Compressive Sensing of Noisy 3-D Images Based on Threshold Selection
Qingzhu Wang*, Mengying Wei*, and Yihai Zhu**
*School of Information Engineering, Northeast Electric Power University
169 Changchun Road, Jilin City, Jilin 130062, China
**Engineering Technology Center, CRRC Changchun Railway Vehicles Co., Ltd.
435 Qingyin Road, Changchun City, Jilin 130062, China
Compressive sensing (CS) of high-order data such as hyperspectral images, medical imaging, video sequences, and multi-sensor networks is certainly a hot issue after the emergence of tensor decomposition. Actually, the reconstruction accuracy with current algorithms is not ideal in some cases of noise. In this paper, we propose a new method that can recover noisy 3-D images from a reduced set of compressive measurements. First, multi-way compressive measurements are performed using Gaussian random matrices. Second, the mapping relationship between the variance of noise and the reconstruction threshold is found. Finally, the original images are recovered through reconstruction of pseudo inverse based on threshold selection. We experimentally demonstrate that the proposed method outperforms other similar methods in both reconstruction accuracy (within a range of the compression ratios and different variances of noise) and processing speed.
-  L. Donoho, “Compressed sensing,” IEEE Trans. on Information Theory, Vol.52, No.4, pp. 1289-1306, 2006.
-  E. Candes and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?,” IEEE Trans. on Information Theory, Vol.52, No.12, pp. 5406-5425, 2006.
-  L. Lim and P. Comon, “Multiarray signal processing: Tensor decomposition meets compressed sensing,” Comptes Rendus Mecanique, Vol.338, No.6, pp. 311-320, 2006.
-  N. Sidiropoulos and A. Kyrillidis, “Multi-way compressed sensing for sparse low-rank tensors,” IEEE Signal Processing Letters, Vol.19, No.11, pp. 757-760, 2012.
-  M. Duarte and R. Baraniuk, “Kronecker product matrices for compressive sensing,” IEEE ICASSP 2010, pp. 3650-3653, 2010.
-  M. F. Duarte and R. Baraniuk, “Kronecker Compressive Sensing,” IEEE Trans. on Image Processing, Vol.21, No.2, pp. 494-504, 2012.
-  C. F. Caiafa and A. Cichocki, “Computing Sparse Representations of Multidimensional Signals Using Kronecker Bases,” Neural Computation, Vol.25, No.1, pp. 186-220, 2012.
-  C. F. Caiafa and A. Cichocki, “Multidimensional Compressed Sensing and their Applications,” Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, Vol.3, No.6, pp. 355-380, 2013.
-  Q. Li, D. Schonfeld, and S. Friedland, “Generalized Tensor Compressive Sensing,” IEEE Int. Conf. on Multimedia & Expo., pp. 1-6, 2013.
-  C. F. Caiafa and A. Cichocki, “Block Sparse Representations of Tensors Using Kronecker Bases,” IEEE Int. Conf. on Acoustics, Vol.22, No.10, pp. 2709-2712, 2012.
-  C. F. Caiafa and A. Cichocki, “Stable, robust and super fast reconstruction of tensors using multi-way projections,” IEEE Trans. Signal Process, Vol.63, No.3, pp. 780-793, 2015.
-  Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. Vol.13, No.4, pp. 600-612, 2004.
-  Y. August, C. Vachman, Y. Rivenson, and A. Stern, “Compressive Hyperspectral Imaging by Random Separable Projections in both the Spatial and the Spectral Domains,” Applied optics, Vol.52, No.10, pp. 46-54, 2013.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 International License.