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

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 i...

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Bibliographic Details
Published in:Numerical algorithms 2015-07, Vol.69 (3), p.495-516
Main Authors: Jiang, Le, Huang, Jin, Lv, Xiao-Guang, Liu, Jun
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Computed tomography
Computer Science
Image restoration
Mathematical analysis
Numeric Computing
Numerical Analysis
Optimization models
Original Paper
Particle emission
Positron emission
Regularization
Theory of Computation
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Summary: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.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-014-9908-y