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Noisy Image Reconstruction Via Fast Linearized Lagrangian Dual Alternating Direction Method of Multipliers

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Abstract

In this paper, an efficient noisy image reconstruction algorithm based on compressed sensing in the wavelet domain is proposed. The new algorithm is composed of three steps. Firstly, the noisy image is represented with its coefficients using the discrete wavelet transform. Secondly, the measurement is obtained by using a random Gaussian matrix. Finally, a fast linearized Lagrangian dual alternating direction method of multipliers is proposed to reconstruct the sparse coefficients, which will be converted by the inverse discrete wavelet transform to the reconstructed image. Our experimental results show that the proposed reconstruction algorithm yields a slightly higher peak signal to noise ratio reconstructed image as well as a much faster convergence rate as compared to some existing reconstruction algorithms.

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Acknowledgments

This work is supported by the National Basic Research Program of China (973 Program) (No. 2011CB302903), the National Natural Science Foundation of China (Nos. 60971129, 61070234, 61271335, 61271240), the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions–Information and Communication Engineering, the Research and Innovation Project for College Graduates of Jiangsu Province (No. CXZZ12_0469), and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 13KJB510020).

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Authors and Affiliations

  1. College of Communication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Zhen-Zhen Yang

  2. Key Lab of Broadband Wireless Communication and Sensor Network Technology, Ministry of Education, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Zhen-Zhen Yang & Zhen Yang

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  1. Zhen-Zhen Yang
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  2. Zhen Yang
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Correspondence to Zhen-Zhen Yang.

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Yang, ZZ., Yang, Z. Noisy Image Reconstruction Via Fast Linearized Lagrangian Dual Alternating Direction Method of Multipliers. Wireless Pers Commun 82, 143–156 (2015). https://doi.org/10.1007/s11277-014-2199-8

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