Energy Variational Method And Its Application In Medical Image Processing

Image process and analysis aim to improve the image quality through post-processing and rapidly extract the information that the specific application needs from huge mount of image data. Variational energy method is one of the most important methods in applied mathematics. In the last few decades have seen a great many applications and developments of variational methods in image pro-cessing. Super-resolution and segmentation are two typical problems in (medical) image processing. The first task targets to increase the amount of information and the second is to extract the boundary the specific object. Focussing on these two problems, we present here several efficient formulations of these problems based the variational method, relaxation, convex optimization and the theory of low rank matrix recovery, while also taking account of the features of specific data and the needs of their applications. Several efficient computational schemes and algorithms are also developed for the corresponding energies. With these new models and algorithms, we are trying to build a bridge for the daily clinical practice and the image processing techniques. Main research includes:Firstly, A region appearance based adaptive variational model is proposed for the liver segmentation from CT image, which is a typical problem in medical image processing. Due to intensity overlapping, ambiguous edges and complex backgrounds, liver segmentation is a difficult task.the non-uniform distributions of discriminative image features pose further challenges. In view of this, a spa-tially varying weight is incorporated by the proposed hybrid model such that the model can locate liver regions and edges selectively according to intensity, gradient and local context. Given the adhering tissues and weak edges, a novel potential field based on global and local region appearance is introduced to re-solve ambiguity. The experiments on standard data sets show that through the adaptive integration of different image cues, the proposed model can efficiently address complex background, intensity overlapping and weak edges. Moreover, it is robust to initialization and data quality. Quantitative validations and com- parative results demonstrate the accuracy, efficiency and robustness of the model and thus can well satisfy the clinical requirement.Secondly, we propose a constrained convex model with an efficient algo-rithm for liver segmentation problem, which is complicated by complex back-ground and intensity overlapping. Nonconvex models are prone to get stuck in local minima and thus sensitive to initialization. While convex models can be minimized globally with any initialization, one of the biggest challenges is to define an energy with meaningful global minimizer, especially for problems with complex background and ambiguous edges. In this paper we proposed a model which combined a novel intensity-edge term, a region appearance term and user specified constrains in initial stage,which can maximally restrict the solution space to target segmentation. Also we prove the optimal property thresholded solution of the convex model. Moreover, we proposed an accelerated primal-dual algorithm.Finally, we propose a structural low rank regularization method for the sin-gle image super-resolution. As is well known, single image super-resolution is a highly ill-posed problem due to the large amount of missing information in reg-ular positions. To obtain stable and reasonable solution, the general approach is to introduce regularization terms. One popular method is the learning based approach which can be adaptive to data structure. However, the results are heav-ily affected by the content of training data and learning algorithms. Moreover, they are plagued by artifacts such as inconsistent reconstructions and outliers which usually have significantly different values than neighborhoods. To address these problems, we propose a new variational energy with a structural low rank regularization, which produces clear reconstruction by fusing different coarse re-constructions. With the assumption of randomness and sparsity of the outliers, the proposed model can simultaneously remove the artifacts and keep the image structures.