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

作者: 赵毅智 , 钱 建 :杭州电子科技大学通信工程学院,杭州; 汪立新 :中国电子科技集团公司第36研究所,嘉兴;杭州电子科技大学通信工程学院,杭州;

关键词: 压缩感知测量矩阵稀疏字典互相干性KSVD-ETFCompressed Sensing Measurement Matrix Sparse Dictionary Mutual Coherence KSVD-ETF

摘要:
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。

Abstract:
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.

文章引用: 赵毅智 , 汪立新 , 钱 建 (2014) 一种基于KSVD-ETF的测量矩阵优化方法。 图像与信号处理, 3, 15-18. doi: 10.12677/JISP.2014.31003

参考文献

[1] Donoho, D. (2006) Compressed sensing. IEEE Transactions on Information Theory, 52, 1289-1306.

[2] Candes, E.J. and Wakin, M.B. (2008) An introduction to compressive sampling. IEEE Signal Processing Magazine, 25, 2130.

[3] 张凯, 杜小勇, 王壮 (2011) 基于压缩感知的空间目标三维雷达成像方法. 信号处理, 9, 1406-1411

[4] Tropp, J.A. and Gilbert, A.C. (2007) Signal recovery from random measurements via orthogonal matching pursuit. IEEE Transactions on Information Theory, 12, 4655-4666.

[5] 刘丹华, 石光明, 周佳社 (2008) 一种冗余字典下的信号稀疏分解新方法. 西安电子科技大学学报, 35, 228-232.

[6] Candes, E.J., Romberg, J. and Tao, T. (2006) Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 52, 489-509.

[7] Strohmer, T. (2008) A note on equiangular tight frames. Linear Algebra, 429, 326-330.

[8] Renes, J.M. (2007) Equiangular tight frames from paley tournamenrs. Linear Algebra, 426, 497-501.

[9] Zahedi, R., Pezeshki, A. and Chong, E.K.P. (2010) Robust measurement design for detecting sparse signals: Equiangular uniform tight frames and grassmannian packings. American Control Conference, Baltimore, June 30-July 2 2010, 4070-4075.

[10] Tropp, J.A., Dhillon, I.S., Heath, R.W. and Strohmer, T. (2005) Designing structured tight frames via an alternating projection method. IEEE Transactions on Information Theory, 51, 188209.

[11] Endra (2011) Color image reconstruction from compressive sensing with optimized measurement matrix, Binus ICT National Conference, 15-16.

[12] Elad, M. (2007) Optimized projections for compressed sensing. IEEE Transactions on Signal Processing, 55, 5695-5702.

[13] Duarte-Carvajalino, J.M. and Sapiro, G. (2009) Learning to sense sparse signals: Simultaneous sensing matrix and sparsifying dictionary optimization. IEEE Transactions on Image Processing, 18, 1395-1408.

[14] Xu, J.P., Pi Y.M. and Cao, Z.J. (2010) Optimized projection matrix for compressive sensing. EURASIP Journal on Advances in Signal Processing, 2010, 560349.

[15] Oey, E. and Gunawan, D. (2011) Image reconstruction from compressive sensing with optimized measurement matrix, 12th International Conference on Quality in Research (QiR), 4-7 July 2011.

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