Multiscale Geometric Analysis's Application To Image Denosing, Image Enhancement And Image Fusion

Image sparse representation is the basic problem in image processing, multiscalegeometric analysis (MGA) is a new branch of image sparse representation, it provides aneffective way for sparsely representing geometrical structure information in image. Thispaper focuses on researching contourlet transform and its application to image processing.Based on introduction of construction of contourlet transform and implementation offilter bank, firstly this paper analyses statistical character of contourlet coefficients intheory and experiment aspects, such as marginal statistics, joint statistics and hiddenmarkov tree model. Then it does some research on image denoising, feature enhancement,resolution enhancement and image fusion using contourlet transform.The primary contributions of this paper contain the following points:1) Research the theory of image denoising by threshold based on contourlettransform, propose a new image denoising algorithm called successive scanshrinkage using the statistical model of contourlet and the quad-tree structure ofcontourlet coefficients. This algorithm exploits the distribution differencesbetween noise coefficients and image coefficients in contourlet transformdomain, it can effectively filter noise and keep the edges and textures of theimage. After a lot of experiments and comparative analysis, we prove theeffectivity of contourlet transform.2) Research the image feature enhancement algorithm based on contourlettransform, the algorithm of fuzzy image feature enhancement is designed basedon the generalized fuzzy set. The result shows it can enhance some edge detailof image, greatly enhance the contrast radio of image.3) To solve single image super-resolution problem, this paper utilizes the ability ofsparsely representing curve singularity and spatial directional tree structure ofcontourlet coefficients, researches and fulfills a algorithm of image resolutionenhancement based on learning coefficients. Knowing the correlation ofadjacent domains, we propose an improved rapid learning algorithm. Theexperiment proves that this algorithm can achieve a better balance betweenspeed and quality of reconstruction image.4) Research the multi-focus image fusion algorithm based on contourlet transform, knowing the multi-scale and multi-direction decomposition character ofcontourlet transform, we design different fusion rules based on feature andregional energy towards different directional subbands. Finally we give a newimage fusion algorithm in contourlet domain. The experiment shows that thisalgorithm performs better than the multi-focus image fusion algorithm inwavelet domain.