Research of ECG Inverse Problem Based on ADMM Iterative Algorithm

心电图是心脏电活动的反映，可以通过传感器来测量人体表面电位得到。心电图是一种使用最广泛的常规临床诊断工具，它能够准确地反映出病人的心脏健康状况，降低诊断成本，对于心脏疾病的诊断具有非常重要的意义。 心电逆问题研究的主要目标是还原心电图，它首先通过体表电位测量仪得到体表电位，接着通过CT影像获取的心脏和躯干的几何信息计算出传递矩阵，然后运用数学方法求解心电逆问题方程，从而获得心外膜电位分布，最后据此诊断心脏的病理状况。求解心电逆问题最大的难点是其不适定性和解的非唯一性。论文采用基于心外膜电位的心电逆问题研究，能够很好地克服解的非唯一性这一难点。为了克服不适定性，需要引入正则化技术来解决，常用的...The electrocardiogram is a reflection of the electrical activity of the heart which can be obtained by measuring the body surface potential by the sensor. ECG is one of the most widely used clinical diagnostic tools, it can accurately reflect the patient's heart health, reduce the cost of diagnosis, which is of great significance for heart disease. The main goal of the study of ECG inverse proble...学位：工程硕士院系专业：信息科学与技术学院_工程硕士(计算机技术)学号：2302014115318

Sparse Targets Angular Super-resolution Reconstruction Method under Unknown Antenna Pattern Errors for Scanning Radar

Scanning radar angular super-resolution technology is based on the relationship between the target and antenna pattern, and a deconvolution method is used to obtain angular resolution capabilities beyond the real beam. Most current angular super-resolution methods are based on ideal distortion-free antenna patterns and do not consider pattern changes in the actual process due to the influence of factors such as radar radome, antenna measurement errors, and non-ideal platform motion. In practice, an antenna pattern often has unknown errors, which can result in reduced target resolution and even false target generation. To address this problem, this paper proposes an angular super-resolution imaging method for airborne radar with unknown antenna errors. First, based on the Total Least Square (TLS) criterion, this paper considers the effect of the pattern error matrix and derive the corresponding objective function. Second, this paper employs the iterative reweighted optimization method to solve the objective function by adopting an alternative iteration solution idea. Finally, an adaptive parameter update method is introduced for algorithm hyperparameter selection. The simulation and experimental results demonstrate that the proposed method can achieve super-resolution reconstruction even in the presence of unknown antenna errors, promoting the robustness of the super-resolution algorithm

Convolutional neural network's image moment regularizing strategy

卷积神经网络的池化策略包含极大池化和平均池化,极大池化选择池化区域中的最大值,极易出现过抑合现象;平均池化对池化区域中所有元素赋予相同权重,降低了高频分量的权重。本文提出将矩池化作为卷积神经网络的正则化策略,矩池化将几何矩概念引入到卷积神经网络的池化过程中,首先计算池化区域的中心矩,然后根据类插值法依概率随机地从中心矩的4个邻域中选择响应值。在数据集MNIST、CIFAR10、CIFAR100上的实验结果表明随着训练迭代次数的增加,矩池化的训练误差和测试误差最低,矩池化的高差别性和强鲁棒性使其获得了比极大池化和平均池化更好的泛化能力。There are two kinds of pooling strategies for convolutional neural network( CNN) as follows: max pooling and average pooling. Max pooling simply chooses the maximum element,which makes this strategy extremely prone to overfitting. Average pooling endows all elements with the same weight,which lowers the weight of the high-frequency components. In this study,we propose moment pooling as a regularization strategy for CNN. First,we introduce the geometric moment to CNN pooling and calculate the central moment of the pooling region. Then,we randomly select the response values based on the probability-like interpolation method from the four neighbors of the moment as per their probability. Experiments on the MNIST,CIFAR10,and CIFAR100 datasets show that moment pooling obtains the fewest training and test errors with training iteration increments. This strategy's robustness and strong discrimination capability yield better generalization results than those from the max and average pooling methods.国家自然科学基金资助项目(61202143,61572409);; 福建省自然科学基金资助项目(2013J05100

The Low-rank Matrix Completion Based on S_1/2 Modeling and the Research of its APG Algorithm

低秩矩阵填充问题（Low-rankMatrixCompletion）是指对于有部分位置上元素未知的矩阵，在假设矩阵低秩的前提下，可以通过优化算法来将其填充成一个完整的矩阵。低秩矩阵填充在机器学习、图像处理、推荐系统等领域发挥着重要的作用，是现今处理海量、高维数据的有力分析工具。本文首先介绍了低秩矩阵填充模型的理论发展，再分别根据将原模型进行凸松弛和非凸松弛后的改进模型综述了目前主要的算法，其中包括凸松弛的SVT算法，APG算法，ALM算法和非凸松弛的WMMN模型，并分析说明了不同算法在不同的领域，针对不同的模型有着各自的优势。 目前主要用于解决低秩矩阵填充的模型是用矩阵核范数来逼近目标函...Low-rank matrix completion refers to problem that use optimization algorithm to fill a matrix which have unknown elements into a complete matrix.In general,we assume the incomplete matrix is a low-rank matrix.This methods have played an important role in areas such as machine learning, image processing, recommendation systems and so on,it's a powerful analysis tool of high-dimensional data.In this...学位：理学硕士院系专业：数学科学学院_应用数学学号：1902014115262

Novel Edge-preserving Algorithm for Defocus Blurred Image Restoration

图像复原过程中图像的主观视觉质量与图像的局部细节信息之间密切相关。针对散焦模糊图像,提出一种新的图像复原方法。所提方法在传统双边总变分正则化方法基础上,通过引入一种具有结构自适应的局部权值函数,构造了一种新的图像复原目标函数。该目标函数综合考虑了图像的全局与局部统计特性,即在整体保真情况下还充分考虑了图像的局部结构信息,使得所提复原方法能更有效地保持图像的边缘等细节信息。与传统bTV正则化方法的比较实验表明,所提方法在边缘保持方面更有效,复原后的图像具有更好的主、客观视觉质量。Relevant research on image restoration indicates that image's subjective visual quality is closely related to its local details.A novel restoration algorithm for defocus blurred image was proposed.The proposed algorithm based on BTV regularization framework by introducing a local adaptive weighted function constructs a new cost function for ima-ge restoration.This cost function which not only takes into account the global data-fidelity,but also considers the local statistical properties of image,meaning to fully consider the local structural features of image under global data-fidelity,hence behaves much better in edge preservation.Experimental results confirm the effectiveness of the proposed method.The image is restored with better subjective and objective visual quality,compared with other methods such as traditio-nal BTV regularization approach.福建省自然科学基金(2008J0032;2009J01301;2009J01302);厦门大学985二期信息创新平台资助项目(0000-X07204);厦门市科技计划高校创新项目(3502Z20083006)资

Research on Super Resolution Image Reconstruction Based on Edge Preservation

超分辨率图像复原是病态反问题，通常采用基于正则化的方法进行求解。超分辨率图像复原最初只是在频域进行，但是频域方法的观测模型仅局限于全局平移运动模型和线性移不变模糊，实用范围有限，目前研究方法基本都在空域。最大后验概率（Maximumapriori，MAP）方法因为可以在解中可以直接加入先验约束、有较好的降噪能力和收敛稳定性高等特点，是空域法中的一种主流方法。 本文在充分分析各种常用的先验模型对超分辨率复原效果影响的情况下，为了更好的保持图像的弱边缘，基于MAP框架，提出了两种有效的边缘保持超分辨率图像复原方法。一是在双边滤波MAP超分辨率复原方法基础上，提出了基于自适应梯度模板的先验模型正则...SR reconstruction is an ill-posed inverse problem, usually it needs regularization approaches to stabilize the result, and SR reconstruction approach is proposed in frequency domain originally, however the observation model is limited in global translational motion and LSI（Linear shift invariant） blur, the frequency domain related approach is limited in practice, so the spatial domain related appr...学位：工学硕士院系专业：信息科学与技术学院通信工程系_信号与信息处理学号：2332007115216

定量磁化率成像重建方法及其应用

磁共振成像(MRI)中,相位图像包含丰富的组织磁化率变化信息,获取相位图像不需要额外的扫描时间.组织中的顺磁性物质会影响组织磁化率差异,从而导致局部磁场不均匀.对组织内顺磁性物质的定量有利于许多脑血管疾病和神经系统疾病的诊断,但利用局部相位信息重建组织磁化率分布是一个不适定逆问题,目前仍然有许多问题亟待解决.该文着重介绍定量磁化率成像(QSM)的原理、重建方法及其在MRI中的应用.国家自然科学基金资助项目(81171331,11174239);中央高校基本业务费资助项目(2010121101

基于正则化与B样条曲线的桥梁影响线识别方法

为了快速评估既有桥梁的安全性,研究了基于多源实测信息快速准确识别桥梁影响线的方法。首先利用桥梁动力响应及车辆移动的实测信息,建立影响线识别的数学模型。在模型中引入Tikhonov正则化方法以解决病态矩阵求解问题,通过设置罚函数项以取得较光滑并贴近真实的影响线。然后通过基函数扩展法重构影响线,将其表示为一系列三次B样条基函数的线性组合,从而将问题从识别众多影响线因子简化为识别少量基函数权重系数。为了验证上述方法的可行性,先在实验室模拟钢制试验小车在钢筋混凝土三跨连续梁模型上移动的过程。基于实测布置于梁底的多测点挠度和应变响应时程以及相应的试验车信息,可识别出不同位置测点的挠度和应变影响线。试验结果表明无论是影响线的总体形状还是局部峰值,识别解与基准解均能较好地吻合。该方法还被进一步应用到一座简支现浇预应力混凝土箱梁桥。该试验通过实测检测车过桥期间的桥梁跨中截面若干测点的动应变、动挠度以及车辆重力、实时位置等信息,准确识别了对应于不同车道的挠度和应变影响线。通过对比桥梁静载实测和影响线虚拟加载结果,发现两者偏差绝对值在5%以内。在一定程度上表明了该影响线识别方法具有较高精度,并具备工程应用的良好潜力。国家自然科学基金项目(NSFC-51778550);;福建省自然科学基金项目(2017J01101);;厦门市科技局科技计划项目(3502Z20163002);;厦门大学校长基金项目(20720180060

Image Super-resolution Reconstruction Algorithm Based on Spatial Adaptive Regularization

为提高稀疏表示系数的精度和图像的分辨率,提出一种基于稀疏表示和正则化技术的超分重建算法.首先引入自回归正则化项,通过样本图像来训练出描述图像局部; 结构的自回归模型,每个图像块自适应选择一个自回归模型用以调节解空间,实现图像局部的自适应性控制.然后,引入非局部相似正则化项作为自回归正则化项的; 补充,用于保持图像边缘清晰度.从而,完整构造出一种基于自回归正则化和非局部相似正则化的稀疏编码目标函数.为了进一步恢复图像,实现图像去噪、去模糊; ,利用总变分正则化实现全局优化.实验结果表明,与L1SR、SISR、ANR、NE + LS、NE + NNLS、NE + LLE和A + (16; atoms)等算法相比,无论在主观视觉效果还是客观评价指标上,提出的算法都取得了更好的超分重建效果.In order to improve the accuracy of sparse representation coefficients; and the resolution of the image,a novel super reconstruction algorithm; based on sparse representation and regularization technique is proposed.; First,the auto-regressive (AR) regularization term is introduced in; sparse coding objective function. The AR model which describes the local; structure of the image can be trained by using the sample images. And; each image patch adaptively selects an AR model to adjust the solution; space and realize the image local adaptive control. Then,the non-local; (NL) similarity regularization term is introduced as a complement to the; AR regularization term,which is used to preserve the edge sharpness of; the image. Therefore,the sparse coding objective function is constructed; based on the AR regularization and NL similarity regularization. In; order to restore the image and improve the performance of image; denoising and deblurring further,the total-variation regularization is; adopted to realize the global optimization. Experimental results; validate that compared with L1SR,SISR,ANR,NE + LS,NE + NNLS,NE + LLE and; A + (16 atoms) methods,the proposed approach achieves better; super-resolution reconstruction effects in both subjective visual; effects and objective evaluation criteria.国家自然科学基金项目; 泉州市科技计划项目; 华侨大学研究生科研创新能力培育计划项