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Alternating direction method for the high-order total variation-based Poisson noise removal problem

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Abstract

The restoration of blurred images corrupted by Poisson noise is an important task in various applications such as astronomical imaging, electronic microscopy, single particle emission computed tomography (SPECT) and positron emission tomography (PET). The problem has received significant attention in recent years. Total variation (TV) regularization, one of the standard regularization techniques in image restoration, is well known for recovering sharp edges of an image, but also for producing staircase artifacts. In order to remedy the shortcoming of TV in Poissonian image restoration, we consider a high-order total variation-based optimization model. The optimization model is converted to a constrained problem by variable splitting and then is addressed with the alternating direction method. Numerical results from the Poisson noise removal problem are given to illustrate the validity and efficiency of the proposed method.

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Author information

Authors and Affiliations

  1. Huaihai Institute of Technology, School of Science, Lianyungang, Jiangsu, 222005, People’s Republic of China

    Le Jiang & Xiao-Guang Lv

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 610054, People’s Republic of China

    Le Jiang, Jin Huang & Jun Liu

  3. School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu, 210097, People’s Republic of China

    Xiao-Guang Lv

Authors
  1. Le Jiang
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  2. Jin Huang
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  3. Xiao-Guang Lv
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  4. Jun Liu
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Corresponding author

Correspondence to Xiao-Guang Lv.

Additional information

This research is supported by NSFC (61370147, 61401172), Sichuan Province Sci. & Tech. Research Project (2012GZX0080), Nature Science Foundation of Jiangsu Province (BK20131209), Postdoctoral Research Funds (2013M540454, 1301064B).

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Jiang, L., Huang, J., Lv, XG. et al. Alternating direction method for the high-order total variation-based Poisson noise removal problem. Numer Algor 69, 495–516 (2015). https://doi.org/10.1007/s11075-014-9908-y

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  • DOI: https://doi.org/10.1007/s11075-014-9908-y

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