The Algorithm Research Of Image De-noising Based On Wavelet Transform

There is much noise in image. In order to further image analysis and communication, the noise needs to be reduced in image pre-processing. Recently,The theory of wavelet analysis achieves attention all over the world. It is also a pop-researching field internationally and arouses extensive attention and upstairs recognition in science and technology field. The development of wavelet analysis forces the development of many other studies and fields. Depending on its well de-noising capability and unique advantage, the wavelet theory gains extensive attention in signal de-noising and image de-noising. This paper mainly research on the application of the theory of wavelet in image de-noising, the main content is as follows:(1)The second chapter is the preparation.We introduce the basic theory of wavelet transform, wavelet transform of image and stationary wavelet transform.(2)In the third chapter, we introduces the theory and methods of wavelet de-noising. Including rationale and methods of wavelet de-noising and wavelet thresholding. We mainly study on the method of wavelet thresholding de-noising which advanced by Donoho. At the same time , we show several wavelet thresholding functions that usually used, we also give the method of threshold estimation, the influences of the selection of wavelet bases working on the de-noising results and the evaluatable criterion of the de-noising results.(3)In the forth chapter, we research on the dependencies between wavelet coefficients each other. We put forward a method of image de-noising based on intra-inter scale dependencies among wavelet coefficients. Wavelet transform has the property of de-correlation which makes wavelet transform of image can achieve relatively few wavelet coefficients. Just because of this, wavelet transform has being widely used in image compression and image de-noising. But wavelet coefficents also have relation between each other. In general, the dependencies can be sorted to two species : intra-scale dependencies and inter-scale dependencies. Soft thresholding and hard thresholding are two of the traditional wavelet de-noising methods, which only consider the wavelet coefficient currently disposed, and didn't consider the dependencies between them, so they have limitations. In reference[21], they advanced a de-noising method of Contex-Based, which only consider the intra-scale dependencies but ignore the inter-scale dependencies. We give a new thresholding function based on intra-inter scale dependencies between wavelet coefficients. In numerical experiment, we used 8 bit standard test images of Lena, Barbara and Goldhill, which are model representatives of smooth images, textural images and edged images separately, so they can show the adaptness of the method we have proposed to some extent. At the same time, we adopt Daubechies4, biorthogonal Daubechies 9/7 and Daubechies 8 scalar wavelets in image de-noising. Experimental results indicates the effectiveness of our method.(4)In the fifth chapter, we study on the Higher Order Statistics (HOS), and further we give a method combining HOS filtering with wavelet thresholding de-nosing method. HOS not only can distinguish minimum phase systerm, but also can distinguish non-minimum phase systerm, simultaneously, we adopt the third-order cumulant to describe the details of images, because the third-order cumulant is non-sensitive to Gaussian noise. Considering a digital image f (i ,j){i = 0,1....M?1;j=0,1....N?1}, for each pixel (i ,j), there are eight pixel around it, we can decompose them to four small windows according to 45°and 135°orientation. Then we calculate the third-order cumulants in each small window separately and choose the window which has the smallest one(that is the image has the least details in this place). In this window, we take the mean value of the four pixel as the value of (i ,j). Thus, we can find places which have the least details to smooth, preserving details of images preferably. We adopt stationary wavelet transform, which can conquer the deficiency othorganal wavelet transform possesses and eliminate Gibbs-like effects. In numerical experiment, we used 8 bit standard test images of Lena, Barbara and Goldhill with the size of 512×512, and we adopt Daubechies4 scalar wavelets in image de-noising. Experimental results show that our method deals well with both preserving edge details and smoothing, and yields better visual quality and PSNR gains.In the aspect of image de-noising, the wavelet theory arouses many researchers'attention by its proper character. With the research going deeply, many new methods appear continually. To thresholding method, there are many improving method and new method appearing. There are also many problems which need to be researched and discussed, such as the threshold adoption, the estimation of wavelet coefficient and the adoption of wavelet group, and so on. In addition, Donoho advanced a method to estimate noise variance. But it doesn't consider prior information of images, so it is still necessary to discuss and research. Up to date, applying wavelet to de-noising has many regions to perfect, this is also one important researching area.Although wavelet de-noising method has already be significant branch and primary research aspect in de-noising and image resumption, it is not enough to research de-noising method under non-Gaussian distribution. Now many researchers pay more attention to this field. Non-Gaussian noise distributive model and how to expand the wavelet de-noising method reducing Gauss noise to reducing non-Gaussian noise, these are all worth to discuss and research.Now the achievement of wavelet de-noising methods not only widen the application field using the wavelet de-noising, but also force the development of these fields. At the same time, all new problems, which are feed back during the application, will enrich the wavelet de-noising content and force the development of wavelet de-noising.