一种基于KSVD-ETF的测量矩阵优化方法

The Optimization Design of Measurement Matrix Based on KSVD-ETF

压缩感知将数据的采样和压缩同时处理,仅需少量测量就能重建信号。测量矩阵直接影响着信号适应的稀疏度范围和重建效果。为了减小测量矩阵与稀疏变换矩阵的互相干性,提出一种基于KSVD-ETF的测量矩阵和稀疏表达字典联合优化的方法,在对测量矩阵进行ETF优化的同时利用KSVD方法更新优化表达字典,实验结果中利用该方法优化矩阵所得重建信号PSNR有所提高,表明优化测量矩阵的方法在重建效果方面有一定的优势。

Compressive sensing, a novel signal acquisition method, is a joint sensing-compression process which requires a small number of measurements to reconstruct signal. Measurement matrix, a very important part in compressive sensing, directly affects the adaptive sparsity, the required number of measurements and the reconstruct performance of the signal. In order to decrease the mutual coherence between the measurement matrix and sparse transformed matrix and improve the quality of reconstruction, this paper addresses the joint optimization between measurement matrix and sparse dictionary based on the KSVD-ETF. While optimizing the measurement matrix by ETF, we use the KSVD method to update the dictionary. The PSNR of the reconstructed signal is improved with the optimized measurement matrix from the experimental results, indicating that this method of optimizing the measurement matrix has certain advantages in the effect of reconstruction.