Researches On Directional Image Representations And Denoising Algorithm

Among the present image representations, wavelet transformation has been adopted widely. However, in high dimensions (such as two dimensions), wavelets expose an inherent limitation. It is because wavelets are optimal bases in catching zero-dimension singularities but not for one-dimension or higher dimensions singularities. This disappointing behavior indicates that more powerful directional image representations are necessary in higher dimensions. In recent researches about directional image representations, Ridgelet, Curvelet and Contourlet gradually are accepted for their fixed transforms and flexible directional image expansions.In this dissertaion, firstly the above transformation methods are studied in detail, including theories, construction methods, performances, application fields and so on. During the process of research, this dissertation has developed wavelet base vectors to simplify the computation and has proposed the improved finite ridgelet; Then based on the directional filter bank of Contourlet and All phase digital filters, tow construction methods of the novel all phase directional filter banks (APDFB) are acquired respectively by constructing directional templates or by rotating images and iterating fan filters. Not considering subsample, these two filter banks retain more image details and better direction selectivity. As to the image reconstruction, the original image can be obtained only by adding all directional images and reconstruction filter is unnecessary; Furthermore, an all phase multiscale decomposition method is proposed to substitute the Laplacian pyramid applied in the original Contourlet. To combine it with APDFB, a novel all phase Contourlet discrete transform is accomplished.Finally this dissertaion summarizes all sorts of image denoising methods and provides the results and comparisons of all denoising methods. The conclusion is that improved finite ridgelet transform adapts to denoise images with linear singularitiesand All phase Contourlet has excellent performances in denoising natural images especially those with more details.