压缩感知观测信号的低秩稀疏分解

低秩稀疏分解是可应用于视频监控的一种视频分析方法，与满足Nyquist定理的采样信号相比，压缩感知观测信号的低秩稀疏分解难度更大。借鉴在低秩稀疏分解时将信号投影到其低秩部分的正交空间方法，提出先压缩观测再投影与先投影再压缩观测两种不同的压缩观测与投影方法，推导出每种方法的投影与压缩观测合并算子，分别对稀疏前景与低秩背景进行压缩感知重构，实现时变稀疏信号压缩观测的低秩稀疏分解。由于背景的缓慢变化会使低秩矩阵的正交空间发生改变，应用结构相似度来判断相邻帧低秩矩阵的变化情况，并估计该正交空间是否需要更新。实验结果表明，与SpaRcs方法相比，该方法能够在较低的压缩采样率下实现更精确的信号低秩背景与稀疏前景的直接分离重构，每帧图像压缩感知重构结果的峰值信噪比最多能够提高2 dB左右。

Low-Rank and Sparse Decomposition of Compressive Sensing Observation Signals

Low-rank and sparse decomposition can be used in video surveillance analysis.This composition is more difficult to perform on Compressive Sensing(CS) videos than on videos sampled by the Nyquist theorem.Inspired by the method of projecting Nyquist-sampled signals into the orthogonal space of their low-rank section, two different CS and projection methods are proposed for the low-rank and sparse decomposition of CS videos.The first method projects measurements of CS videos into the orthogonal space of their low-rank partition.The second method performs the CS measurement after projection.For both methods, the operator can measure the CS videos and calculate the orthogonal projection simultaneously. The sparse foreground is reconstructed via CS, followed by the low-rank background. Because the progressive change in the background may change the orthogonal space of the low-rank matrices, the Structural Similarity(SSIM) metric is used to assess whether the orthogonal space of the low-rank matrices is changed.Experimental results show that compared with the SpaRcs method, the proposed method achieves better low-rank and sparse decomposition results, as well as improves the Peak Signal-to-Noise Ratio(PSNR) of the recovery images by a maximum level of 2 dB.