近邻局部OMP稀疏表示图像去噪

目的 基于分类的稀疏字典去噪算法改善了字典训练阶段的效率问题，但稀疏分解阶段仍是全字典匹配，影响算法运行速度。为了解决稀疏去噪算法在稀疏分解阶段因复杂矩阵运算及字典全局搜索导致的算法效率低，以及冗余的稀疏字典因无法描述图像具体特征而影响图像去噪效果的问题，提出改进算法。方法 首先稀疏分解阶段，在原正交匹配追踪算法基础上引入字典原子聚类思想，提出局部正交匹配追踪算法，将全局搜索优化为局部搜索；为保证局部搜索仍能保持良好的匹配结果，提出近邻择优策略，计算聚类中心与信号原子的距离，从而按照某一阈值自适应地选择最优的n个子字典作为稀疏分解的匹配空间；最后将图像分解为内容簇和背景簇，对内容簇采用基于近邻的局部K奇异值分解（K-SVD）算法去噪，背景簇采用均值滤波方法去噪。结果 对USC标准数据库中大量图像进行去噪实验，本文算法去噪结果的峰值信噪比值比K-SVD算法平均提高了1.53 dB，比2维块匹配（BM3D）算法平均提高了0.72 dB，比聚类的稀疏表示去噪（CSR）算法平均提高了0.5 dB；运行时间比原算法提高了23.2%。结论 本文算法针对灰度图像去噪，在去噪效果及去噪效率方面均有改善，尤其对细节纹理较丰富的灰度图像去噪具有一定的应用价值。

Image denoising based on sparse representation of neighbor local OMP

Objective Sparse denoising algorithm is advantageous in optimizing the denoising effect but is inefficient because of its complex matrix operations in the sparse decomposition and dictionary training stages.Although classification is applied in the dictionary training stage,the method can still be enhanced.An improved algorithm is proposed to solve problems of inefficiency caused by complex matrix operations and global searching of the dictionary in the sparse decomposition stage.Method First,a local orthogonal matching pursuit algorithm,which introduces dictionary clustering based on orthogonal matching pursuit to generate sub-dictionaries,is proposed.Another novel element of this work is that a neighbor-prioritizing method,which selects n optimal sub-dictionaries as matching space to sparse decompose,is proposed to optimize the denoising effect.Finally,the content cluster of the noisy image is denoised using the neighbor local K-SVD algorithm based on the clustering-based denoising method.Result Experiments on several images in the USC standard image library show that the proposed method leads to better denoising effect than that of other algorithms.The peak signal-to-noise ratio of the proposed algorithm is 1.53 dB higher than that of the K-SVD algorithm,0.72 dB higher than that of the BM3D algorithm,and 0.5 dB higher than that of the CSR algorithm on average.The running time of this algorithm is faster than that of the original algorithm.Conclusion The proposed algorithm improves the effect and efficiency of gray image denoising and presents certain popularization value on gray images with much detail and texture.