Inverse Problem Theory and Methods for Model Parameter Estimation - A. Tarantola(牛叉)

本文提出了一种通过具有两个垂直线性阵列的窄带多输入多输出（MIMO）雷达系统进行二维成像的系统模型和方法。 此外，我们的方法的成像公式是通过傅立叶积分处理开发的，并且还检查了天线阵列的参数，包括跨范围分辨率，所需大小和采样间隔。 与在反向合成Kong径雷达（ISAR）成像中多次快照照明期间对散射回波进行采样的空间顺序过程不同，该方法利用空间并行过程在单个快照照明期间对散射回波进行采样。 因此，可以避免ISAR成像中的复杂运动补偿。 此外，在我们的阵列配置中，采用了以正交多相序列编码的多个窄带频谱共享波形。 来自不同滤波器带的压缩回波的主瓣可能位于同一范围内，因此，经典ISAR成像中的范围对准是不必要的。 提供基于合成数据的数值模拟以测试我们提出的方法。

在该项目中，使用自适应神经模糊推理系统 (ANFIS) 解决了 2R 平面机器人的逆运动学问题。 此代码包括 2-DOF 平面机器人的动画。

论文Deep_Convolutional_Neural_Network_for_Inverse_Problems_in_Imagin

提出了使用改进的伪逆方法从CIE三刺激值恢复光谱反射率的过程。 与以前的光谱恢复方法不同，此方法使用基于颜色特征匹配的新样本选择标准来选择一系列合适的样本，以创建自适应的变换矩阵来重建光谱反射率。 考虑到计算时间和准确性，通过预先划分光谱反射率来创建动态子组，并通过动态子组中的样本与目标样本之间的样本相似性/不相似性来创建自适应子集。 因此，代替仅将一个变换矩阵应用于重构过程，而是使用颜色特征匹配从自适应子集获得了一系列自适应变换矩阵。 这项研究应用了三个不同的光谱反射率数据集和三个不同的误差度量。 根据所考虑的所有误差度量，该方法非常准确，并且优于伪逆方法和加权伪逆方法，它们在重构光谱反射率方面是有效的。

This textbook evolved from a course in geophysical inverse methods taught during the past two decades at New Mexico Tech, first by Rick Aster and, subsequently, jointly between Rick Aster and Brian Borchers. The audience for the course has included a broad range of first- or second-year graduate students (and occasionally advanced under- graduates) from geophysics, hydrology, mathematics, astrophysics, and other disciplines. Cliff Thurber joined this collaboration during the production of the first edition and has taught a similar course at the University of Wisconsin-Madison. Our principal goal for this text is to promote fundamental understanding of param- eter estimation and inverse problem philosophy and methodology, specifically regarding such key issues as uncertainty, ill-posedness, regularization, bias, and resolution. We emphasize theoretical points with illustrative examples, and MATLAB codes that imple- ment these examples are provided on a companion website. Throughout the examples and exercises, a web icon indicates that there is additional material on the website. Exercises include a mix of applied and theoretical problems. This book has necessarily had to distill a tremendous body of mathematics and science going back to (at least) Newton and Gauss. We hope that it will continue to find a broad audience of students and professionals interested in the general problem of estimating physical models from data. Because this is an introductory text surveying a very broad field, we have not been able to go into great depth. However, each chapter has a “notes and further reading” section to help guide the reader to further explo- ration of specific topics. Where appropriate, we have also directly referenced research contributions to the field. Some advanced topics have been deliberately left out of this book because of space limitations and/or because we expect that many readers would not be sufficiently famil- iar with the required mathematics. For example, readers with a strong mathematical background may be surprised that we primarily consider inverse problems with discrete data and discretized models. By doing this we avoid much of the technical complexity of functional analysis. Some advanced applications and topics that we have omitted include inverse scattering problems, seismic diffraction tomography, wavelets, data assimilation, simulated annealing, and expectation maximization methods. We expect that readers of this book will have prior familiarity with calculus, dif- ferential equations, linear algebra, probability, and statistics at the undergraduate level. In our experience, many students can benefit from at least a review of these topics, and we commonly spend the first two to three weeks of the course reviewing material from

矩阵二维示例

Inverse Problem Theory and Methods for Model Parameter Estimation （模型参数估计的反问题理论与方法） 作者：(意大利)(Albert Tarantola)塔兰托拉 PDF格式，英文。

Inverse problems arise when we reconstruct a sharper image from a blurred one or reconstruct the underground mass density from measurements of the gravity above the ground. When we solve an inverse problem, we compute the source that gives rise to some observed data using a mathematical model for the relation between the source and the data. This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms. Discrete Inverse Problems: Insight and Algorithms includes a number of tutorial exercises that give the reader hands-on experience with the methods, difficulties, and challenges associated with the treatment of inverse problems. It also includes examples and figures that illustrate the theory and algorithms. Audience This book is written for graduate students, researchers, and professionals in engineering and other areas that depend on solving inverse problems with noisy data. The aim is to provide readers with enough background that they can solve simple inverse problems and read more advanced literature on the subject. Contents Preface; List of Symbols; Chapter 1: Introduction and Motivation; Chapter 2: Meet the Fredholm Integral Equation of the First Kind; Chapter 3: Getting to Business: Discretizations of Linear Inverse Problems; Chapter 4: Computational Aspects: Regularization Methods; Chapter 5: Getting Serious: Choosing the Regularization Parameter; Chapter 6: Toward Real-World Problems: Iterative Regularization; Chapter 7: Regularization Methods at Work: Solving Real Problems; Chapter 8: Beyond the 2-Norm: The Use of Discrete Smoothing Norms; Appendix A: Linear Algebra Stuff; Appendix B: Symmetric Toeplitz-Plus-Hankel Matrices and the DCT; Appendix C: Early Work on 揟ikhonov Regularization? Bibliography; Index. About the Author Per Christian Hansen is Professor of Scientific Computing at the Technical University of Denmark. His publications include two other books on inverse problems, several MATLAB?packages, and many papers on inverse problems, matrix computations, and signal processing. His home page is http://www2.imm.dtu.dk/~pch/. To request an examination copy or desk copy of this book, please use our online request form at www.siam.org/catalog/adopt.php.

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