彩色图像去马赛克的非局部稀疏表示方法

目前，大部分彩色去马赛克（Color DeMosaicking，CDM）算法仅利用了局部的空间和光谱相关性，容易导致CDM复原图像边缘模糊以及细小结构丢失.当图像中出现周期性细小结构时，这些局部方法容易产生诸如锯齿、栅格等失真现象.针对这些问题，我们将字典学习和稀疏编码统一到一个变分框架中，提出了非局部自适应稀疏表示模型.通过非局部相似块聚类自适应地在线学习字典.利用局部和非局部的冗余信息对稀疏编码进行约束，强制稀疏编码靠近其非局部均值以减少编码误差.为了有效抑制服从重尾分布的CDM误差，设计了基于l₁范数的数据项.最后，联合交替最小化方法和算子分裂技巧对模型进行有效求解.实验结果验证了本文模型与数值算法的有效性.

A Nonlocal Sparse Representation Method for Color Demosaicking

Currently,most of the color demosaicking algorithms using only a local spatial and spectral correlation,easily lead restored picture to blur edges and loss of fine structures.When cyclical small structures exist in the image,these local methods are prone to the distortion of the zipper effect,the raster effect,etc.To solve these problems,unifying dictionary learning and sparse coding into a variational framework,a non-local adaptive sparse representation model is proposed through non-local similarity clustering and adaptive dictionary online learning.Using the local and non-local redundancy,sparse coding constraints forced sparse coding close to its non-local means to reduce coding errors.Moreover,the fidelity term is characterized by l₁-norm to suppress the heavy-tailed visual artifacts.Finally,the joint alternating minimization method and operator splitting techniques are utilized to effectively solve the model.Experimental results demonstrate the effectiveness of the proposed model and the numerical algorithm.