Image reconstruction from under-sampled data had always been challenging due to its implicit ill-posed nature until, that is, the emergence of compressed sensing. This paper proposes a new compressed sensing-based model and an efficient algorithm for image reconstruction from sparse observations, based upon a generalized multiple sparse restrictions framework to describe both local similarities and nonlocal similarities at the regularization stage. An efficient split Bregman method is employed to decouple the nonlinear optimization problem in order to iteratively approach the optimum solution. To obtain better restoration for multiband images, a principle component analysis is suggested to improve the signal-to-noise ratio of auxiliary parameters, and the noise variance in the wavelet domain is calculated adaptively. A comparison between filters showed that eight 3×3 sized filters learned from the model of fields of experts are by far the best filters to earn high peak signal-to-noise ratio. The proposed split Bregman optimization compressed sensing algorithm with fields of experts trained filters is compared to alternative methods such as Orthogonal Matching Pursuit, Compressive Sampling Matching Pursuit, Group-based Sparse Representation, and Compressive Sensing based on Bregman Split and principal component analysis. The experimental results of nine images show that the new method has competitive results for single-band images and outweighs all the other methods for color images, and so it is an appropriate model for reconstructing multichannel images.
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This work is supported by the National Natural Science Foundation of China (No. 41471368 and No. 41571413).
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Wei, J., Huang, Y., Lu, K. et al. Fields of Experts Based Multichannel Compressed Sensing. J Sign Process Syst 86, 111–121 (2017). https://doi.org/10.1007/s11265-015-1065-6
- Compressed sensing
- Markov random fields
- Total variation
- Image reconstruction