Alternating Optimization of Sensing Matrix and Sparsifying Dictionary for Compressed Sensing
Alternating Optimization of Sensing Matrix and Sparsifying Dictionary for Compressed Sensing
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DOI：
10.1109/tsp.2015.2399864
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发表时间：
2015-03
影响因子：
5.4
通讯作者：
Huang Bai;Gang Li;Sheng Li;Qiuwei Li;Qianru Jiang;Liping Chang
中科院分区：
文献类型：
--
作者：
Huang Bai;Gang Li;Sheng Li;Qiuwei Li;Qianru Jiang;Liping Chang
研究了压缩感知系统中感知矩阵和稀疏字典的交替优化问题。在J.M. Duarte-Carvajalino和G. Sapiro算法是一种新的最优稀疏化字典设计算法，它嵌入了一个优化的感知矩阵。最优字典设计问题的封闭形式的解决方案。提出了一种新的传感矩阵优化方法，并给出了相应的优化算法。仿真实验和真实的图像实验结果表明，所提出的算法具有良好的性能，优化后的感知矩阵和字典设计的压缩感知系统在信号重构精度上优于现有的压缩感知系统。特别是，所提出的CS系统的产量在一般情况下大大改善的性能比那些使用以前的方法设计的峰值信噪比方面的应用程序的图像压缩。
This paper deals with alternating optimization of sensing matrix and sparsifying dictionary for compressed sensing systems. Under the same framework proposed by J. M. Duarte-Carvajalino and G. Sapiro, a novel algorithm for optimal sparsifying dictionary design is derived with an optimized sensing matrix embedded. A closed-form solution to the optimal dictionary design problem is obtained. A new measure is proposed for optimizing sensing matrix and an algorithm is developed for solving the corresponding optimization problem. Experiments are carried out with synthetic data and real images, which demonstrate promising performance of the proposed algorithms and superiority of the CS system designed with the optimized sensing matrix and dictionary to existing ones in terms of signal reconstruction accuracy. Particularly, the proposed CS system yields in general a much improved performance than those designed using previous methods in terms of peak signal-to-noise ratio for the application to image compression.