13 March 2013 Fast and efficient signal reconstruction from structurally sampling partial Fourier data by chaotic dynamical system
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Abstract
We consider the problem of both fast acquisition and efficient image reconstruction from partial Fourier data due to the missing or compressed information. We investigate the possibility of using different chaotic sequences to construct measurement matrices in Fourier data. In particular, we consider sequences generated by Chen chaotic system. We investigate the accuracy of reconstruction based on our proposed accelerated Dykstra-like proximal algorithm when to use different chaotic systems to construct measurement matrices of sparse or nearly sparse signals in frequency domain. We compare the recovery rate of the different chaotic sequences with Gaussian random sequences. We also investigate the recovery rate on the initial values of the chaotic systems. In practice, the relationship between the structurally sampling matrices controlled by the initial values of the chaotic systems and the structure of the sparse signal is a promising problem to enhance the recovery rate and to perform fast and efficient compressed sensing. The performance of the proposed Chen chaotic compressed sensing is analyzed by using numerical simulation with radio interferometric image and magnetic resonance image.
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Weizhi Xu, Weizhi Xu, Liqing Zhang, Liqing Zhang, } "Fast and efficient signal reconstruction from structurally sampling partial Fourier data by chaotic dynamical system", Proc. SPIE 8784, Fifth International Conference on Machine Vision (ICMV 2012): Algorithms, Pattern Recognition, and Basic Technologies, 87841T (13 March 2013); doi: 10.1117/12.2014152; https://doi.org/10.1117/12.2014152
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