求解几种稀疏表示模型的ADMM算法研究
1. 对几种稀疏表示模型进行介绍，主要包括对模型的假设和求解算法的探讨。
2. 对ADMM算法进行简单的介绍，主要包括对算法的框架、求解步骤、收敛性及停机准则的探讨。
3. 利用ADMM算法对以上几种稀疏表示模型进行求解。对L1规划问题的求解可以利用二次逼近以及软阈值函数。
4. 利用AR人脸数据库以及扩展的Yale B人脸数据库验证不同模型的分类性能。同时在无遮挡实验中利用PCA算法对人脸图像进行特征提取。
关键词 稀疏表示 ADMM算法 人脸识别 软阈值函数
毕业论文设计说明书外文摘要
Title Research on the solution of some sparse representation models based on ADMM
Abstract
Recently sparse representation has been successfully applied in face recognition. Some sparse representation based classification models have also been developed. The core of these models is to solve l1-minimization problem. The alternating direction method of multipliers (ADMM) can be used to solve these sparse representation models since ADMM is well suited to distributed convex optimization. In this paper, we mainly discuss the ADMM algorithm and its applications in some sparse representation models. The main work of this paper can be described as follows:
1. Some sparse representation models are introduced, including some discussion on their assumptions and algorithms.
2. ADMM is introduced, including some discussion on its framework, algorithm, convergence and stopping criterion.
3. Solving these models via ADMM algorithm. Quadratic approximation and soft-thresholding function are chosen to be used in the procedure.
4. The experiments on the Extended Yale B database and the AR database demonstrate the performances of different models. In this paper. The PCA (Principle Component Analysis) algorithm is used to obtain the principle component of facial image in the experiments without occlusion.
Keywords Sparse representation, ADMM, Face recognition, Soft-thresholding function.
目 次
1 绪论 1
1.1 人脸识别的研究历史与国内外现状 1
1.1.1 研究历史 1
1.1.2 国内外现状 2
1.2 基于稀疏表示的人脸识别的研究背景与进展 2
1.2.1 研究背景 2
1.2.2 研究进展 2
1.3 基于稀疏表示的人脸识别研究内容与研究方法 3
1.3.1 研究内容 3
1.3.2 研究方法 4
1.4 论文的研究内容以及章节安排 4
2 稀疏表示模型 5
2.1 SRC模型 5
2.1.1 理论基础与假设 5
2.1.2 框架与算法 6
2.2 RSC模型 7
2.2.1 理论基础与假设 7
2.2.2 框架与算法 9
2.3 结构稀疏模型 10
2.3.1 理论基础与假设 10
2.3.2 算法与框架 11
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