Image Restoration Using Joint Statistical Modeling in Space-Transform Domain

This paper presents a novel strategy for high-fidelity image restoration by characterizing both local smoothness and nonlocal self-similarity of natural images in a unified statistical manner. The main contributions are three-folds. First, from the perspective of image statistics, a joint statistical modeling (JSM) in an adaptive hybrid space-transform domain is established, which offers a powerful mechanism of combining local smoothness and nonlocal self-similarity simultaneously to ensure a more reliable and robust estimation. Second, a new form of minimization functional for solving image inverse problem is formulated using JSM under regularization-based framework. Finally, in order to make JSM tractable and robust, a new Split-Bregman based algorithm is developed to efficiently solve the above severely underdetermined inverse problem associated with theoretical proof of convergence. Extensive experiments on image inpainting, image deblurring and mixed Gaussian plus salt-and-pepper noise removal applications verify the effectiveness of the proposed algorithm.Comment: 14 pages, 18 figures, 7 Tables, to be published in IEEE Transactions on Circuits System and Video Technology (TCSVT). High resolution pdf version and Code can be found at: http://idm.pku.edu.cn/staff/zhangjian/IRJSM

A Block-Based Regularized Approach for Image Interpolation

This paper presents a new efficient algorithm for image interpolation based on regularization theory. To render a high-resolution (HR) image from a low-resolution (LR) image, classical interpolation techniques estimate the missing pixels from the surrounding pixels based on a pixel-by-pixel basis. In contrast, the proposed approach formulates the interpolation problem into the optimization of a cost function. The proposed cost function consists of a data fidelity term and regularization functional. The closed-form solution to the optimization problem is derived using the framework of constrained least squares minimization, by incorporating Kronecker product and singular value decomposition (SVD) to reduce the computational cost of the algorithm. The effect of regularization on the interpolation results is analyzed, and an adaptive strategy is proposed for selecting the regularization parameter. Experimental results show that the proposed approach is able to reconstruct high-fidelity HR images, while suppressing artifacts such as edge distortion and blurring, to produce superior interpolation results to that of conventional image interpolation techniques

Reconstruction of 7T-Like Images From 3T MRI

In the recent MRI scanning, ultra-high-field (7T) MR imaging provides higher resolution and better tissue contrast compared to routine 3T MRI, which may help in more accurate and early brain diseases diagnosis. However, currently, 7T MRI scanners are more expensive and less available at clinical and research centers. These motivate us to propose a method for the reconstruction of images close to the quality of 7T MRI, called 7T-like images, from 3T MRI, to improve the quality in terms of resolution and contrast. By doing so, the post-processing tasks, such as tissue segmentation, can be done more accurately and brain tissues details can be seen with higher resolution and contrast. To do this, we have acquired a unique dataset which includes paired 3T and 7T images scanned from same subjects, and then propose a hierarchical reconstruction based on group sparsity in a novel multi-level Canonical Correlation Analysis (CCA) space, to improve the quality of 3T MR image to be 7T-like MRI. First, overlapping patches are extracted from the input 3T MR image. Then, by extracting the most similar patches from all the aligned 3T and 7T images in the training set, the paired 3T and 7T dictionaries are constructed for each patch. It is worth noting that, for the training, we use pairs of 3T and 7T MR images from each training subject. Then, we propose multi-level CCA to map the paired 3T and 7T patch sets to a common space to increase their correlations. In such space, each input 3T MRI patch is sparsely represented by the 3T dictionary and then the obtained sparse coefficients are used together with the corresponding 7T dictionary to reconstruct the 7T-like patch. Also, to have the structural consistency between adjacent patches, the group sparsity is employed. This reconstruction is performed with changing patch sizes in a hierarchical framework. Experiments have been done using 13 subjects with both 3T and 7T MR images. The results show that our method outperforms previous methods and is able to recover better structural details. Also, to place our proposed method in a medical application context, we evaluated the influence of post-processing methods such as brain tissue segmentation on the reconstructed 7T-like MR images. Results show that our 7T-like images lead to higher accuracy in segmentation of white matter (WM), gray matter (GM), cerebrospinal fluid (CSF), and skull, compared to segmentation of 3T MR images