《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。

• 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
• 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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【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

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

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

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

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

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

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.

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.

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.

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.

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.

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.

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.

5+阅读 · 2019年10月28日
Amy Zhao,Guha Balakrishnan,Frédo Durand,John V. Guttag,Adrian V. Dalca
4+阅读 · 2019年2月25日