Research On Image Denoising Based On The Fractional Wavelet Transform

In the process of the image capture and image transmission, noise wi11be produced unavoidably.The existence of image noise severely affects the effect of subsequent image processing. To enhancethe image quality, image denoising becomes a very important work of image preprocessing. Now, as anew time-frequency analysis method, wavelet transform(WT) has important significance in the actualapplication. Combined with WT and fractional theory, fractional wavelet transform(FWT) extendsmultiresolution analysis to the time domain-general frequency domain. Its theory and its applicationin image denoising is of great worth.In this paper, research on2-D FWT and its applications in image denosing is made. The mainresearch works can be summarized as follows:(1) The recent research situation of FWT is analyzed. The definitions of1-D and2-D FWT aresummarized. Besides, based on2-D WT and2-D fractional Fourier transform(FRFT), the method torealize2-D FWT discrete algorithm is given.(2) A new method for filtering the single and known noise in the fractional time-frequency domainis proposed in this paper. The2-D FWT theory is applied to image denoising, and compares with imagedenoising method based on2-D WT and2-D FRFT. Image denoising simulation studies have shownthat, this method can separate the image from noise as possible as it can in fractional wavelet domain,and preserve detail information effectively and reduce the noise at the same time.(3) In view of the unknown image noise in actual application environment, new objectiveevaluation standards for image denoising in fractional wavelet domain are defined, and based on noiseestimation a method to estimate the value of optimal fractional order is put forward. The results ofexperiment show that, the optimal order can be selected reasonably, and the unknown image noise canbe filtered effectively in the estimated optimal2-D fractional wavelet domain.(4) Combining the2-D FWT with median filtering, employing impulse noise detection andresidual noise estimation, a new image filtering method for filtering mixed and unknown noise isproposed in this paper. The results of experiment show that, this method gives consideration to goodproperties of median filtering removing the impulse noise and good abilities of2-D FWT removing thegaussian white noise with threshold denoising method. And it improves image visual effect in a certainextent.