in guidance system. It is a key problem for the guidance system to determine the target accurately and quickly. The main factor affects its accuracy is the noise inherent in the imaging procedure. It is a hotspot to establish a new method to reduce the noise while keep the detail information of the infrared image well. Because of the preferable time-frequency resolving characteristics, wavelets are applied to the image processing studies. The orthogonal discrete wavelet transform (DWT) is particularly useful for non-stationary signal analysis, such as noises and transients. So many methods about image denoising are presented in recent years. However, in signal denoising, the DWT is known to create artifacts around the discontinuities of the input signal. These artifacts degrade the performance of the threshold-based denoising algorithm. In this paper, the stationary wavelet is used in the infrared image denoising field for removing the random noises and the results show that stationary wavelet is superior to classic wavelet in such application. II. STATIONARY WAVELET TRANSFORM The orthogonal DWT is formed on the basis of lowpass, highpass filter banks and decimator, we know that the signal length halves after the every calculation due to the function of down sampling. The stationary wavelet transform[1](SWT) is a nonorthogonal wavelet transform., which

can be found by modifying the orthogonal DWT. The basic principals of the SWT are described as follows, during the several level decomposition procedure, the original signal is not decimated when the highpass and lowpass filters are applied to the signal. However, the filters at each level are modified by padding them out with zeros. Each level has the sufficient coefficients to approach the threshold. The wavelet and scale coefficients are of the same length with the original signal. Filters padding with zeros chart is shown in Fig.1.

]1[−rG

* This research is supported the Research Fund for the Doctoral Program of Higher Education, NO:20020699014.

↑2↑2↑2upper sample ]1[−rH

][r

H

][rG

hj gj Fig.1. Filters padding with zeros

_______________________________________________________________________________www.paper.edu.cnConsidering the multi-sampling filter banks, SWT decomposition is shown in Eqns.1. ∑∑∑∑∑∑∑∑

−↑↑−↑↑−↑↑−↑↑−−=−−=−−=−−=122121122121122121122121,,1222111213,,,,1222011212,,,,1222111201,,,,122201120,,)2()2()2()2()2()2()2()2(nnnnjkkjnnnnjkkjnnnnjkkjnnnnjkkj

AknhknhDAknhknhDAknhknhD

AknhknhA

jjjjjjjj

(1)

where jjhh2120↑↑、respectively denote the (12−j) zeros padded between 10hh、

.the

inverse transform of SWT is shown in Eqns.2.

{

}∑∑

∑∑∑∑∑∑∑−−−−+−−−−+−−−−+−−−−==−1221122112211221213,,2211112,,2201111,,221110,,22011030,,1)2()2()2()2()2()2()2()2(41kkkkjkkkkjkkkkjkkkkjinnjDikngikngDikngikngDikngikngAikngikngA

(2)

From the above two equations, we can verify that SWT includes redundant information, and has the translation invariance characteristics. The redundancy of this transform facilitates the identification of salient features in a signal, especially for recognising the noises. III. IMPLEMENTATION OF SWT IN INFRARED IMAGE DENOISING AND RESULTS Donoho and Johnstone [2][4] pioneered the use of thresholding in signal denoising. The