Study On Image Sparse Representation Based On Combined Transforms And Its Application

Experts and scholars have been dedicating to seeking a sparse representation of objective things, in the fields of computer vision, mathematics, data compression, and so on. The validity of image sparse representation, refers to the ability of capturing important information with less mathematical description—the capacity of image sparse representation. Image sparse representation is hot research spot in the field of image processing in recent years. For practical applications, the image sparse representation must be implemented through structural transforms and fast algorithm. Therefore, it plays an important theoretical significance in promotion of the next generation of image processing applications, that effective image sparse representation can obtain efficient non-linear approximation.Firstly, this paper begins with the description of the terms of the image effective representation, the significance of sparse approximation, features of multi-scale geometric analysis, analysis and comparison the non-linear approximation representation of ridgelet transform and curvelet transform, summarizing approximation nature of the multi-scale geometric transformation method and the problems and further research directions.Aiming at the problems of image sparse representation for the linear singular characteristics based on the two-dimensional wavelet transform, for example, the edges of image, a new directional adaptive red-black wavelet transform is proposed. The lifting process of the traditional red-black wavelet transform considers the predicted point have the same relevance with the four points around, so using a four-point neighborhood to predict. In fact, the predicted point should have the different relevance with the neighborhood four points, in particular, for the localized linear singularity. For the localized straight or curved linear singularity, the predicted point should have a stronger correlation with three points of the four. So we can use these three points to achieve the lifting process. Therefore, we can use fully the direction of local relevance to select adaptively three or four points, which makes the image representation of edges part and the texture structure sparser. The experiment results show that the proposed algorithm can improve the image visual quality and the validity of the image sparse representation.Combined transform for image sparse representation can be implemented in the cascade form of several transforms. The theory of combined transform image sparse representation theory has been studied in this paper. A new combined image sparse representation method is presented, combined wavelet transform and curvelet transform for image representation. This method makes use of image morphological component analysis method, the image is separated into two different types of image components, respectively, carried out using wavelet transform and curvelet transform. This method takes full use of the advantages of both transforms in image denoising applications and get a better quality of denoising image.