基于可分凸优化的图像分解和波前重建的模型与算法研究

项目名称： 基于可分凸优化的图像分解和波前重建的模型与算法研究

项目编号： No.11301055

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 张文星

作者单位： 电子科技大学

项目金额： 23万元

中文摘要： 近几年来，作为最优化领域的研究热点，稀疏优化被广泛应用于图像科学、生物医学和空间科学等领域。其中，在模式识别、材料分析以及空间探测中有着重要实际意义的图像分解和波前重建问题是稀疏优化的重要研究内容。目前，图像分解和波前重建问题的数学模型所能处理的图像类型有限，数值求解过程的计算量偏大，解的精度较低。基于我们的前期工作，本项目旨在进一步拓展图像分解和波前重建问题的可分凸优化模型，建立：（1）能处理缺损图像（同时具有模糊、信息缺失、低分辨率和噪声等）的图像分解模型；（2）能获取高精度波前梯度、位相和点扩散函数的波前重建模型；（3）设计问题驱动的处理可分凸优化的并行算法，并用其处理（1）-（2）中的数学模型，最终实现图像分解和波前重建问题在并行机群上的快速、鲁棒求解。

中文关键词： 凸优化；算子分裂算法；图像分解；波前重建；并行计算

英文摘要： Sparse optimization has recently received wide attention from various areas such as imaging sciences, biomedicine, astronomy and space sciences. Among important topics of sparse optimization are image decomposition and wavefront reconstruction which play significant roles in many specific fields such as pattern recognition, materials analysis and space explorations. Typically, the existing models and algorithms for handling image decomposition and wavefront reconstruction have some limitations. For instance, the models for image decomposition are inapplicable to decompose a target image with the hybrid corruptions, e.g., convolution, missing pixel values, low-resolution and additive noise, whilst the models for wavefront reconstruction are incapable of providing solution with high accuracy. Moreover, the computational efforts for solving those models are numerically intensive because of the nonsmooth objective functions and ill-posed linear operators. Researchers in these fields are devoted to some challenging problems such as generalizing the applicable range of images for these two tasks, developing more efficient numerical solvers, and improving the accuracy of solutions. In this project, we aim at extending our previous research results on image decomposition and wavefront reconstruction in the following asp

英文关键词： Convex programming；Operator splitting method；Image decomposition；Wavefront reconstruction；Parallel computing