为实现图像超分辨力重建, 提出了一个自适应半耦合稀疏字典学习算法。由于耦合字典学习算法中存在稀疏编码约束条件太过严苛的缺点, 本文采用半耦合的字典学习算法。根据在半耦合的字典学习算法中全局字典表达的局限性, 分析和采用了多字典训练算法及相应的重建方法。提出了基于自适应图像块聚类算法的半耦合稀疏字典学习算法。仿真实验结果显示, 新算法重建得到的 Butterfly,Cameraman,Foreman,Plants,Hat和Lena等图像的峰值信噪比 (PSNR)分别比用基于K-means聚类算法的半耦合稀疏字典学习算法得到的重建图像高出 0.18 dB,0.16 dB,0.52 dB, 0.21 dB,0.23 dB和0.14 dB。该算法可以得到更好的图像重建效果。

In order to achieve higher resolution images, a semi-coupled sparse dictionary learning algorithm by using adaptive image blocks clustering algorithm is proposed. The theoretical basis of semi-coupled sparse dictionary learning algorithm and adaptive image blocks clustering algorithm are studied in this paper. Firstly, according to the application of sparse representation theory in image superresolution algorithm, the coupled and semi -coupled sparse dictionary learning algorithm are introduced. The coupled dictionary learning algorithm assumes that sparse codings of corresponding high and low resolution image blocks are equal, but this assumption is too strict. The semi-coupled dictionary learningalgorithm relaxes this assumption, assuming that sparse codings of corresponding high and low resolutionimage blocks are notequal, but satisfying a linear mapping. Secondly, because the semi -coupled sparse dictionary learning algorithm is more reasonable than the coupled sparse dictionary learning algorithm, in this paper, the semi-coupled sparse dictionary learning algorithm is adopted. Then, according to the limitations of expression of the global dictionary, the multi-dictionary learning algorithm is analyzed. Finally, through the analysis of the traditional image blocks clustering algorithm, a semi -coupled sparse dictionary learning algorithm by using adaptive image blocks clustering algorithm is proposed. The experimental results show that the Peak Signal to Noise Ratios(PSNR) of Butterfly, Cameraman, Foreman, Plants, Hat and Lena images obtained by the proposed algorithm are higher than that of the semi-coupled sparse dictionary learning algorithm based on K-means clustering algorithm by 0.18 dB,0.16 dB,0.52 dB,0.21 dB,0.23 dB and 0.14 dB respectively. According to the results, a conclusion is drawn that better reconstruction images can be obtained by the proposed method.