The Research Of Wavelet Transform On Image Denoising

The denoising of a natural image is a classic problem in signal processing. Wavelets have been found with wide applications in image denoising due to time-frequency localization and multiscale decomposition property. The success of wavelet is mainly due to the good performance for piecewise smooth function. Unfortunately, such is not the case in two dimension. In essence, wavelets are good at catching zero-dimensional or point singularities, but images which are represented by two-dimensional piecewise smooth signals have one-dimensional singularities. In the image denoising algorithms, it is also a hotspot to overcome the lack of shift invariance of discrete wavelet transform.To overcome the challenging problem, we make deeply study for the methods of Multiscale Geometry Analysis (MGA). A novel image denoising method by incorporating the undecimated wavelets with the ordinary curvelet transform is proposed. The shift invariant property of the undecimated wavelet and the high directional sensitivity of the curvelet transform make the new method a very good choice for image denoising. We apply the digital undecimated curvelet transform to denoise some standard images corrupted with additive white noise. Experimental results show that the new method outperforms VisuShrink, the ordinary curvelet image denoising, and wiener2 filter both in terms of peak signal-to-noise ratio and in visual quality. In particular, our method preserves shape edges better while removing white noise.Translation invariance lies at the heart of many image processing. Because orthogonal ridgelet transform isn't translation invariant, a ridgelet denoising method based on translation invariance is proposed. The experience showed that the proposed approach can remove the visual artifacts, obtaining better visual result and higher PSNR.In addition, we analyze the theories and properties of complex wavelet in detail. The merit of both approximate shift invariance and directional selectivity enables the complex wavelet to overcome the artifacts in the discrete orthogonal wavelet denoising to a certain degree. A novel dual tree complex wavelet denoising algorithm based on translation-invariant theory is introduced to denoise image. Because of the only approximate shift invariant property of dual tree complex wavelet, we apply it to de-noise image that still appears light gibbs artifacts. The new method makes it had full shift invariant property. We compare this method with the translation invariant wavelet method. The experiments show that the new approach can remove the visual artifacts, obtaining better visual result and higher PSNR..