| 摘要: |
| 在求解基追踪问题的线性化Bregman迭代方法基础上，结合了广义逆的迭代技术得到一种稀疏信号重构的新算法。该算法在计算Moore-Penrose广义逆时，采用了迭代计算的方式，与算法本身相结合使得仅有矩阵向量乘积运算，避免了奇异值分解的较大工作量。通过数值试验可知，新算法相对线性化Bregman算法在计算时间上约减少了2/3，同时信号的恢复效果也是稳定有效的。因此，新算法是一种有效可行的信号重建算法。 |
| 关键词: 信号重构 压缩感知 广义逆 线性化Bregman迭代法 稀疏重构 |
| DOI： |
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| 基金项目:国家自然科学基金资助项目（61101208）；中央高校基本科研业务费专项资金（13CX02086A）；国家海洋局海洋遥测工程技术研究中心创新青年基金项目（2012003） |
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| A new signal reconstruction algorithm based on compressed sensing |
| QIAO Tian-tian,ZHANG Yu,LI Wei-guo |
| () |
| Abstract: |
| Combined with the iterative method of generalized inverse, a new algorithm for sparse signal reconstruction is developed based on linearized Bregman iteration for solving the basis pursuit problems.During calculating Moore-Penrose generalized inverse, the algorithm only has the matrix-vector multiplication by iteration combined with its own，so that the singular value decomposition(SVD) is avoided. The numerical experiments show the computation time has reduced by about 2/3 than that of original algorithms. Meanwhile,the recovery of signals is stabe and effective. So this new algorithm is a feasible signal reconstruction algorithm. |
| Key words: signal reconstruction compress sensing generalized inverse linearized Bregman iteration sparse reconstruction |
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