Structured Sparse Representation Based On The Finite Mixture Model For Image Denoising

The finite mixture model based structured sparse representation method for image denoising has been a hot issue in image processing field. Compared with the dictionary learning in traditional sparse representation, the finite mixture model based learning method has the advantages of relatively low computational complexity and the well-understood mathematical behavior. Especially, Gaussian mixture model (GMM) is one of the most frequently used finite mixture model,which has been widely applied in various regions and achieved a good result.However, the traditional GMM based image denoising methods do not consider the gradient information of the image, which lead to the lost of the small-scale textures and details of images during the noise removal. In addition, the traditional GMM is sensitive to noise due to the Gaussian distribution has a short and light tail. When the image is corrupted seriously, the traditional GMM based image denoising methods can't obtain a satisfying denoised result. Therefore, in this paper, we first attempt to incorporate the gradient fidelity term with the GMM based image sparse representation method for preserving more image edges. Meanwhile, we construct an adaptive regularization parameter selection scheme by combing the image gradient with the local entropy of the image, which makes the model parameters can adaptive to the image structure information and preserve more details of the image. In order to overcome the sensitivity to noise of the GMM, we propose a student's-t mixture model (SMM) based structured sparse representation method for image, denoising.Since the student's-t distribution has a heavy tail and is robust to the noise, we can learn a better image prior using the SMM and acquire a better noised result. This paper mainly includes the following four aspects:(1) First, we propose a Gaussian mixture model learning based structured sparse representation method coupling gradient fidelity term for image denoising, which can help preserve more details and edges of the image during the noise removal;(2) Second, we construct an adaptive regularization parameter scheme by combing the image gradient with the local entropy of the image, which makes the model parameters can change their values automatically according to the image information and help preserve more textures of images;(3) Third, we propose a structured sparse representation method for image denoising based on the student's-t mixture priors. This method has a good robustness to the noise and can obtain a good denoised result even the image is corrupted seriously;(4) Moreover, we attempt to add the gradient fidelity term to the SMM,and propose a SMM based structured sparse representation method. Our proposed method not only has a good robustness to the noise,but enables to preserve more fine structures of images.