This paper addresses problems appearing in restoration algorithms based on utilizing both Tikhonov and bilateral total variation (BTV) regularization. The former regularization assumes that prior information has Gaussian distribution which indeed fails at edges, while the later regularization highly depends on the selected bilateral filter's parameters. To overcome these problems, we propose a locally adaptive regularization. In the proposed algorithm, we use general directional regularization functions with adaptive weights. The adaptive weights are estimated from local patches based on the property of the partially restored image. Unlike Tikhonov regularization, it can avoid smoothness across edges by using adaptive weights. In addition, unlike BTV regularization, the proposed regularization function doesn't depend on parameters' selection. The convexity conditions as well as the convergence conditions are derived for the proposed algorithm.

The problem of recovering a high-resolution frame from a sequence of low-resolution frames is considered. In general, video frames cannot be related through global parametric transformation due to the arbitrary individual pixel movement between frame pairs. To overcome this problem, we propose to employ region-matching technique for motion estimation with a modified model for frame alignment. To do that, the reference frame is segmented into arbitrary-shaped regions which are further matched with that of the other frames. Then, the frame alignment is accomplished by optimizing the cost function that consists of L1-norm of the difference between the interpolated low-resolution (LR) frames and the simulated LR frames. The experimental results demonstrate that using region matching in motion estimation step with the modified alignment model works better than other motion models such as affine, block matching, and optical flow motion models.