中图网(原中国图书网):网上书店,尾货特色书店,30万种特价书低至2折!

歡迎光臨中圖網(wǎng) 請 | 注冊

包郵 統(tǒng)計和計算逆問題

出版社:世界圖書出版公司出版時間:2015-01-01
開本: 24開 頁數(shù): 339
中 圖 價:¥35.7(9.2折) 定價  ¥39.0 登錄后可看到會員價
暫時缺貨 收藏
開年大促, 全場包郵
?新疆、西藏除外
本類五星書更多>

統(tǒng)計和計算逆問題 版權(quán)信息

統(tǒng)計和計算逆問題 內(nèi)容簡介

  This book is aimed at postgraduate students in applied mathematics as well as at engineering and physics students with a firm background in mathematics. The first four chapters can be used as the material for a first course on inverse problems with a focus on computational and statistical aspects. On the other hand, Chapters 3 and 4, which discuss statistical and nonstationary inversion methods, can be used by students already having knowldege of classical inversion methods.  There is rich literature, including numerous textbooks, on the classical aspects of inverse problems. From the numerical point of view, these books concentrate on problems in which the measurement errors are either very small or in,which the error properties are known exactly. In real world problems, however, the errors are seldom very small and their properties in the deterministic sense are not well known. For example, in classical literature the error norm is usually assumed to be a known real number. In reality, the error norm is a random variable whose mean might be known.

統(tǒng)計和計算逆問題 目錄

Preface
1 Inverse Problems and Interpretation of Measurements
1.1 Introductory Examples
1.2 Inverse Crimes

2 Classical Regularization Methods
2.1 Introduction: Fredholm Equation
2.2 Truncated Singular Value Decomposition
2.3 Tikhonov Regularization
2.3.1 Generalizations of the Tikhonov Regularization
2.4 Regularization by Truncated Iterative Methods
2.4.1 Landweber-Fridman Iteration
2.4.2 Kaczmarz Iteration and ART
2.4.3 Krylov Subspace Methods
2.5 Notes and Comments

3 Statistical Inversion Theory
3.1 Inverse Problems and Bayes' Formula
3.1.1 Estimators
3.2 Construction of the Likelihood Function
3.2.1 Additive Noise
3.2.2 Other Explicit Noise Models
3.2.3 Counting Process Data
3.3 Prior Models
3.3.1 Gaussian Priors
3.3.2 Impulse Prior Densities
3.3.3 Discontinuities
3.3.4 Markov Random Fields
3.3.5 Sample-based Densities
3.4 Gaussian Densities
3.4.1 Gaussian Smoothness Priors
3.5 Interpreting the Posterior Distribution
3.6 Markov Chain Monte Carlo Methods
3.6.1 The Basic Idea
3.6.2 Metropolis-Hastings Construction of the Kernel
3.6.3 Gibbs Sampler
3.6.4 Convergence
3.7 Hierarcical Models
3.8 Notes and Comments

4 Nonstationary Inverse Problems
4.1 Bayesian Filtering
4.1.1 A Nonstationary Inverse Problem
4.1.2 Evolution and Observation Models
4.2 Kalman Filters
4.2.1 Linear Gaussian Problems
4.2.2 Extended Kalman Filters
4.3 Particle Filters
4.4 Spatial Priors
4.5 Fixed-lag and Fixed-interval Smoothing
4.6 Higher-order Markov Models
4.7 Notes and Comments

5 Classical Methods Revisited
5.1 Estimation Theory
5.1.1 Maximum Likelihood Estimation
5.1.2 Estimators Induced by Bayes Costs
5.1.3 Estimation Error with Affine Estimators
5.2 Test Cases
5.2.1 Prior Distributions
5.2.2 Observation Operators
5.2.3 The Additive Noise Models
5.2.4 Test Problems
5.3 Sample-Based Error Analysis
5.4 Truncated Singular Value Decomposition
5.5 Conjugate Gradient.Iteration
5.6 Tikhonov Regularization
5.6.1 Prior Structure and Regularization Level
5.6.2 Misspeeification of the Gaussian Observation Error Model
5.6.3 Additive Cauchy Errors
5.7 Diseretization and Prior Models
5.8 Statistical Model Reduction, Approximation Errors and Inverse Crimes
5.8.1 An Example: Full Angle Tomography and CGNE
5.9 Notes and Comments

6 Model Problems
6.1 X-ray Tomography
6.1.1 Radon Transform
6.1.2 Discrete Model
6.2 Inverse Source Problems
6.2.1 Quasi-static Maxwell's Equations
6.2.2 Electric Inverse Source Problems
6.2.3 Magnetic Inverse Source Problems
6.3 Impedance Tomography
6.4 Optical Tomography
6.4.1 The Radiation Transfer Equation
6.4.2 Diffusion Approximation
6.4.3 Time-harmonic Measurement
6.5 Notes and Comments

7 Case Studies
7.1 Image Deblurring and Recovery of Anomalies
7.1.1 The Model Problem
7.1.2 Reduced and Approximation Error Models
7.1.3 Sampling the Posterior Distribution
7.1.4 Effects of Modelling Errors
7.2 Limited Angle Tomography: Dental X-ray Imaging
7.2.1 The Layer Estimation
7.2.2 MAP Estimates
7.2.3 Sampling: Gibbs Sampler
7.3 Biomagnetic Inverse Problem: Source Localization
7.3.1 Reconstruction with Gaussian White Noise Prior Model
7.3.2 Reconstruction of Dipole Strengths with the e1-prior Model
7.4 Dynamic MEG by Bayes Filtering
7.4.1 A Single Dipole Model
7.4.2 More Realistic Geometry
7.4.3 Multiple Dipole Models
7.5 Electrical Impedance Tomography: Optimal Current Patterns
7.5.1 A Posteriori Synthesized Current Patterns
7.5.2 Optimization Criterion
7.5.3 Numerical Examples
7.6 Electrical Impedance Tomography: Handling Approximation Errors
7.6.1 Meshes and Projectors
7.6.2 The Prior Distribution and the Prior Model
7.6.3 The Enhanced Error Model
7.6.4 The MAP Estimates
7.7 Electrical Impedance Process Tomography
7.7.1 The Evolution Model
7.7.2 The Observation Model and the Computational Scheme
7.7.3 The Fixed-lag State Estimate
7.7.4 Estimation of the Flow Profile
7.8 Optical Tomography in Anisotropic Media
7.8.1 The Anisotropy Model
7.8.2 Linearized Model
7.9 Optical Tomography: Boundary Recovery
7.9.1 The General Elliptic Case
7.9.2 Application to Optical Diffusion Tomography
7.10 Notes and Comments

A Appendix: Linear Algebra and Functional Analysis
A.1 Linear Algebra
A.2 Functional Analysis
A.3 Sobolev Spaces
B Appendix 2: Basics on Probability
B.1 Basic Concepts
B.2 Conditional Probabilities
References
Index
展開全部

統(tǒng)計和計算逆問題 作者簡介

Jari Kaipio(J. 凱皮奧,芬蘭)是國際知名學(xué)者,在數(shù)學(xué)和物理學(xué)界享有盛譽。本書凝聚了作者多年科研和教學(xué)成果,適用于科研工作者、高校教師和研究生。

商品評論(0條)
暫無評論……
書友推薦
本類暢銷
編輯推薦
返回頂部
中圖網(wǎng)
在線客服
主站蜘蛛池模板: 哈尔滨治「失眠/抑郁/焦虑症/精神心理」专科医院排行榜-京科脑康免费咨询 一对一诊疗 | 德州万泰装饰 - 万泰装饰装修设计软装家居馆 | 带压开孔_带压堵漏_带压封堵-菏泽金升管道工程有限公司 | 自恢复保险丝_贴片保险丝_力特保险丝_Littelfuse_可恢复保险丝供应商-秦晋电子 | 离子色谱自动进样器-青岛艾力析实验科技有限公司 | 电销卡_稳定企业大语音卡-归属地可选-世纪通信 | 板框压滤机-隔膜压滤机-厢式压滤机生产厂家-禹州市君工机械设备有限公司 | 纳米二氧化硅,白炭黑,阴离子乳化剂-臻丽拾科技 | 半自动预灌装机,卡式瓶灌装机,注射器灌装机,给药器灌装机,大输液灌装机,西林瓶灌装机-长沙一星制药机械有限公司 | 长沙网站建设制作「网站优化推广」-网页设计公司-速马科技官网 | 行业分析:提及郑州火车站附近真有 特殊按摩 ?2025实地踩坑指南 新手如何避坑不踩雷 | 铝箔-铝板-花纹铝板-铝型材-铝棒管-上海百亚金属材料有限公司 | 杭州厂房降温,车间降温设备,车间通风降温,厂房降温方案,杭州嘉友实业爽风品牌 | 闭端端子|弹簧螺式接线头|防水接线头|插线式接线头|端子台|电源线扣+护线套|印刷电路板型端子台|金笔电子代理商-上海拓胜电气有限公司 | 精密光学实验平台-红外粉末压片机模具-天津博君 | 升降机-高空作业车租赁-蜘蛛车-曲臂式伸缩臂剪叉式液压升降平台-脚手架-【普雷斯特公司厂家】 | 便携式谷丙转氨酶检测仪|华图生物科技百科 | 上海橡胶接头_弹簧减震器_金属软接头厂家-上海淞江集团 | 长沙一级消防工程公司_智能化弱电_机电安装_亮化工程专业施工承包_湖南公共安全工程有限公司 | 上海盐水喷雾试验机_两厢式冷热冲击试验箱-巨怡环试 | 5L旋转蒸发器-20L-50L旋转蒸发器-上海越众仪器设备有限公司 | 曙光腾达官网-天津脚手架租赁-木板架出租-移动门式脚手架租赁「免费搭设」 | 天津市能谱科技有限公司-专业的红外光谱仪_红外测油仪_紫外测油仪_红外制样附件_傅里叶红外光谱技术生产服务厂商 | 海外整合营销-独立站营销-社交媒体运营_广州甲壳虫跨境网络服务 焊管生产线_焊管机组_轧辊模具_焊管设备_焊管设备厂家_石家庄翔昱机械 | 步进驱动器「一体化」步进电机品牌厂家-一体式步进驱动 | 并离网逆变器_高频UPS电源定制_户用储能光伏逆变器厂家-深圳市索克新能源 | 裹包机|裹膜机|缠膜机|绕膜机-上海晏陵智能设备有限公司 | 碳钢法兰厂家,非标法兰,定制异型,法兰生产厂家-河北九瑞管道 | 电气控制系统集成商-PLC控制柜变频控制柜-非标自动化定制-电气控制柜成套-NIDEC CT变频器-威肯自动化控制 | 阳光1号桔柚_无核沃柑_柑橘新品种枝条苗木批发 - 苧金网 | 铝单板_铝窗花_铝单板厂家_氟碳包柱铝单板批发价格-佛山科阳金属 | 热缩管切管机-超声波切带机-织带切带机-无纺布切布机-深圳市宸兴业科技有限公司 | 欧景装饰设计工程有限公司-无锡欧景装饰官网 | 龙门加工中心-数控龙门加工中心厂家价格-山东海特数控机床有限公司_龙门加工中心-数控龙门加工中心厂家价格-山东海特数控机床有限公司 | 商标转让-购买商标专业|放心的商标交易网-蜀易标商标网 | 二次元影像仪|二次元测量仪|拉力机|全自动影像测量仪厂家_苏州牧象仪器 | 生物颗粒燃烧机-生物质燃烧机-热风炉-生物颗粒蒸汽发生器-丽水市久凯能源设备有限公司 | 礼至家居-全屋定制家具_一站式全屋整装_免费量房设计报价 | 上海办公室装修_上海店铺装修公司_厂房装潢设计_办公室装修 | RV减速机-蜗轮蜗杆减速机-洗车机减速机-减速机厂家-艾思捷 | elisa试剂盒价格-酶联免疫试剂盒-猪elisa试剂盒-上海恒远生物科技有限公司 |