《影像数学方法手册》对成像科学中使用的数学技术进行了全面的论述。材料分为两个中心主题,即逆问题(算法重建)和信号和图像处理。主题中的每个部分包括应用程序(建模)、数学、数值方法(使用案例示例)和开放问题。由该领域的专家撰写的报告在数学上是严谨的。

这个扩展和修订的第二版包含了对现有章节的更新和16个重要的数学方法,如图形切割,形态学,离散几何,偏微分方程,保形方法,等等。这些条目是交叉引用的,以便通过连接的主题轻松导航。该手册有印刷和电子两种形式,增加了200多幅插图和扩展的参考书目。

它将使应用数学的学生、科学家和研究人员受益。从事成像工作的工程师和计算机科学家也会发现这本手册很有用。

目录:

  • Linear Inverse Problems
  • Large-Scale Inverse Problems in Imaging
  • Regularization Methods for Ill-Posed Problems
  • Distance Measures and Applications to Multi-Modal Variational Imaging
  • Energy Minimization Methods
  • Compressive Sensing
  • Duality and Convex Programming
  • EM Algorithms
  • Iterative Solution Methods
  • Level Set Methods for Structural Inversion and Image Reconstruction
  • Expansion Methods
  • Sampling Methods
  • Inverse Scattering
  • Electrical Impedance Tomography
  • Synthetic Aperture Radar Imaging
  • Tomography
  • Optical Imaging
  • Photoacoustic and Thermoacoustic Tomography: Image Formation Principles
  • Mathematics of Photoacoustic and Thermoacoustic Tomography
  • Wave Phenomena
  • Statistical Methods in Imaging
  • Supervised Learning by Support Vector Machines
  • Total Variation in Imaging
  • Numerical Methods and Applications in Total Variation Image Restoration
  • Mumford and Shah Model and its Applications to Image Segmentation andImage - - Restoration
  • Local Smoothing Neighborhood Filters
  • Neighborhood Filters and the Recovery of 3D Information
  • Splines and Multiresolution Analysis
  • Gabor Analysis for Imaging
  • Shape Spaces
  • Variational Methods in Shape Analysis
  • Manifold Intrinsic Similarity
  • Image Segmentation with Shape Priors: Explicit Versus Implicit - Representations
  • Starlet Transform in Astronomical Data Processing
  • Differential Methods for Multi-Dimensional Visual Data Analysis
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相关内容

数字图像处理(Digital Image Processing)是通过计算机对图像进行去除噪声、增强、复原、分割、提取特征等处理的方法和技术。数字图像处理的产生和迅速发展主要受三个因素的影响:一是计算机的发展;二是数学的发展(特别是离散数学理论的创立和完善);三是广泛的农牧业、林业、环境、军事、工业和医学等方面的应用需求的增长。

在Python中获得操作、处理、清理和处理数据集的完整说明。本实用指南的第二版针对Python 3.6进行了更新,其中包含了大量的实际案例研究,向您展示了如何有效地解决广泛的数据分析问题。在这个过程中,您将学习最新版本的panda、NumPy、IPython和Jupyter。

本书由Python panda项目的创建者Wes McKinney编写,是对Python中的数据科学工具的实用的、现代的介绍。对于刚接触Python的分析人员和刚接触数据科学和科学计算的Python程序员来说,它是理想的。数据文件和相关材料可以在GitHub上找到。

  • 使用IPython外壳和Jupyter笔记本进行探索性计算
  • 学习NumPy (Numerical Python)中的基本和高级特性
  • 开始使用pandas库的数据分析工具
  • 使用灵活的工具来加载、清理、转换、合并和重塑数据
  • 使用matplotlib创建信息可视化
  • 应用panda groupby工具对数据集进行切片、切割和汇总
  • 分析和处理有规律和不规则的时间序列数据
  • 学习如何解决现实世界的数据分析问题与彻底的,详细的例子
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题目: Handbook of Mathematical Methods in Imaging

摘要: 该书全面介绍了成像科学中使用的数学技术。材料分为两个中心主题,即反问题(算法重建)和信号与图像处理。主题中的每个部分都涵盖了应用(建模)、数学、数值方法(使用一个实例)和开放性问题。由该领域的专家撰写的报告,在数学上是严谨的。条目是交叉引用的,以便在连接的主题中轻松导航。这本手册有印刷版和电子版两种形式,增加了150多幅插图和扩展书目。

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【导读】一些独特的医学成像视角,如前沿的成像方法、数据分析、与神经认知功能更好的相关性,以及疾病监测的详细示例和总结,可能有助于传达医学成像原理和应用的方法学、技术和发展信息。这本书的目的是为初学者和医学成像领域的专家提供一般的图像和详细的描述成像原理和临床应用。具有最前沿的应用和最新的分析方法,这本书将有望获取医疗成像研究领域的同事的兴趣。精确的插图和彻底的审查,在许多研究课题,如神经成像定量和相关性,以及癌症诊断,是这本书的优势。

  1. 结构和功能连接的纵向变化以及与神经认知指标的相关性 (Longitudinal Changes of Structural and Functional Connectivity and Correlations with Neurocognitive Metrics)By Yongxia Zhou

考虑到许多与年龄相关的风险,包括血管和神经炎症的增加,以及可能混淆基准功能磁共振参数图像,在相对较短的时间内揭示个体水平上的脑功能和微观结构变化尤其重要。细胞水平的轴索损伤和/或脱髓鞘以及弥散的中观水平物质异常聚集和结构/功能异常可在短的亚急性/急性期发生,而与年龄纵向变化相关的文献仅局限于我们以前的fMRI发现。纵向数据用来描述这些多参数,包括随机截距和个体间隔。性别交互作用对DTI分数各向异性(FA)和扩散系数均无显著影响。区间有效区域表现出FA的纵向变化,径向扩散系数(RD)/轴向扩散系数(AX)值与截面数据的老化结果相似。在DTI和fMRI指标之间,以及成像和神经认知数据(包括速度和记忆力)之间,发现了显著的相关性。我们的结果表明,年龄、性别和载脂蛋白E (APOE)基因型对结构和功能连接在短间隔和横断面范围内的显著和一致的影响,以及相关的神经认知功能。

https://www.intechopen.com/books/medical-imaging-principles-and-applications/longitudinal-changes-of-structural-and-functional-connectivity-and-correlations-with-neurocognitive-

  1. 功能磁共振成像在神经性疼痛中的应用 The Application of Functional Magnetic Resonance Imaging in Neuropathic Pain By Zhi Dou and Liqiang Yang

在过去,神经性疼痛一直缺乏理想的影像学研究方法,这不仅限制了我们对神经性疼痛发病机制的研究,而且严重影响了治疗的预后。近年来,随着fMRI技术的飞速发展,越来越多的学者开始将fMRI技术应用于神经性疼痛的研究。这为揭示神经性疼痛的内在机制和改进临床治疗理念提供了新的思路。在这一章中,我们对fMRI在神经性疼痛中的最新研究进行了综述,以便读者更好的了解研究现状和未来的研究方向。

https://www.intechopen.com/books/medical-imaging-principles-and-applications/the-application-of-functional-magnetic-resonance-imaging-in-neuropathic-pain

  1. 电离辐射与物质的相互作用,x射线计算机断层成像,核医学SPECT, PET和PET- ct断层成像 The Ionizing Radiation Interaction with Matter, the X-ray Computed Tomography Imaging, the Nuclear Medicine SPECT, PET and PET-CT Tomography Imaging By Evangelos Gazis

描述了重带电粒子、电子和光子与物质的电离辐射相互作用的机理。这些影响造成能量损失的辐射与吸收或衰减的顺序效应提出。介绍了几种具有相关电子学和数据采集系统(DAQ)的特征检测系统的特点。这些探测器与医学成像传感器系统有关。介绍了单光子计算机断层扫描(SPECT)、正子断层扫描(PET)和PET- ct联合成像在医学成像过程中的特点。计算机x射线断层摄影,称为CT,和核医学断层摄影被提出,实现了大部分以前的部分,因为他们被定义为PET和SPECT成像加上PET与CT的结合PET-CT。

https://www.intechopen.com/books/medical-imaging-principles-and-applications/the-ionizing-radiation-interaction-with-matter-the-x-ray-computed-tomography-imaging-the-nuclear-med

  1. PET-CT的原理及其在肺癌治疗中的应用 PET-CT Principles and Applications in Lung Cancer Management By Long Chen, Hua Sun and Yunchao Huang

肺癌是世界上最常见的恶性肿瘤;正电子发射断层扫描(PET-CT)结合了来自PET的新陈代谢信息和来自CT的解剖学细节,这是目前最先进的技术。本文介绍了PET-CT及其在肺癌诊断、分期和治疗中的应用。从肺癌的临床特点、分型、分级、病理、PET-CT的原则、诊断和治疗的评价等方面进行了综述。详细说明了每种癌症亚型、分期标准和分类。内容将有利于临床医生以及放射科医生。

https://www.intechopen.com/books/medical-imaging-principles-and-applications/pet-ct-principles-and-applications-in-lung-cancer-management

  1. 医学影像处理技术的研究 Research in Medical Imaging Using Image Processing Techniques By Yousif Mohamed Y. Abdallah and Tariq Alqahtani

医学成像是为了识别或研究疾病而获取身体部位的医学图像的过程。全世界每周都有数百万的成像过程。由于图像处理技术的发展,包括图像识别、分析和增强,医学影像正在迅速发展。图像处理增加了检测组织的百分比和数量。本章介绍了简单和复杂的图像分析技术在医学成像领域的应用。本章还总结了如何使用不同的图像处理算法(如k-means、基于roi的分割和分水岭技术)来举例说明图像解释的挑战。

https://www.intechopen.com/books/medical-imaging-principles-and-applications/research-in-medical-imaging-using-image-processing-techniques

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We study the impact of neural networks in text classification. Our focus is on training deep neural networks with proper weight initialization and greedy layer-wise pretraining. Results are compared with 1-layer neural networks and Support Vector Machines. We work with a dataset of labeled messages from the Twitter microblogging service and aim to predict weather conditions. A feature extraction procedure specific for the task is proposed, which applies dimensionality reduction using Latent Semantic Analysis. Our results show that neural networks outperform Support Vector Machines with Gaussian kernels, noticing performance gains from introducing additional hidden layers with nonlinearities. The impact of using Nesterov's Accelerated Gradient in backpropagation is also studied. We conclude that deep neural networks are a reasonable approach for text classification and propose further ideas to improve performance.

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Biomedical image segmentation is an important task in many medical applications. Segmentation methods based on convolutional neural networks attain state-of-the-art accuracy; however, they typically rely on supervised training with large labeled datasets. Labeling datasets of medical images requires significant expertise and time, and is infeasible at large scales. To tackle the lack of labeled data, researchers use techniques such as hand-engineered preprocessing steps, hand-tuned architectures, and data augmentation. However, these techniques involve costly engineering efforts, and are typically dataset-specific. We present an automated data augmentation method for medical images. We demonstrate our method on the task of segmenting magnetic resonance imaging (MRI) brain scans, focusing on the one-shot segmentation scenario -- a practical challenge in many medical applications. Our method requires only a single segmented scan, and leverages other unlabeled scans in a semi-supervised approach. We learn a model of transforms from the images, and use the model along with the labeled example to synthesize additional labeled training examples for supervised segmentation. Each transform is comprised of a spatial deformation field and an intensity change, enabling the synthesis of complex effects such as variations in anatomy and image acquisition procedures. Augmenting the training of a supervised segmenter with these new examples provides significant improvements over state-of-the-art methods for one-shot biomedical image segmentation. Our code is available at https://github.com/xamyzhao/brainstorm.

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Multispectral imaging is an important technique for improving the readability of written or printed text where the letters have faded, either due to deliberate erasing or simply due to the ravages of time. Often the text can be read simply by looking at individual wavelengths, but in some cases the images need further enhancement to maximise the chances of reading the text. There are many possible enhancement techniques and this paper assesses and compares an extended set of dimensionality reduction methods for image processing. We assess 15 dimensionality reduction methods in two different manuscripts. This assessment was performed both subjectively by asking the opinions of scholars who were experts in the languages used in the manuscripts which of the techniques they preferred and also by using the Davies-Bouldin and Dunn indexes for assessing the quality of the resulted image clusters. We found that the Canonical Variates Analysis (CVA) method which was using a Matlab implementation and we have used previously to enhance multispectral images, it was indeed superior to all the other tested methods. However it is very likely that other approaches will be more suitable in specific circumstance so we would still recommend that a range of these techniques are tried. In particular, CVA is a supervised clustering technique so it requires considerably more user time and effort than a non-supervised technique such as the much more commonly used Principle Component Analysis Approach (PCA). If the results from PCA are adequate to allow a text to be read then the added effort required for CVA may not be justified. For the purposes of comparing the computational times and the image results, a CVA method is also implemented in C programming language and using the GNU (GNUs Not Unix) Scientific Library (GSL) and the OpenCV (OPEN source Computer Vision) computer vision programming library.

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We introduce a new multi-dimensional nonlinear embedding -- Piecewise Flat Embedding (PFE) -- for image segmentation. Based on the theory of sparse signal recovery, piecewise flat embedding with diverse channels attempts to recover a piecewise constant image representation with sparse region boundaries and sparse cluster value scattering. The resultant piecewise flat embedding exhibits interesting properties such as suppressing slowly varying signals, and offers an image representation with higher region identifiability which is desirable for image segmentation or high-level semantic analysis tasks. We formulate our embedding as a variant of the Laplacian Eigenmap embedding with an $L_{1,p} (0<p\leq1)$ regularization term to promote sparse solutions. First, we devise a two-stage numerical algorithm based on Bregman iterations to compute $L_{1,1}$-regularized piecewise flat embeddings. We further generalize this algorithm through iterative reweighting to solve the general $L_{1,p}$-regularized problem. To demonstrate its efficacy, we integrate PFE into two existing image segmentation frameworks, segmentation based on clustering and hierarchical segmentation based on contour detection. Experiments on four major benchmark datasets, BSDS500, MSRC, Stanford Background Dataset, and PASCAL Context, show that segmentation algorithms incorporating our embedding achieve significantly improved results.

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Many problems on signal processing reduce to nonparametric function estimation. We propose a new methodology, piecewise convex fitting (PCF), and give a two-stage adaptive estimate. In the first stage, the number and location of the change points is estimated using strong smoothing. In the second stage, a constrained smoothing spline fit is performed with the smoothing level chosen to minimize the MSE. The imposed constraint is that a single change point occurs in a region about each empirical change point of the first-stage estimate. This constraint is equivalent to requiring that the third derivative of the second-stage estimate has a single sign in a small neighborhood about each first-stage change point. We sketch how PCF may be applied to signal recovery, instantaneous frequency estimation, surface reconstruction, image segmentation, spectral estimation and multivariate adaptive regression.

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Image segmentation is the process of partitioning the image into significant regions easier to analyze. Nowadays, segmentation has become a necessity in many practical medical imaging methods as locating tumors and diseases. Hidden Markov Random Field model is one of several techniques used in image segmentation. It provides an elegant way to model the segmentation process. This modeling leads to the minimization of an objective function. Conjugate Gradient algorithm (CG) is one of the best known optimization techniques. This paper proposes the use of the Conjugate Gradient algorithm (CG) for image segmentation, based on the Hidden Markov Random Field. Since derivatives are not available for this expression, finite differences are used in the CG algorithm to approximate the first derivative. The approach is evaluated using a number of publicly available images, where ground truth is known. The Dice Coefficient is used as an objective criterion to measure the quality of segmentation. The results show that the proposed CG approach compares favorably with other variants of Hidden Markov Random Field segmentation algorithms.

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Image segmentation is still an open problem especially when intensities of the interested objects are overlapped due to the presence of intensity inhomogeneity (also known as bias field). To segment images with intensity inhomogeneities, a bias correction embedded level set model is proposed where Inhomogeneities are Estimated by Orthogonal Primary Functions (IEOPF). In the proposed model, the smoothly varying bias is estimated by a linear combination of a given set of orthogonal primary functions. An inhomogeneous intensity clustering energy is then defined and membership functions of the clusters described by the level set function are introduced to rewrite the energy as a data term of the proposed model. Similar to popular level set methods, a regularization term and an arc length term are also included to regularize and smooth the level set function, respectively. The proposed model is then extended to multichannel and multiphase patterns to segment colourful images and images with multiple objects, respectively. It has been extensively tested on both synthetic and real images that are widely used in the literature and public BrainWeb and IBSR datasets. Experimental results and comparison with state-of-the-art methods demonstrate that advantages of the proposed model in terms of bias correction and segmentation accuracy.

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