Restoring Poissonian Images by a Combined First-Order and Second-Order Variation Approach

Le Jiang,Jin Huang,Jun Liu,Xiao-Guang Lv

doi:10.1155/2013/274573

Abstract

The restoration of blurred images corrupted by Poisson noise is an important topic in imaging science. The problem has recently received considerable attention in recent years. In this paper, we propose a combined first-order and second-order variation model to restore blurred images corrupted by Poisson noise. Our model can substantially reduce the staircase effect, while preserving edges in the restored images, since it combines advantages of the first-order and second-order total variation. We study the issues of existence and uniqueness of a minimizer for this variational model. Moreover, we employ a gradient descent method to solve the associated Euler-Lagrange equation. Numerical results demonstrate the validity and efficiency of the proposed method for Poisson noise removal problem.

Highlights

Image restoration problem has been widely studied in the areas of image processing
We study the issues of existence and uniqueness of a minimizer for this variational model
We present a combined first-order and second-order variation model to restore blurred images corrupted by Poisson noise and study the issues of existence and uniqueness of a minimizer for this variational model

Summary

Introduction

The goal of image restoration is to reconstruct an approximation of an original image from a blurred and noisy one [1,2,3,4]. Given a blurred and noisy image g = Ku + V or g = KuV, where u is the original image, V represents the noise, and the blurring operator K is a point spread function (PSF); the restoration problem involving the additive noise or multiplicative noise is to recover u from the observed image g. The additive noise and multiplicative noise models have been extensively studied. We consider the problem of seeking the approximations of original images from blurred images corrupted by Poisson noise. 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) [20,21,22,23,24]

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Conclusion