中文

Operations Research Transactions ›› 2015, Vol. 19 ›› Issue (4): 59-71.doi: 10.15960/j.cnki.issn.1007-6093.2015.04.006

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Measurement method of block compressed sensing based  on partial trigonometric function transform matrices

 CHEN Jian1, SU Kaixiong1,*, PENG Zheng2, SU Lichao3   

  1. 1.College of Physics and Information Engineering, Fuzhou University, Fuzhou 350116, China; 2.College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, China; 3.School of Information Science and Engineering, Xiamen University, Xiamen 361005, Fujian,  China
  • Received:2015-01-04 Online:2015-12-15 Published:2015-12-15

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Abstract:

To improve the measurement efficiency and reconstruction performance of the block compressed sensing (BCS), two measurement methods of compressed
sensing, based on partial discrete cosine transform in repeated block diagonal structure (abbreviated as PDCT-RBDS), and respectively, partial discrete sine transform in repeated block diagonal structure (abbreviated as PDST-RBDS), are proposed because of that the DCT (discrete cosine transform) and DST (discrete sine transform) have the property of collecting energy. The measurement matrices adopted are a structural deterministic matrix under the low complexity, and satisfy with the restricted isometry property (RIP). Moreover, by relating with sampling energy, the restricted isometry constant (RIC) and the lower bound of measurements for exact recovery are deduced. The experimental results, which compared with the partially random Gaussian matrices in repeated block diagonal structure (abbreviated as PRGS-RBDS) and partially Bernoulli matrices in repeated block diagonal structure (abbreviated as
PBNL-RBDS), indicate that, about 1---5 dB gain in the PSNR and 0.05 gain in the SSIM are observed, and the recovery time and storage space for measurement matrices are greatly reduced. The method is particularly suitable for the applications of image compressing in large scale and video data processing in real time.

Key words: Block Compressed Sensing, Structurally Random Matrices, Discrete Cosine Transform, Discrete Sine Transform