Generalized approach for accelerated maximum likelihood based image restoration applied to three-dimensional fluorescence microscopy

For deconvolution applications in three-dimensional microscopy we derived and implemented a generic, accelerated maximum likelihood image restoration algorithm. A conjugate gradient iteration scheme was used considering either Gaussian or Poisson noise models. Poisson models are better suited to low intensity fluorescent image data; typically, they show smaller restoration errors and smoother results. For the regularization, we modified the standard Tikhonov method. However, the generic design of the algorithm allows for more regularization approaches. The Hessian matrix of the restoration functional was used to determine the step size. We compared restoration error and convergence behaviour between the classical line-search and the Hessian matrix method. Under typical working conditions, the restoration error did not increase over that of the line-search and the speed of convergence did not significantly decrease allowing for a twofold increase in processing speed. To determine the regularization parameter, we modified the generalized cross-validation method. Tests that were done on both simulated and experimental fluorescence wide-field data show reliable results.     

高阶混合正则化图像盲复原方法

提出了一种高阶混合正则化图像盲复原方法,用于实现模糊噪声图像的清晰化盲复原。根据自然图像边缘的稀疏特性,对图像的边缘细节成分进行了全变差(total variation TV)正则化约束,根据自然图像同性质平滑区域内像素值的变化规律,将一种高阶的类Tikhonov正则化约束运用于图像的平滑区域中,提出了一种新的高阶混合正则化模型。最后,提出一种多变量分裂布雷格曼(Multi-variable Split Bregman MSB)最优化迭代策略对提出的模型进行最优化求解。实验结果表明,提出的方法能够很好地保护图像的边缘细节,同时有效地消除图像平滑区域内的阶梯和假边缘瑕疵。与近几年的一些较好的图像盲复原方法相比,本文方法的信噪比增量(increase of the signal to noise ratio ISNR)增加了0.03~2.5 dB。     

Application of regularized Richardson-Lucy algorithm for deconvolution of confocal microscopy images

Although confocal microscopes have considerably smaller contribution of out-of-focus light than widefield microscopes, the confocal images can still be enhanced mathematically if the optical and data acquisition effects are accounted for. For that, several deconvolution algorithms have been proposed. As a practical solution, maximum-likelihood algorithms with regularization have been used. However, the choice of regularization parameters is often unknown although it has considerable effect on the result of deconvolution process. The aims of this work were: to find good estimates of deconvolution parameters; and to develop an open source software package that would allow testing different deconvolution algorithms and that would be easy to use in practice. Here, Richardson-Lucy algorithm has been implemented together with the total variation regularization in an open source software package IOCBio Microscope. The influence of total variation regularization on deconvolution process is determined by one parameter. We derived a formula to estimate this regularization parameter automatically from the images as the algorithm progresses. To assess the effectiveness of this algorithm, synthetic images were composed on the basis of confocal images of rat cardiomyocytes. From the analysis of deconvolved results, we have determined under which conditions our estimation of total variation regularization parameter gives good results. The estimated total variation regularization parameter can be monitored during deconvolution process and used as a stopping criterion. An inverse relation between the optimal regularization parameter and the peak signal-to-noise ratio of an image is shown. Finally, we demonstrate the use of the developed software by deconvolving images of rat cardiomyocytes with stained mitochondria and sarcolemma obtained by confocal and widefield microscopes.     

应用Hopfield神经网络和小波域隐Markov树模型的图像复原

为了解决传统的Hopfield神经网络图像复原算法对噪声抑制和图像细节保护不能很好兼顾的问题,提出了一种基于改进的连续Hopfield神经网络和小波域隐Markov树(HMT)模型的复原算法。将小波域HMT模型作为图像小波系数统计关系的先验知识,并以正则化项的形式引入到神经网络模型中,最终利用Hopfield神经网络的能量收敛特性完成图像复原。同时,提出了一种高度并行的网络权值矩阵计算方法,通过对模板图像进行算子操作,分批求取网络权值,避免了大型矩阵的乘法运算。实验结果表明,无论是对真实图像还是人工生成图像,算法复原结果的视觉效果均有明显改善,提高信噪比(ISNR)较传统同类算法增加0.3dB以上,达到了同时抑制噪声和保护图像细节的目的。     

一种Lucy-Richardson算法和小波变换结合的图像复原算法

Lucy-Richardson(LR)算法作为图像复原的经典算法之一,在进行图像复原时,对退化过程的先验知识要求少且复原效果好,然而由于算法采用迭代逼近的方法,故算法耗时长。针对这一缺点,用LR算法与小波变换结合的图像复原算法(即联合算法),分级对图像进行处理,在减小噪声干扰的同时提高算法的恢复效率。实验结果证明该方法在合理的范围内,以牺牲部分复原效果为代价却有效地提高了复原算法的效率。     

Increasing axial resolution of 3D data sets using deconvolution algorithms

Deconvolution algorithms are tools for the restoration of data degraded by blur and noise. An incorporation of regularization functions into the iterative form of reconstruction algorithms can improve the restoration performance and characteristics (e.g. noise and artefact handling). In this study, algorithms based on Richardson-Lucy deconvolution algorithm are tested. The ability of these algorithms to improve axial resolution of three-dimensional data sets is evaluated on model synthetic data. Finally, unregularized Richardson-Lucy algorithm is selected for the evaluation and reconstruction of three-dimensional chromosomal data sets of Drosophila melanogaster. Problems concerning the reconstruction process are discussed and further improvements are proposed.     

基于各向异性Markov随机场的三维显微图像复原

提出了基于小波域各向异性马尔可夫随机场模型的三维显微图像复原算法。小波是当前研究的热点,它能够很好地刻画图像的边缘信息。为了有效地保留图像的边缘,根据小波变换后各个子带小波系数的方向性特点,以各向异性马尔可夫随机场模型作为小波系数的先验概率模型进行正则化处理;本文采用正则化比例系数自适应调整方法,当算法收敛到全局最优时,正则化比例系数也达到最优选择;考虑到噪声的影响,算法在每一步迭代求解过程中,对估计出的图像进行去噪处理。实验结果表明,本文算法能够有效地保留图像边缘等细节信息,去除层间干扰并抑制噪声。     

One method for restoration of blurred images

A new method is proposed to reduce image distortions caused by random noise and rectilinear uniform motion of the object or recording system. The of a restoration model is based on a statistical regularization method, and the obtained system of linear equations and inequalities is solved using a multistep support vector method. An advantage of this approach is that the iterative nature of the algorithm makes it possible to take into account the a priori information on the solution represented by the inequalities. The results of numerical experiments showing the efficiency of the algorithm are given.     

自适应背景光估计与非局部先验的水下图像复原

有效地实现单幅水下降质图像复原对水下资源探索及环境监控领域的清晰图像获取具有极其重要的意义。为解决常用暗通道先验方法来复原图像时,背景光的估计易受白色物体干扰,且无法有效估计前景中白色物体透射率,复原质量不高的问题。本文提出了自适应背景光估计与非局部先验的水下图像复原算法。首先根据背景光具有高亮度及平坦性的特点,利用阈值分割算法获得背景光的候选区域,再通过图像的色调信息从候选信息中选取最佳的背景光点。随后,利用各颜色通道光的波长与散射系数的相关性,提出了适用于水下图像的非局部先验,并利用该先验估计各通道的透射率。最后针对复原结果中,因水下介质,微生物,水流影响而产生的加性噪声,设计去噪的最小优化问题,并利用引导滤波求解该问题,以去除复原结果中的加性噪声。实验表明:该算法在确保运行效率的基础上,准确地估计透射率,较常用算法的复原精度提高了约18%。证明了该算法能有效用于单幅水下图像复原的工程实践中。     

基于小波变换的正则化盲图像复原算法

提出了一种将小波变换和自适应正则化方法相结合的盲图像复原算法。该算法先对退化后的图像进行小波分解,得到图像在不同子频段的信息;然后针对各个子频段内图像的频率和方向特性,使用不同的自适应正则化复原方法,在图像的低频子频段进行去模糊;高频子频段则进行抑制噪声和保边缘特征;最后通过小波逆变换得到复原后的图像。实验结果表明, MSE减少了1.60,信噪比增量为1.76,算法性能和复原效果相对空间自适应正则化方法,都有一定的提高。     

抑制寄生波纹的红外图像降晰函数辨识算法

提出了一种针对军事目标红外模糊图像复原的降晰函数辨识算法。该算法根据气动光学效应形成湍流流场的机理建立相应的模型,将点扩展函数简化为可用参数描述的高斯函数形式;利用红外图像的边缘梯度变化特性提出边缘清晰度改善量,并作为降晰函数参数辨识的评价标准,清晰度改善量取最大值时对应的参数就是观测图像的最佳降晰函数参数;针对复原过程中可能出现的振铃效应,运用细节规整化思想衍生的加权空间复原算法,自适应地抑制寄生波纹的产生。实验验证表明,本文方法能有效地复原红外模糊图像,且对降晰函数的辨识准确率高,相对误差可以降低至4.5%左右。另外,抑制振铃寄生波纹效果良好。复原后图像在各项质量评价指标上都有很大提高,峰值信噪比提高量超过9.4dB,综合评价指数ImageQ提高了20以上。     

A comparison of image restoration approaches applied to three-dimensional confocal and wide-field fluorescence microscopy

We have compared different image restoration approaches for fluorescence microscopy. The most widely used algorithms were classified with a Bayesian theory according to the assumed noise model and the type of regularization imposed. We considered both Gaussian and Poisson models for the noise in combination with Tikhonov regularization, entropy regularization, Good's roughness and without regularization (maximum likelihood estimation). Simulations of fluorescence confocal imaging were used to examine the different noise models and regularization approaches using the mean squared error criterion. The assumption of a Gaussian noise model yielded only slightly higher errors than the Poisson model. Good's roughness was the best choice for the regularization. Furthermore, we compared simulated confocal and wide-field data. In general, restored confocal data are superior to restored wide-field data, but given sufficient higher signal level for the wide-field data the restoration result may rival confocal data in quality. Finally, a visual comparison of experimental confocal and wide-field data is presented.     

运动模糊图像的实时恢复算法

提出了一种新的处理运动模糊图像的方法,以一维维纳滤波(1DWF)来快速恢复二维的模糊图像。给出了1DWF算法可行性的理论论证,并给出了1DWF算法及其它常用图像恢复算法的实验结果和对比评价。运算量分析表明:1DWF算法的运算量只有二维维纳滤波运算量的1/3;实验结果显示:在P4 3.0G主频的PC机上,1DWF算法可以使得512×512的8位灰度测试图像在36 ms内完成图像恢复。对图像恢复质量的评价结果显示:1DWF算法的图像恢复质量与原维纳滤波的恢复效果相同,验证了在单处理器上实时、高质恢复模糊图像的可行性。     

基于非负支撑域受限递归逆滤波的自适应图像盲复原

针对原始非负支撑域受限递归逆滤波(NAS-RIF)算法存在的缺点,提出了一种自适应的NAS-RIF图像盲复原算法.首先,在NAS RIF算法的代价函数中加入正则化约束项和空域加权因子,通过自适应地调整正则化参数和空域加权因了来改善算法的抗噪性能,并确保复原的逼真和平滑.然后,在算法的每次迭代中,采用图像分割技术找到准确的目标支持域,并用背景的平均值取代非均匀背景.最后,利用N步重置共轭梯度法优化代价函数,加快了算法的收敛速度.在不同信噪比条件下对两种模糊图像进行了实验,结果显示,采用本文算法得到的信噪比增益(△SNR)分别为6.315 3 dB和8.910 6 dB,表明该算法具有较好的噪声抑制和边缘细节恢复效果.对低信噪比的退化图像,本文算法也能得到更好的复原结果.     

基于L0稀疏先验的相机抖动模糊图像盲复原

提出了一种基于L0稀疏先验的改进正则化模糊图像盲复原算法来解决相机抖动所产生的模糊问题。根据模糊图像的梯度分布要比清晰图像稠密并且暗通道的稀疏性也相对较小这一固有属性建立了新的优化模型。针对L0范数的高度非凸性和暗通道稀疏优化过程中涉及到的非线性最小化问题,提出了一种近似线性映射矩阵,并用半二次分解法对L0最小化问题进行求解。最后,采用快速傅里叶变换在频域中对模糊核及清晰图像进行交替迭代运算得到复原图像。对多幅不同类型的模糊图像进行了实验,结果显示:复原图像平均灰度梯度高达11.411,图像信息熵达到7.304,处理365×285的图像只需8.07s。提出的算法有效抑制了图像边缘处的振铃效应,完整保留了清晰的细节信息的同时显著提高了运算速度,并适用于多种不同类型图像的盲复原。     

空间目标图像的非凸稀疏正则化波后复原

现有的空间目标图像波后处理方法多直接套用自然光学图像的复原技术,效果并不理想。本文通过分析空间目标图像的近似稀疏性和灰度值服从超拉普拉斯分布的独有特点,提出了一个采用正则化方法的非凸稀疏正则化空间目标图像复原模型。在数值计算过程中,根据交替方向乘数法将复原模型分解为两个子问题,对凸优化子问题采用快速傅里叶变换求解,对非凸优化子问题采用固定点迭代方法求解。文中设计了非凸稀疏正则化空间目标图像波后复原的完整算法流程,并针对模拟图像和真实空间目标图像进行了对比验证。结果显示:相对于最近的流行算法,提出方法的最大峰值信噪比提高了2dB,最大平均结构相似度提高了0.17,最大信息熵提高了3.85,图像清晰度提高了2.65。     

Noise suppression of point spread functions and its influence on deconvolution of three-dimensional fluorescence microscopy image sets

The point spread function (PSF) is of central importance in the image restoration of three-dimensional image sets acquired by an epifluorescent microscope. Even though it is well known that an experimental PSF is typically more accurate than a theoretical one, the noise content of the experimental PSF is often an obstacle to its use in deconvolution algorithms. In this paper we apply a recently introduced noise suppression method to achieve an effective noise reduction in experimental PSFs. We show with both simulated and experimental three-dimensional image sets that a PSF that is smoothed with this method leads to a significant improvement in the performance of deconvolution algorithms, such as the regularized least-squares algorithm and the accelerated Richardson–Lucy algorithm.     

利用相位差异技术恢复宽带白光图像

研究了用于扩展目标成像的相位差异技术。该技术利用焦面和离焦面上的两幅图像之间的相位差异来估算波前相位畸变,同时对采集的图像进行恢复。设计了白光目标成像实验系统,用宽带白光作光源,在实验室搭建实验平台,模拟无穷远处目标和波前相位畸变。采用直角梯形分光棱镜将光路分为两个通道,在一台相机上同时采集两个通道像面上的图像,消除了相机不同产生的差异,极大地抑制了噪声对图像恢复的影响,分光后系统抗两个通道独立的高斯白噪声的能力为10%。实验结果显示恢复后的图像分辨率提高了19%,表明该技术是适合光电成像系统的图像恢复技术。     

Projection Error Propagation-based Regularization (PEPR) method for resistivity reconstruction in Electrical Impedance Tomography (EIT)

A novel Projection Error Propagation-based Regularization (PEPR) method is proposed to improve the image quality in Electrical Impedance Tomography (EIT). PEPR method defines the regularization parameter as a function of the projection error developed by difference between experimental measurements and calculated data. The regularization parameter in the reconstruction algorithm gets modified automatically according to the noise level in measured data and ill-posedness of the Hessian matrix. Resistivity imaging of practical phantoms in a Model Based Iterative Image Reconstruction (MoBIIR) algorithm as well as with Electrical Impedance Diffuse Optical Reconstruction Software (EIDORS) with PEPR. The effect of PEPR method is also studied with phantoms with different configurations and with different current injection methods. All the resistivity images reconstructed with PEPR method are compared with the single step regularization (STR) and Modified Levenberg Regularization (LMR) techniques. The results show that, the PEPR technique reduces the projection error and solution error in each iterations both for simulated and experimental data in both the algorithms and improves the reconstructed images with better contrast to noise ratio (CNR), percentage of contrast recovery (PCR), coefficient of contrast (COC) and diametric resistivity profile (DRP).