Circuits, Systems, and Signal Processing

, Volume 38, Issue 1, pp 304–328 | Cite as

Image Block Compressive Sensing Reconstruction via Group-Based Sparse Representation and Nonlocal Total Variation

  • Jin Xu
  • Yuansong Qiao
  • Zhizhong Fu
  • Quan Wen


Compressive sensing (CS) has recently drawn considerable attentions in signal and image processing communities as a joint sampling and compression approach. Generally, the image CS reconstruction can be formulated as an optimization problem with a properly chosen regularization function based on image priors. In this paper, we propose an efficient image block compressive sensing (BCS) reconstruction method, which combine the best of group-based sparse representation (GSR) model and nonlocal total variation (NLTV) model to regularize the solution space of the image CS recovery optimization problem. Specifically, the GSR model is utilized to simultaneously enforce the intrinsic local sparsity and the nonlocal self-similarity of natural images, while the NLTV model is explored to characterize the smoothness of natural images on a larger scale than the classical total variation (TV) model. To efficiently solve the proposed joint regularized optimization problem, an algorithm based on the split Bregman iteration is developed. The experimental results demonstrate that the proposed method outperforms current state-of-the-art image BCS reconstruction methods in both objective quality and visual perception.


Block compressive sensing Group-based sparse representation Nonlocal total variation Joint regularization Split Bregman iteration 



This work has been supported in part by the National Natural Science Foundation of China under Grant 61671126 and Science Foundation Ireland (SFI) under Grant 13/SIRG/2178. The authors would like to thank the authors of [4, 11, 19, 27, 28, 29] and [33] for kindly providing their software or codes to reproduce their experimental results in Sect. 5 and thank the anonymous reviewers for their constructive suggestions to improve the manuscript. They also would like to express their gratitude to Dr. Nasser Eslahi (Tampere University of Technology, Finland) for fruitful discussions.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Information and Communication EngineeringUniversity of Electronic Science and Technology of ChinaChengduChina
  2. 2.Software Research InstituteAthlone Institute of TechnologyAthloneIreland
  3. 3.School of Computer Science and EngineeringUniversity of Electronic Science and Technology of ChinaChengduChina

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