Multimedia Tools and Applications

, Volume 75, Issue 23, pp 16417–16438 | Cite as

Reconstruction algorithm for block-based compressed sensing based on mixed variational inequality

  • Kaixiong Su
  • Jian Chen
  • Weixing Wang
  • Lichao Su


Block compressed sensing based on mixed variational inequality (BCS-MVI) is proposed to improve the performance of current reconstruction algorithms for block-based compressed sensing. In the measurement phase, an image is sampled block by block. In the recovery period, BCS-MVI takes the sparse regularization of the natural image as prior knowledge and approaches the target function within the entire image through the modified augmented Lagrange method (ALM) and alternating direction method (ADM) of multipliers. Moreover, for the reconstruction problem including two regularization terms, an adaptive weight (−AW) strategy based on the gray entropy of the initialized image is studied. BCS-MVI achieves an average PSNR gain of 0.5–2.0 dB and an SSIM gain of 0.02–0.05 over previous block-based compressed sensing methods, and the reconstructing time only slightly fluctuates with the sampling rate. The algorithm is suitable for applications in multimedia data processing with fixed transmission delays.


Mixed variational inequality Image reconstruction Block-based compressed sensing Alternating direction method 



The paper is supported by the National Natural Science Foundation of China (No. 61170147 and 61471124), and the Natural Science Foundation of Fujian Province (No. 2013 J01234, 2014 J01234 and 2015 J01251). The wonderful lectures and patient help of Prof. Peng Zheng in the College of Mathematics and Computer Science at Fuzhou University is greatly appreciated, as are the wonderful lectures and scholarly communications from Prof. He Bing-sheng and Mrs. Tao Ming at Nanjing University.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.College of Physics and Information EngineeringFuzhou UniversityFuzhouChina
  2. 2.School of Information Science and EngineeringXiamen UniversityXiamenChina

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