基于稀疏分解的Besov空间上的医学图像反卷积

在稀疏分解框架下,建立在Besov光滑空间上的图像变分泛函反卷积模型.在负Hilbert-Sobolev空间上约束数据项,正则项用稀疏性和光滑性来约束,冗余字典的L1范数作为稀疏性度量,用Besov空间上的半范数作为图像光滑性度量,保证稀疏性的同时也兼顾光滑性.该模型直接求解很困难,文中采用分裂算子的方法,把原模型分裂成图像域反卷积和稀疏表示这两个模型,交叉迭代求解,并给出模型求解的详细伪代码.实验验证算法的收敛性,并和其它模型进行比较,结果表明本文模型反卷积效果较好.

Medical Image Deconvolution in Besov Space Based on Sparse Decomposition

In the framework of sparse decomposition,an image deconvolution functional variation model in the Besov smooth space is proposed. The data item is constrained in the negative Hilbert-Sobolev space, while the regularization item is constrained by sparsity and smoothness. Both the sparsity and the smoothness are taken into account by regarding the L1 norm of the redundant dictionary as a sparsity measure and semi-norm as image smoothness measure in Besov space. The operator splitting method is adopted due to the difficulty in solving this mode directly. The original model is split into two parts: image deconvolution and sparse decomposition. Thus,it is solved using cross-iterative method. The resolution of the model pseudo-code is given in detail and the convergence of the algorithm is verified experimentally. The results show that deconvolution model is better than other models.