﻿ 改进的分裂Bregman方法荧光显微图像复原 Improved Split Bregman Method for Fluorescence Microscopic Image Restoration

Modeling and Simulation
Vol.05 No.03(2016), Article ID:18309,8 pages
10.12677/MOS.2016.53011

Improved Split Bregman Method for Fluorescence Microscopic Image Restoration

Changchun Zhang, Yu Wang*, Hongbing Xiao

School of Computer and Information Engineering, Beijing Technology and Business University, Beijing

Received: Jul. 24th, 2016; accepted: Aug. 14th, 2016; published: Aug. 17th, 2016

ABSTRACT

Fluorescence microscopic image restoration has many very important applications such as astronomical imaging, electronic microscopy, single particle emission computed tomography (SPECT) and positron emission tomography (PET). Traditional total variation imaging restoration based on split Bregman algorithm can preserve sharp edges and save the image texture. Serious staircase effect phenomena, however, is generally accompanied. Therefore an improved image restoration algorithm is proposed based on split Bregman in this paper, which is mainly considered two aspects. One is that the total variation regularization model is used, which is an effective tool to recover blurred images. The other is that the weight function of the total variation is involved, which can not only suppress the staircase effect, but also preserve the image texture information. By appropriately choosing the reasonable parameters, the better restoration results can be obtained. The experimental results on synthetic images and real fluorescence microscopic images show the effectiveness and feasibility of the proposed algorithm.

Keywords:Split Bregman Algorithm, Weighted, Total Variation Regularization, Image Restoration

1. 引言

Brette等人 [13] 提出了基于各项同性扩散的目标边缘保护先验知识，即全变差正则化 [11] 。全变差图像复原是基于变分的思想，把全变差图像复原模型转化为一个偏微分方程求解的过程。目前典型求解方法是根据Wang Yilun、Yang Junfeng等 [14] 提出的基于变量分离和半二次惩罚函数法的快速全变差反卷积算法 [15] (Fast Total Variation deconvolution, FTVd)，把图像复原模型看作是一个无约束问题优化求解，实验结果验证了FTVd的有效性和稳定性。Setzer等 [16] 提出了分裂Bregman算法复原被泊松噪声污染的模糊图像，与其他的图像复原算法相比，它的优点在于不存在内部迭代及迭代过程中不产生负像素值。后来，王静等人 [7] 提出了基于分裂Bregman方法的全变差图像去模糊算法，首先利用辅助变量及其二次惩罚泛函把全变差去模糊优化问题转化成一个等价的无约束优化问题，然后基于Bregman迭代将其分解为两个子优化问题采用交替最小化方法 [15] 进行求解，接着根据子问题结构特点，采用离散傅里叶变换及收缩技术实现子优化问题的快速计算。

2. 相关工作

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2.1. 基本分裂Bregman算法

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s.t.(3)

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2.2. 算法收敛性

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3. 改进的图像复原算法

3.1. 算法改进

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, (14)

s.t.(15)

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3.2. 算法流程

4. 评价准则

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5. 仿真结果与分析

5.1. 合成图像

5.2. 真实图像

Table 1. The flow of the improved split Bregman image restoration method

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Figure 1. Synthetic image (a) original image, (b) degraded image

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Figure 2. Restored images by (a)FTVd-FM method (SNR = 45.50 dB), (b) traditional split Bregman method (SNR = 45.50 dB), (c) our method (SNR = 49.68 dB)

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Figure 3. (a) The degradation of the image, the restored image by the (b) FTVd-FM method, (c) traditional split Bregman method, and (d) our method

(a) (b) (c) (d)

Figure 4. A close-up of (a) Figure 3 (a), the corresponding close-up of (b) Figure 3 (b), (c) Figure 3 (c) and (d) Figure 3 (d)

6. 结束语

Improved Split Bregman Method for Fluorescence Microscopic Image Restoration[J]. 建模与仿真, 2016, 05(03): 81-88. http://dx.doi.org/10.12677/MOS.2016.53011

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