中文摘要：

目的过去几年,基于稀疏表示的单幅图像超分辨获得了广泛的研究,提出了一种小波域中双稀疏的图像超分辨方法。方法由小波域中高频图像的稀疏性及高频图像块在空间冗余字典下表示系数的稀疏性,建立了双稀疏的超分辨模型,恢复出高分辨率图像的细节系数;然后利用小波的多尺度性及低分辨率图像可作为高分辨率图像低频系数的逼近的假设,超分辨图像由低分辨率图像的小波分解和估计的高分辨率图像的高频系数经过二层逆小波变换来重构。结果通过大量的实验发现,双稀疏的方法不仅较好地恢复了图像的局部纹理与边缘,且在噪声图像的超分辨上也获得了不错的效果。结论与现在流行的使用稀疏表示的超分辨方法相比,双稀疏的方法对噪声图像的超分辨效果更好,且计算复杂度减小。

英文摘要：

Objective Super-resolution is a challenging technique for recovering lost information according to natural image priori. As an important priori, sparse has been widely studied in the field of image processing, such as in image recovery, inpainting, demosaicing, and denoising. Given the development of compressed sensing theory and the Ll op- timization method, a large number of super resolution methods have been proposed based on sparse representation. An example is the single image super-resolution based on sparse representation, which has been widely studied in recent years. Method Based on the super-resolution model through sparse representation, where the feature image patch can be represented sparsely, a novel method conducted in the wavelet domain is proposed in this work. Our method is based on the sparse of high-frequency image patches and high-frequency image patches in redundant dictionaries. First, a decomposed coefficient image is obtained after using the discrete wavelet transform in a low-resolution image. Second, in connection with the high-frequency coefficients of the low-resolution image, a double sparse model with super-resolution is established to recover the detail coefficients of a high-resolution image correspondingly. Third, the decomposed coefficients of the low- resolution image and the recovered high-frequency coefficients of the high-resolution image are merged into wavelet coeffi- cients for second floor decomposition. Finally, with the multi-scale property of wavelet and the assumption that a low-reso- lution image can be used as a high-resolution image of low frequency coefficient approximation, a super-resolution image is reconstructed with two layers of inverse wavelet transformation with low-resolution image wavelet decomposition and esti-mated high-frequency coefficients of high-resolution images. In the model solving process, we adopt a fast solving method called the constrained splitting Bregman method, which is widely used to solve the L1 problem. Unlike the method for joint f