基于凸优化及加权范数的稀疏信号重建（已处理）.doc

基于凸优化及加权范数的稀疏信号重建 本科毕业设计(论文)题目 基于凸优化及加权范数的稀疏信号重建 学生姓名: 专 业: 电子信息工程 指导教师: 完成日期:年5月31日 摘 要 2004年由Donoho等人提出的压缩感知理论(CS理论)表明利用信号的稀疏性或可压缩性,能够以极少量的线性测量值恢复原始信号,而远低于奈奎斯特采样定律的限制。该理论使得数据获取和数据压缩可以同时进行,成功克服了数据采样、存储等过程中的资源浪费问题。对该理论的研究,关键是如何通过重建算法从压缩感知得到的低维数据中精确的恢复出原始的高维数据。 通过学习国内外关于压缩感知理论及现有重建算法的文献,系统研究了压缩感知理论的框架,并介绍了几种典型的重建算法(凸优化算法和贪婪算法)及其优缺点。由于利用基于最小l1范数的凸优化算法来恢复稀疏信号具有很高的准确度,其应用十分广泛,故对这类算法进行了深入研究。 但是基于最小l1范数的重建算法对大系数的稀疏信号重建还不够准确,于是提出了一种改进的算法即基于加权最小l1范数的凸优化算法,对这种算法的求解过程及其参数的确定方法进行了重点研究。仿真实验表明1)测量数量对重建效果影响较大;2)恢复结果可以在一定迭代步数内收敛;3)对于带噪声信号,基于加权最小l1范数的重建算法恢复效果明显优于传统的最小l1范数算法。校正参数的选取对重建效果也有影响,对这方面的改进算法还有待进一步研究。 关键词:压缩感知,稀疏信号,重建算法,加权l1范数ABSTRACT The theory of compressed sensing CS implemented by Donoho, etc, has shown that sparse or compressible signals can be reconstructed from a surprising small number of linear measurements, and is far lower than the limits of the Nyquist sampling theory. It compresses the signal when sampling it. In this way, we can overcome an amount of problems such as physical resources wasting in the process of data sampling, data storing and so on. It is the key point how to reconstruct the high dimensional data from the low dimensional data. The compressed sensing theory and the existing reconstruction algorithms is reviewed. And then the framework of compressed sensing theory is studied. A few typical reconstructed algorithms convex optimization algorithms and greedy algorithms are introduced. Convex optimization algorithms based on l1 norm minimization has been widely used because of high reconstruction accuracy. So, this kind of algorithms is studied deeply. However, the algorithms based on l1 norm minimization are not precise enough to reconstruct the large coefficients, so an improved algorithm, the reweighted l1 minimization reconstruction algorithm, is proposed. The solving process and methods to determine the parameters are focused on. The experimental results show