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杨波1, 吴纪桃1, 谢晓振2(1.北京航空航天大学数学与系统科学学院, 北京 100191;2.西北农林科技大学理学院, 杨凌 712100)

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。
Single image super-resolution in wavelet domain with double sparse

Yang Bo1, Wu Jitao1, Xie Xiaozhen2(1.School of Mathematics and System Science, Beihang University, Beijing 100191, China;2.College of Science, Northwest A&F University, Yangling 712100, China)

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 L1 optimization 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 coefficients for second floor decomposition. Finally, with the multi-scale property of wavelet and the assumption that a low-resolution 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 estimated 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 feature spaces, the constrained splitting Bregman method uses two dictionaries with high and low feature spaces. The low-resolution dictionary is learned from a low-resolution feature space using the k-svd method while the resolution dictionary is learned from least square approximation. Result The sparse model of redundant dictionary is known to recover good texture and denoise at the same time. The double sparse method has the advantage of the famous SR method through sparse representation and obtains good denoising performance. Through several experiments for standard pictures, the double sparse method restores image local texture and edges well and achieves a good effect on a noised image because of the use of multi-scale property and sparse with high-frequency coefficients. Our method involves less computational complexity compared with the popular sparse super-resolution method because of the use of only three quarters of the image patches of the original image. Conclusion The sparse model is widely used in image recovery. Based on the sparse of detail coefficients in wavelet domain and on the sparse of feature image patches under redundant dictionaries, a novel single image super-resolution method in wavelet domain is proposed in this work. The double sparse method preserves good local texture and edges and obtains better results for noised image with less computational complexity compared with the conventional method via sparse representation.