Research On Image Sparse Representation Theory And Its Applications

Image representation is the basic problem in image processing. Efficient representation of image contents lies at the foundation of image processing tasks. Efficiency of a representation refers to the ability to capture significant information of an object of interest in a small description. That is the ability of sparse representation. Recently, image sparse representation has been the hot topic of image representation. The researches of theory models and construction methods of basis based on human visual system, rapid and efficient image sparse representation algorithm will be help to promote the development of image processing. Those researches will provide new theory and method for image representation. It is of great importance in both theory and application.Supported by the National Science Foundation of China, this thesis concentrates on the image sparse representation theories, methods and the image processing applications based on sparse representation. We make deeply study for the applications based on multiscale geometry analysis, theories of overcomplete sparse image representation and its applications, theories of sparse image representation via combined transforms and its applications.Firstly, the definition of image representation, measure of sparsity, and the basic methods of sparse representation are reviewed. And then, we analyze the performance of nonlinear approximation of Ridgelet, Curvelet, Contourlet and Bandelet transform.Ridgelet transform as one of the multiscale geometry analysis methods can sparsely represent the line singularities. Based on the property of Ridgelet sparse representation to line singularities, a blind digital image watermarking algorithm is proposed. The algorithm can exactly determine the important coefficients of image in vision and adaptively embed watermarks into the original image. Experimental results show the proposed watermarking algorithm ensures the invisibility of watermarks and improves the robustness.Aiming at the problem of image denoising based on shrinkage in Ridgelet domain, a new hybrid denoising algorithm via combined Ridgelet shrinkage and total variation minimization model is proposed. Ridgelet coefficients are firstly thresholded, and then the thresholded coefficients are filtered by total variation diffusion. The hybrid denoising algorithm preserves the advantages of these two image denoising methods and has better general performance.The marginal statistical model of Curvelet coefficients is studied. And a new image denoising algorithm based on marginal statistical model of Curvelet coefficients and maximum a posteriori (MAP) estimator is proposed, where the normal inverse Gaussian (NIG) distribution is used as the prior model of curvelet coefficients of images. Under this prior, a Bayesian Curvelet estimator is derived by using the MAP rule. The proposed denoising algorithm can reduce the noise efficiently and keep the details meanwhile.Based on the multidirection and anisotropy of Curvelet transform, a new image fusion algorithm in Curvelet domain is proposed. The algorithm uses local direction energy ratio to measure the significance of features and uses local direction energy entropy to adaptively restrain noise disturb. The new fusion algorithm can sufficiently preserve image features and restrain noise disturb. It is more suited to real image fusion system.Overcomplete sparse representation can obtain the sparsest possible representation of the object and a resolution of sparse objects that is much higher-resolution than that possible with traditional non-adaptive approaches. We study the theories of overcomplete sparse image representation based on redundant dictionary and its application. (1) The spare decomposition method of overcomplete image sparse representation is studied. And a multi-atom matching pursuit method based on incoherent decomposition of redundant dictionary is proposed. In this method, the image is decomposed by several the best matching atoms selected at each iteration. The performances of the proposed method are comparable with those of the matching pursuit. And the speed for image sparse decomposition is greatly improved. It will be help to the research of applications based on overcomplete sparse representation. (2) The problems of redundant dictionary construction in overcomplete sparse representation are studied. A method of multiscale Ridgelet dictionary construction is proposed. The new constructed dictionary satisfies the human visual system characteristics. It is multiresolution, multiscale, anisotropic and multidirectional. It can provide sparser representation for images. (3) A still image coding scheme based on multi-atom matching pursuit and redundant multiscale Ridgelet dictionary is proposed. In this scheme, the image is firstly sparsely decomposed, and then the decomposed coefficients are adaptively quantized and encoded. The performances of the new coding scheme are shown to compare favorably against those of the state of the art JPEG-2000 scheme at low bit rate. The new coding scheme is more suitable to the image and video coding at low or very low bit rate.Image sparse representation via combined transforms means that an image is sparsely represented by overcomplete dictionary combined by several transforms. In this dissertation, we study the theories of sparse representation via combined transforms and its applications. Firstly, we study the methods of sparse representation via combined transforms and propose an iterative shrinkage algorithm. The iterative shrinkage can use the rapid algorithm of each transform. It is simple and rapidly convergent. It is more suited to use in large data. And then, a hybrid image restoration algorithm via combined Fourier and Curvelet transform is proposed. The Fourier shrinkage and Curvelet shrinkage are used to reduce the colored noise and the remaining noise separately. The hybrid restoration algorithm can restore the degraded images very well. In the end, an image interpolation algorithm via combined wavelet and Curvelet transform is proposed. The new interpolation algorithm exploits wavelet and Curvelet transforms'sparse representation of different kind of image contents. The image interpolation problem is turned to be image restoration problem enforced a sparsity constraint on the coefficients. We use an iterative shrinkage projection process to drive the solution towards an improved high-resolution image. Experimental results show the new interpolation algorithm substantially improves the subjective quality of interpolated images.