Research On Optimization Model And Algorithm In Digital Image Processing

Digital image processing has a wide range of applications in many fields, such as aerospace, robot vision, and biomedical science. Due to the limitation of the imaging devices and adverse factors in image transfer processes, the observed image may be degraded, such as blurred, corrupted by some noise and lose some image information. Many scientific researchers show the great concern on how to improve the resolution of the image, and repair the damaged image.Image restoration problems are ill-posed problems from a mathematical point of view. Image restoration problems can be transformed to optimization problems by introducing some prior constraints. This thesis centres around modeling on the image restoration and hyperspectral unmixing problems. Several optimization models are proposed for image deblurring, image denoising, image inpainting and hyperspectral unmixing.Then the corresponding algorithms are designed. The main contents of this thesis are as follows:1. A modified 7)1minimization model for image deblurring and denoising problems is proposed, which is solved by an efficient alternative iterative algorithm: a combination of the fast iterative shrinkage-thresholding algorithm and the dual algorithm. And the convergence of this algorithm is investigated. Numerical experiments demonstrate the efficiency and viability of this algorithm.2. In many practical situations, the observed images are usually corrupted by mixed noise. A combined total variation and high-order total variation model is proposed to restore blurred images corrupted by mixed Gaussian plus impulse noise. This model takes the good nature of the total variation regularization and high-order total variation regularization. It reduces the stair-case effects caused by total variation norm and at the same time keeps the edges well. The alternating direction method of multipliers is employed to solve the proposed model. Numerical experiments illustrate the superiority of the proposed method.3. Speckle noise contamination is a common issue in ultrasound imaging system.We propose a hybrid total variation and high-order total variation based model for speckle noise removal in ultrasound imaging, which is solved by an efficient algorithm. Numerical experiments demonstrate that our method can remove speckle noise efficiently while balance the edges and smooth areas of the restored images.4. Based on the assumption that images consist of smooth components and edges,a new image inpainting model is established. The reproducing kernel Hilbert space is used to model the smooth component of the image while Heaviside function variations are used to model the edges. Numerical experiments verify that this method is superior or at least competitive to some state-of-the-art methods.5. By employing the intrinsic structure of the hyperspectral data, we propose a semisupervised graph-regularized sparse model for hyperspectral unmixing. This model is solved by a symmetric alternating direction method of multipliers. The convexity of this model and the uniqueness of the unmixing result are proved. Numerical experiments show that this method can obtain desirable unmixing results.