Research Of Image Denoising Based On Curvelet Transform And Partial Differential Equation

Image denoising is one of the most basic subject of the image processing. In the process of image acquisition and transmission, by virtue of the interior and exterior of the image systems suffer from various of interfering signal, which leading to noise pollution of different degree. Image denoising is the form that extracting the useful information and eliminating the noise from an image to obtain the visual effect of original image. Image denoising is the foundation and the critical step of the subsequent image processing, it plays an significant role in the image processing. At present image denoising is applied to a mount of scientific and technological fields such as:astronomy, economy field, medical image, military reconnaissance, law, computer vision, optical remote sensing, the technologies of aeronautics and astronautics, meteorology cloud image analysis, material science, arts field, videos and multimedia image processing and so on.Curvelet transform and partial differential equations are both effective image denoising methods. People have done lots of research on them in the past two decades and obtain many achievements. Curvelet transform has good approximated performance of the curve characteristics for an image, partial differential equations have superior described abilities of image and perfect features of edge protection. Due to their good properties are applied to all branches of image processing.In the paper, we study the image denoising theories based on curvelet transform and partial differential equations and analysis their advantages and disadvantages firstly. Because there are local linear correlations of the curvelet transform, some surrounding effects named scratches occurring when eliminating noise. Curvelet transform is a perfect tool for image denoising. For using the total variation to perform denoising, it can obtain strong filtering result only by a few iterations when there is small noise. For big noise, in order to obtain the optimal peak signal to noise ratio, with the increasing of iterations and the smoothing strength, the edges of image is becoming blurring, at the same time, it brings large computational redundancy. There are some "block" effects of denoised image inevitably due to second-order partial differential equations process image by dividing it into many parts. Consequently, a new hybrid denoising method is proposed combining curvelet based method and TV method based on analysis the two algorithms deeply. Perform curvelet transform to image (we use Unequally-space Fast Fourier Transform method to implement it in this paper), then perform further TV filtering to do second denoising processing. The experiment results show that the new algorithm can restrain the surrounding effect just only by a few iterations effectively. it improves the curvelet method to great degree. The hybrid method needing less time than TV method is another advantages.