We study the complementary behaviors of external and internal examples in image restoration, and are motivated to formulate a composite dictionary design framework. The composite dictionary consists of the global part learned from external examples, and the sample-specific part learned from internal examples. The dictionary atoms in both parts are further adaptively weighted to emphasize their model statistics. Experiments demonstrate that the joint utilization of external and internal examples leads to substantial improvements, with successful applications in image denoising and super resolution.
We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2D image fragments (e.g., blocks) into 3D data arrays which we call "groups." Collaborative Altering is a special procedure developed to deal with these 3D groups. We realize it using the three successive steps: 3D transformation of a group, shrinkage of the transform spectrum, and inverse 3D transformation. The result is a 3D estimate that consists of the jointly filtered grouped image blocks. By attenuating the noise, the collaborative filtering reveals even the finest details shared by grouped blocks and, at the same time, it preserves the essential unique features of each individual block. The filtered blocks are then returned to their original positions. Because these blocks are overlapping, for each pixel, we obtain many different estimates which need to be combined. Aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy. A significant improvement is obtained by a specially developed collaborative Wiener filtering. An algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail; an extension to color-image denoising is also developed. The experimental results demonstrate that this computationally scalable algorithm achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality. We propose a super-resolution method that exploits selfsimilarities and group structural information of image patches using only one single input frame. The super-resolution problem is posed as learning the mapping between pairs of low-resolution and high-resolution image patches. Instead of relying on an extrinsic set of training images as often required in example-based super-resolution algorithms, we employ a method that generates image pairs directly from the image pyramid of one single frame. The generated patch pairs are clustered for training a dictionary by enforcing group sparsity constraints underlying the image patches. Super-resolution images are then constructed using the learned dictionary. Experimental results show the proposed method is able to achieve the state-of-the-art performance.