收稿日期: 2015-08-26
修回日期: 2015-11-18
网络出版日期: 2016-07-30
基金资助
国家自然科学基金(No.61371102，No.61001092)资助
Low Complexity Recovery Algorithms of ImageCompressed Sensing Based on Statistics
Received date: 2015-08-26
Revised date: 2015-11-18
Online published: 2016-07-30
提出了一种基于图像统计信息的低复杂度高性能压缩感知还原方法.通过分析自然图像在小波表示下能量的分布特点，建立指数衰减模型，并将其作为统计先验应用于还原算法中.还原算法分为列(行)方向还原，行(列)方向还原两步骤进行，同时引入包含图像小波域能量统计先验的权重矩阵，并约束还原结果符合该权重矩阵的能量分步特点.根据实际应用的不同，该方法包含两种不同复杂度的还原策略，分别为一次直接(one-time direct，OTD)还原和两次迭代(two times iterative，TTI)还原.OTD策略在两步骤中均使用相同的权重矩阵，还原速度较快；TTI策略在第2步还原时通过二次迭代修正权重矩阵以获得更精确的还原结果.实验表明：OTD还原速度较传统方法有大幅度提高，同时还原质量也有所提升；TTI在OTD基础上以牺牲一部分还原速度为代价，获得了更好的还原质量，同时还原速度较传统方法亦有提高.
杨竞然, 吴绍华, 王海旭, 李佳慧 . 基于统计的图像压缩感知低复杂度还原方法[J]. 应用科学学报, 2016 , 34(4) : 417 -429 . DOI: 10.3969/j.issn.0255-8297.2016.04.007
Based on statistical prior information of image representations in the wavelet domain, we propose a low-complexity high-performance recovery method coupled with a separable image sensing encoder. By analyzing energy distribution of natural images in the wavelet domain, we develop an exponential decay model and use it as statisticalprior information in the algorithm. Particularly, the recovery process is composed of two steps, in which row-wise (or column-wise) intermediates and column-wise (or row-wise) final results are reconstructed sequentially. In each step, reconstruction is constrained to conform to the statistical prior by introducing a weight matrix. For different applications, we present two recovery strategies with different levels of complexity, namely one-time direct (OTD) recovery strategy and two-times iterative (TTI) recovery strategy. With OTD, the same weight matrix is used in both recovery steps to boost the recovery speed, whereas with TTI, the weight matrix in the second step is iteratively refined to enhance accuracy of recovery. Simulation results show that, compared to the traditional method, the proposed method boosts performance of compressed sensing recovery. In particular, the method with OTD can achieve much faster recovery speed and better recovery quality. Meanwhile, the best recovery quality can be obtained with TTI at the expense of slightly lowered recovery speed, yet still faster than traditional methods.
[1] Dohoho D L. Compressed sensing [J]. IEEE Transactions on Information Theory, 2006, 52(4): 383-395.
[2] Candes E J. The restricted isometry property and its implications for compressed sensing [J]. Comptes Rendus Mathematique, 2008, 346(9): 589-592.
[3] Hayashi K, Nagahara M, Tanaka T. A user's guide to compressed sensing for communications systems [J]. IEICE Transactions on Communications, 2013, 96(3): 685-712.
[4] Tropp J A, Gilbert A C. Signal recovery from random measurements via orthogonal matching pursuit [J]. IEEE Transactions on Information Theory, 2007, 53(12): 4655-4666.
[5] Blumensath T, Davies M E. Gradient pursuits [J]. IEEE Transactions on Signal Processing, 2008, 56(6): 2370-2382.
[6] Daubechies I, Defrise M, Mol C D. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint [J]. Communications on Pure and Applied Mathematics, 2004, 57(11): 1413-1457.
[7] Gilbert A, Strauss M, Tropp J. One sketch for all: fast algorithms for compressed sensing[C]//Proceedings of the thirty-ninth annual ACM symposium on Theory of computing, San Diego, CA, VSA, 2007: 237-246.
[8] Fang Y. Sparse matrix recovery from random samples via 2D orthogonal matching pursuit [R]. IEEE Transactions on Signal Processing, 2011.
[9] Rivenson Y, Stern A. Compressed imaging with a separable sensing operator [J]. IEEE Signal Processing Letters, 2009, 16(6): 449-452.
[10] Lin Y, Wu S H, YU Jia, Lin X D. Separate-combine recovery for compressed sensing of large images [C]//IEEE International Conference on Communications, 2014: 4601-4606.
[11] Cevher V. Learning with compressible priors [C]//Advances in Neural Information Processing Systems, 2009: 261-269.
[12] Rao X, Lau V K N. Compressive sensing with prior support quality information and application to massive MIMO channel estimation with temporal correlation [J]. IEEE Transactions on Signal Processing, 2015, 63(18): 4914-4924.
[13] Zhang L. Image adaptive reconstruction based on compressive sensing via CoSaMP [C]//IEEE International Conference on Information Science and Control Engineering, Shanghai, China, 2015: 760-763.
[14] Ferreira J C, Flores E L, Carrijo G A. Quantization noise on image reconstruction using model-based compressive sensing [J]. IEEE Latin America Transactions, 2015, 13(4): 1167-1177.
[15] Mishra K V, Cho M, Kruger A, Xu W Y. Spectral super-resolution with prior knowledge [J]. IEEE Transactions on Signal Processing, 2015, 63(20): 5342-5357.
[16] 何宜宝, 毕笃彦. 基于广义拉普拉斯分布的图像压缩感知重构[J]. 中南大学学报:自然科学版, 2013, 44(8): 3196-3202. He Y B, Bi D Y. Image compressed sensing reconstruction based on generalized Laplacian distribution [J]. Journal of Central South University: Science and Technology, 2013, 44(8): 3196-3202. (in Chinese)
/
| 〈 |
|
〉 |
