如何设计更加高效并能保持图像几何和纹理结构的多幅图像超分辨模型和算法是目前该领域有待解决的难点问题.针对图像的几何、纹理结构形态,分别建立符合类内强稀疏而类间强不相干的几何结构和纹理分量稀疏表示子成份字典,形成图像的多形态稀疏表示模型,进而提出一种新的基于多形态稀疏性正则化的多帧图像超分辨凸变分模型,模型中的正则项刻画了理想图像在多成份字典下的稀疏性先验约束,保真项度量其在退化模型下与观测信号的一致性,采用交替迭代法对该多变量优化问题进行数值求解,每一子问题采用前向后向的算法分裂法进行快速求解.针对可见光与红外图像序列进行了数值仿真,实验结果验证了本文模型与数值算法的有效性.

It is difficult to design an effective image super-resolution model and algorithm that can preserve the geometric structures and texture.Two incoherent geometry and texture sub-dictionaries are constructed,which can provide sparse representations of geometry and texture structures respectively.Thus,a multi-morphology sparse representation model is established.Furthermore,a convex variational model is proposed for multi-frame image super-resolution with multi-morphology sparsity regularization.The regularization term constrains the underlying image to have a sparse representation in a multi-component dictionary.The fidelity term restricts the consistency with the measured image in terms of the data degradation model.An alternate minimization iteration algorithm is proposed to solve it numerically and proximal forward-backward operator splitting method is adopted for each sub-problem.Numerical experiments for optics and infrared images are presented and the experimental results demonstrate that our super-resolution model and numerical algorithm are both effective.