Department of Automation, Tsinghua University, Beijing, China.
IEEE Trans Image Process. 2012 May;21(5):2369-78. doi: 10.1109/TIP.2011.2177989. Epub 2011 Dec 2.
Perfect compressed sensing (CS) recovery can be achieved when a certain basis space is found to sparsely represent the original signal. However, due to the diversity of the signals, there does not exist a universal predetermined basis space that can sparsely represent all kinds of signals, which results in an unsatisfying performance. To improve the accuracy of recovered signal, this paper proposes an adaptive basis CS reconstruction algorithm by minimizing the rank of an accumulated matrix (MRAM), whose eigenvectors approximate the optimal basis sparsely representing the original signal. The accumulated matrix is constructed to efficiently exploit the second-order statistical property of the signal's autocorrelations. Based on the theory of matrix completion, MRAM reconstructs the original signal from its random projections under the observation that the constructed accumulated matrix is of low rank for most natural signals such as periodic signals and those coming from an autoregressive stationary process. Experimental results show that the proposed MRAM efficiently improves the reconstruction quality compared with the existing algorithms.
当找到一个特定的基空间来稀疏地表示原始信号时，可以实现完美的压缩感知（CS）恢复。然而，由于信号的多样性，不存在一个通用的预定基空间可以稀疏地表示所有类型的信号，这导致了性能不理想。为了提高恢复信号的准确性，本文提出了一种通过最小化累积矩阵的秩（MRAM）来实现自适应基 CS 重建算法，其特征向量近似于稀疏表示原始信号的最优基。累积矩阵是为了有效地利用信号自相关的二阶统计特性而构建的。基于矩阵补全理论，MRAM 从其随机投影中重建原始信号，前提是对于大多数自然信号（如周期性信号和来自自回归平稳过程的信号），所构建的累积矩阵的秩较低。实验结果表明，与现有算法相比，所提出的 MRAM 能够有效地提高重建质量。
