基于局部字典搜索和多原子匹配追踪的图像逼近算法

摘要

Global searching in dictionary with single atom being selected in each iteration leads to greedy algorithms' high complexity in sparse decomposition.Given this,we propose an improved matching pursuit (MP) algorithm named local dictionary searching and multi-atoms matching pursuit (LMMP).Calculation showed that the order of kernel atoms in the adjacent generation of MP algorithm is basically stable,the best atom just to search in local dictionary consisting of the front order atoms.Searching for multiple incoherent atoms on single iteration to further improve the speed of MP algorithm.Reduce the approximation error by updating the residual image one by one atom in turn.Theoretical analysis indicates that the LMMP algorithm is convergent and its time complexity is several orders of magnitude lower than the MP.Experimental results show that the LMMP algorithm outperforms other global searching methods in computational speed and approximation performance.%鉴于全局搜索和单原子选择的逼近方式是导致图像稀疏分解贪婪算法复杂度高的主要原因,对传统的匹配追踪(MP)算法进行改进,提出基于局部字典搜索和多原子匹配追踪(LMMP)的逼近算法.采用基于二维快速哈莱特变换的内积批量计算方法,实验计算发现核原子在MP算法相邻代中的位序基本稳定,最佳原子只需在排序靠前的原子组成的局部字典中搜索,一次迭代搜索多个非相干原子,进一步提高匹配追踪算法速度,逐原子依次更新残差可减小逼近误差.理论分析表明,LMMP算法是收敛的,且时间复杂度比MP算法低数个数量级.从实验结果看出,LMMP算法与其他全局搜索算法相比,在运算速度和逼近性能上有明显优势.