The Study Of Image De-noising In Contourlet Domain Based On PCA

The traditional wavelet transform provides a multi-resolution expansion for signals. Due to the ability of providing local time-frequency information in the wavelet domain at the same time, it is applied to many research areas. But since the separable wavelet cannot optimally express the one-dimensional singularity in image signals, a lot of directional multi-resolution algorithms have been developed in recent years, such as Ridgelet, Curvelet, Wedgelet, Bandelet, and Contourlet, which are generally called Xlet. The purpose is to look for the good basis function that can optimally express the edge characters of images. All these algorithms are established on wavelet theory. Therefore, we can consider them as the up-to-date development of wavelet technology. Among them, Contourlet performs better in the field of image processing.Contourlet transform is a kind of wavelet that combines multi-resolution analysis and directional filtering. Besides its characters of multi-resolution and time-frequency locality, it also possesses some other characters like directional and anisotropy. Therefore, Contourlet can efficiently capture the contours of natural images and carry out sparse expansion. The coefficients can have better clustering in a certain direction and we fully exploit it for our de-noising algorithm.Image de-noising is a widely used technology in the field of image processing. The main purpose is to increase the Signal Noise Ratio and maintain the texture and details of images. As a result, wavelet theory obtains a wide recognition because of its advantage in estimation of noise variance and the performance of de-noising results. However, the traditional wavelet can just distinguish the information in three directions without posting the clustering of coefficients. Therefore, it restrains the de-noising effect.This paper proposes an improved scheme basing on the traditional threshold de-noising method, which not only increases the Signal Noise Ratio, but also significantly improve the visual effect of images. The characters are as follows:(1) This method utilizes noise energy, instead of its variance, to perform image de-noising based on PCA in Contourlet domain.(2) There is no need to estimate the noise variance in this algorithm, which makes it more applicable. Most of current wavelet de-noising methods are based on the estimation of noise variance. But in the Contourlet transform, it is difficult to precisely estimate the noise variance through establishing math models for the coefficients distribution is not Gaussian.Basing on this, we also acquire better visual effect and PSNR when using it in the process of nonsubsampled Contourlet transform and modifying energy estimation.