The influence of the regularization parameter and the first estimate on the performance of Tikhonov regularized non-linear image restoration algorithms

This paper reports studies on the influence of the regularization parameter and the first estimate on the performance of iterative image restoration algorithms. We discuss regularization parameter estimation methods that have been developed for the linear Tikhonov–Miller filter to restore images distorted by additive Gaussian noise. We have performed experiments on synthetic data to show that these methods can be used to determine the regularization parameter of non-linear iterative image restoration algorithms, which we use to restore images contaminated by Poisson noise. We conclude that the generalized cross-validation method is an efficient method to determine a value of the regularization parameter close to the optimal value. We have also derived a method to estimate the regularization parameter of a Tikhonov regularized version of the Richardson–Lucy algorithm.   These iterative image restoration algorithms need a first estimate to start their iteration. An obvious and frequently used choice for the first estimate is the acquired image. However, the restoration algorithm could be sensitive to the noise present in this image, which may hamper the convergence of the algorithm. We have therefore compared various choices of first estimates and tested the convergence of various iterative restoration algorithms. We found that most algorithms converged for most choices, but that smoothed first estimates resulted in a faster convergence.     

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.     

电磁层析成像图像重建中的修正共轭梯度算法

通过研究共轭梯度算法,推导出适用于电磁层析成像的修正共轭梯度算法,该方法提高了收敛速度,改善了电磁层析成像重建图像的质量。首先以共轭搜索方向充分下降为充分条件,理论推导出修正共轭梯度算法。然后从相对图像误差、相关系数和收敛曲线几个方面出发,评价了Landweber迭代法、单步Tikhonov正则化方法、共轭梯度法和修正共轭梯度法在电磁层析成像图像重建中的结果,得出结论:修正共轭梯度方法的相对图像误差最小,重建图像和原图像的相关系数最高,收敛情况优于共轭梯度算法。     

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).     

改进恒模盲均衡在医学CT图像盲恢复中的应用

利用图像退化与信号码间干扰产生之间的相似性,将盲均衡算法应用于医学CT(computer tomography)图像的盲恢复中。提出一种基于降维处理的分数低阶恒模盲均衡算法,算法利用线性变换将图像恢复过程等效为一维盲均衡运算,建立了降维处理的医学CT图像盲均衡恒模代价函数,算法权向量的更新中引入了代价函数的二阶Hessian矩阵,从而提高了算法的收敛速度,改善了恒模算法性能。仿真结果验证了算法的有效性,新算法改善了峰值信噪比和恢复效果,提高了运算效率。     

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。     

边缘保持正则化低码率压缩图像后处理算法

从图像恢复的角度,提出以正则化方法完成后处理任务。分析了正则化方法的模型,并给出了边缘保持的正则化函数所应具有的特性。从复杂性、健壮性和对边缘细节粒度控制的能力三个方面选择了相应的势能函数,然后以半二次正则化将能量函数进行转换,使其快速达到最小化。最后给出了整个交替迭代后处理算法的描述。该方法对图像边缘细节具有自适应性,并能较快地取得最小值。实验结果显示,该算法能有效地提高低码率压缩图像的客观质量和视觉效果。     

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。     

基于全局和局部特征融合的图像匹配算法研究

针对移动机器人视觉同时定位与地图构建过程中图像处理速度慢以及特征点匹配实时性和准确性差的问题,提出基于颜色特征和改进SURF算法融合的图像匹配算法。首先,采用颜色特征对图像序列进行粗匹配,选取与测试图像最相近的5幅图像作为待匹配图像;其次,改进SURF算法,用Krawtchouk矩对采用Hessian矩阵获取的关键点进行描述,计算关键点的梯度方向和幅值,得到新的特征向量,对待匹配图像提取改进SURF特征再与测试图像进行精确匹配,得到最佳匹配图像,此匹配算法提高了移动机器人图像处理的速度和精度。实验结果表明,改进算法的误匹配率降低10%左右,程序运行时间减少,在可靠性得到保证的同时适应于实时性应用。