Mean Shift: A Method for Measurement Matrix of Compressive Sensing

In this work, we propose a mean shift based measurement matrix for compressive sensing and systematically investigate the possibility of constructing measurement matrix with mean shift of different chaotic sequences. With this matrix, we apply it in compressive sensing of digital images and compare the accuracy of reconstruction while using it to construct measurement matrices. The experimental results showed that mean shift based measurement matrix for compressive sensing can not only lead to visible PSNR improvements over state-of the-art method such as Gaussian random matrix method, but also preserve much better the image structures when compressed and generate good recovered visual quality.

[1]  Yizong Cheng,et al.  Mean Shift, Mode Seeking, and Clustering , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Dorin Comaniciu,et al.  Mean Shift: A Robust Approach Toward Feature Space Analysis , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  Wotao Yin,et al.  Bregman Iterative Algorithms for (cid:2) 1 -Minimization with Applications to Compressed Sensing ∗ , 2008 .

[4]  Tom Goldstein,et al.  The Split Bregman Method for L1-Regularized Problems , 2009, SIAM J. Imaging Sci..

[5]  Jian-Feng Cai,et al.  Linearized Bregman Iterations for Frame-Based Image Deblurring , 2009, SIAM J. Imaging Sci..

[6]  Xavier Bresson,et al.  Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction , 2010, J. Sci. Comput..

[7]  Hong Sun,et al.  Compressive Sensing With Chaotic Sequence , 2010, IEEE Signal Processing Letters.

[8]  Lei Yu,et al.  Compressive sensing matrix designed by tent map, for secure data transmission , 2011, Signal Processing Algorithms, Architectures, Arrangements, and Applications SPA 2011.

[9]  Bin Dong,et al.  Fast Linearized Bregman Iteration for Compressive Sensing and Sparse Denoising , 2011, ArXiv.

[10]  Lei Zhang,et al.  Log-Euclidean Kernels for Sparse Representation and Dictionary Learning , 2013, 2013 IEEE International Conference on Computer Vision.

[11]  Themos Stafylakis,et al.  A Study of the Cosine Distance-Based Mean Shift for Telephone Speech Diarization , 2014, IEEE/ACM Transactions on Audio, Speech, and Language Processing.