图像有噪低秩结构及其恢复方法研究

项目名称： 图像有噪低秩结构及其恢复方法研究

项目编号： No.61203245

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 自动化学科

项目作者： 马杰

作者单位： 河北工业大学

项目金额： 24万元

中文摘要： 低秩结构恢复问题衍生于矩阵重建和压缩感知问题，为图像结构特征分析带来新的途径，由于模型易于理解且符合实际的物理意义，成为最近研究的热点问题。本课题以低秩结构模型和可行的恢复算法为研究对象，对符合实际问题的扩展模型和算法效率的提升问题进行科学研究。具体内容包括：在梳理现有低秩结构恢复模型的基础上，研究更切实际的有噪非负稀疏矩阵扩展模型，分析噪声水平对低秩结构的影响，比较不同信噪比下扩展问题的稳定性和收敛性；算法上，以高效的增广拉格朗日乘子法为基础，研究一种新颖的基于邻近点的改进算法，实现容易且占用内存少，并考虑算法实现时效率的进一步提升的策略；最后，通过街景文字对齐矫正的仿真实例，搭建实验评估平台，验证、分析和优化所提模型和算法。本项目旨在揭示有噪低秩结构模型及其适用的高效恢复方法，为模型进一步扩展、低秩结构的应用实践乃至矩阵重建问题研究提供借鉴和技术支撑。

中文关键词： 矩阵恢复；低秩；收缩算子；稀疏表示；增广拉格朗日乘子法

英文摘要： The problem on low-rank structure recovery is derived from the matrix recovery and compressive sensing, and it establishes a new way to study the image features. Now it has become a hot pot in the field of the information theory because the low-rank model is easy to understand and agrees with the real physical meaning. On the basis of the low-rank structure model and the feasible restroration algorithm, this project aims to expand the exsisting low-rank model according to pratical problems and further improve the efficiency of recovery algorithm. The main contents include: combing the existing low rank structure recovery model, studying impoved low-rank models with noise and nonegative sparse matrix, evaluating the effects of different noise levels to impoved low-rank models, comparing the stability and convergence of the extended algorithm under different SNR. In algoritm, an impoved augmented lagrangian multiplier method using proximal point algorithm is described and it is convenient to be realized with low storage memory. In addition, some pratical strategis are considered to further improve the efficiency. Finally, a simluation experiment on Chinese character alignment correction is demonstrated to verify and optimize the proposed model and algorithm under experimental platforms for research. The project re

英文关键词： matrix recovery；low rank；shrinkage；sparse representation；augmented Lagrange multiplier