## The Factorization Method for Inverse Problems

*Andreas Kirsch and Natalia Grinberg*

- Published in print:
- 2007
- Published Online:
- September 2008
- ISBN:
- 9780199213535
- eISBN:
- 9780191707629
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213535.001.0001
- Subject:
- Mathematics, Applied Mathematics

This book is devoted to problems of shape identification in the context of (inverse) scattering problems and problems of impedance tomography. In contrast to traditional methods which are based on ... More

## INTRODUCTION

*Moody T. Chu and Gene H. Golub*

### in Inverse Eigenvalue Problems: Theory, Algorithms, and Applications

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566649
- eISBN:
- 9780191718021
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566649.003.0001
- Subject:
- Mathematics, Applied Mathematics

This chapter introduces the underlying difference between a forward problem and an inverse problem. Fundamental issues such as solvability, computability, sensitivity, and feasibility are raised. ... More

## APPLICATIONS

*Moody T. Chu and Gene H. Golub*

### in Inverse Eigenvalue Problems: Theory, Algorithms, and Applications

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566649
- eISBN:
- 9780191718021
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566649.003.0002
- Subject:
- Mathematics, Applied Mathematics

Inverse eigenvalue problems arise in a remarkable variety of applications. This chapter briefly highlights a few applications. The discussion is divided into six categories of applications: feedback ... More

## Numerical Methods for Image Registration

*Jan Modersitzki*

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528418
- eISBN:
- 9780191713583
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528418.001.0001
- Subject:
- Mathematics, Applied Mathematics

This text provides an introduction to the theoretical, practical, and numerical aspects of image registration, with special emphasis on medical imaging. Given a so-called reference and template ... More

## The MUSIC algorithm and scattering by an inhomogeneous medium

*Andreas Kirsch and Natalia Grinberg*

### in The Factorization Method for Inverse Problems

- Published in print:
- 2007
- Published Online:
- September 2008
- ISBN:
- 9780199213535
- eISBN:
- 9780191707629
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213535.003.0004
- Subject:
- Mathematics, Applied Mathematics

This chapter examines the case of a penetrable scatterer with an index of refraction that can be space-dependent and is assumed to be different from the constant background index. The inverse ... More

## Alternative sampling and probe methods

*Andreas Kirsch and Natalia Grinberg*

### in The Factorization Method for Inverse Problems

- Published in print:
- 2007
- Published Online:
- September 2008
- ISBN:
- 9780199213535
- eISBN:
- 9780191707629
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213535.003.0007
- Subject:
- Mathematics, Applied Mathematics

The Factorization Method is not the only sampling method. This final chapter introduces three alternative methods which belong to this class but, in contrast to the Factorization Method, are based on ... More

## MEG: An Introduction to Methods

*Peter Hansen, Morten Kringelbach, and Riitta Salmelin (eds)*

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780195307238
- eISBN:
- 9780199863990
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195307238.001.0001
- Subject:
- Neuroscience, Behavioral Neuroscience, Techniques

Magnetoencephalography (MEG) is an exciting brain imaging technology that allows real-time tracking of neural activity, making it an invaluable tool for advancing our understanding of brain function. ... More

## Inverse problems

*Fox Colin, Haario Heikki, and Christen J Andrés*

### in Bayesian Theory and Applications

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199695607
- eISBN:
- 9780191744167
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199695607.003.0031
- Subject:
- Mathematics, Probability / Statistics

This chapter discusses the features that are characteristic for the problems most typically treated under the umbrella of inverse problems. It begins by listing representative examples of inverse ... More

## Recording Strategies, Reference Issues, and Dipole Localization

*Paul L. Nunez and Ramesh Srinivasan*

### in Electric Fields of the Brain: The neurophysics of EEG

- Published in print:
- 2006
- Published Online:
- May 2009
- ISBN:
- 9780195050387
- eISBN:
- 9780199865673
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195050387.003.0007
- Subject:
- Neuroscience, Neuroendocrine and Autonomic, Techniques

Every EEG measurement depends on the locations of the recording and so-called reference electrode. The measured potential difference is a property of the path between electrode pairs. This applies to ... More

## The Fundamental Theorem of Linear Algebra

*Gidon Eshel*

### in Spatiotemporal Data Analysis

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691128917
- eISBN:
- 9781400840632
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691128917.003.0010
- Subject:
- Environmental Science, Environmental Studies

This chapter summarizes pictorially some of the linear algebraic foundations discussed thus far by revisiting the fundamental theorem of linear algebra, the unifying view of matrices, vectors, and ... More

## Volume Source and Volume Conductor

*Jaakko Malmivuo*

### in Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields

- Published in print:
- 1995
- Published Online:
- March 2012
- ISBN:
- 9780195058239
- eISBN:
- 9780199847839
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195058239.003.0007
- Subject:
- Neuroscience, Techniques

This chapter characterizes the nature of bioelectric sources and conductors. It points out that in contrast to electronic circuits, in which the electric properties of the components are ... More

## INTRODUCTION

*Jan Modersitzki*

### in Numerical Methods for Image Registration

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528418
- eISBN:
- 9780191713583
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528418.003.0001
- Subject:
- Mathematics, Applied Mathematics

This chapter states the problem of image registration and presents various applications, including remote sensing and medical image registration. Three examples which serve as test cases throughout ... More

## How the Stage Was Set When We Began

*Zygmunt Pizlo, Yunfeng Li, Tadamasa Sawada, and Robert M. Steinman*

### in Making a Machine That Sees Like Us

- Published in print:
- 2014
- Published Online:
- August 2014
- ISBN:
- 9780199922543
- eISBN:
- 9780190228385
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199922543.003.0001
- Subject:
- Psychology, Cognitive Neuroscience, Vision

A new, and very novel, analytical definition of shape is explained after a brief history of interest in automata since ancient times and a description of the book’s intent is presented. The new ... More

## Noninvasive Estimation of Local Field Potentials: Methods and Applications

*Rolando Grave de Peralta Menendez, Micah M. Murray, Gregor Thut, Theodor Landis, and Sara L. Gonzalez Andino*

### in Brain Signal Analysis: Advances in Neuroelectric and Neuromagnetic Methods

- Published in print:
- 2009
- Published Online:
- August 2013
- ISBN:
- 9780262013086
- eISBN:
- 9780262258876
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262013086.003.0003
- Subject:
- Neuroscience, Techniques

This chapter offers a novel method for estimating local field potentials (LFPs) via a newly developed solution for the neuroelectromagnetic inverse problem, and discusses an approach to construct ... More

## Theoretical Methods for Analyzing Volume Sources and Volume Conductors

*Jaakko Malmivuo*

### in Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields

- Published in print:
- 1995
- Published Online:
- March 2012
- ISBN:
- 9780195058239
- eISBN:
- 9780199847839
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195058239.003.0011
- Subject:
- Neuroscience, Techniques

This chapter presents theoretical methods, the first two of which (the solid angle theorem and the Miller-Geselowitz model) are used to evaluate the electric field in a volume conductor produced by ... More

## Magnetoencephalography Source Estimation: Transforming the Sensor-Level Signals to Estimates of Brain Activity

*Matti S. Hämäläinen*

### in Fifty Years of Magnetoencephalography: Beginnings, Technical Advances, and Applications

- Published in print:
- 2020
- Published Online:
- August 2020
- ISBN:
- 9780190935689
- eISBN:
- 9780190935719
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190935689.003.0006
- Subject:
- Neuroscience, Techniques, History of Neuroscience

This chapter describes the source estimation approaches to magnetoencephalography (MEG) analysis. Both MEG and electroencephalography (EEG) are measures of ongoing neuronal activity, and are ... More

## The Basis of ECG Diagnosis

*Jaakko Malmivuo*

### in Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields

- Published in print:
- 1995
- Published Online:
- March 2012
- ISBN:
- 9780195058239
- eISBN:
- 9780199847839
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195058239.003.0019
- Subject:
- Neuroscience, Techniques

This chapter discusses the forward problem of ECG diagnosis. This leads to the solution of the inverse problem through the empirical approach. The empirical approach is acceptable in this case, ... More

## The Need for and Road to Hybrid Magnetoencephalography–Magnetic Resonance Imaging

*Risto J. Ilmoniemi*

### in Fifty Years of Magnetoencephalography: Beginnings, Technical Advances, and Applications

- Published in print:
- 2020
- Published Online:
- August 2020
- ISBN:
- 9780190935689
- eISBN:
- 9780190935719
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190935689.003.0007
- Subject:
- Neuroscience, Techniques, History of Neuroscience

This chapter addresses the need for hybrid magnetoencephalography (MEG) and magnetic resonance imaging (MRI) systems. The importance of combining MEG with MRI was realized early. The most important ... More

## A Complete Info-Metrics Framework

*Amos Golan*

### in Foundations of Info-Metrics: Modeling, Inference, and Imperfect Information

- Published in print:
- 2017
- Published Online:
- November 2017
- ISBN:
- 9780199349524
- eISBN:
- 9780199349555
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199349524.003.0009
- Subject:
- Economics and Finance, Econometrics

In this chapter I develop the complete info-metrics framework for inferring problems and theories under all types of uncertainty and missing information. That framework allows for uncertainty in the ... More

## Which Part of the Neuronal Current can be Determined by Electroencephalography?

*A. S. Fokas, Parham Hashemzadeh, and Richard M. Leahy*

### in Fifty Years of Magnetoencephalography: Beginnings, Technical Advances, and Applications

- Published in print:
- 2020
- Published Online:
- August 2020
- ISBN:
- 9780190935689
- eISBN:
- 9780190935719
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190935689.003.0005
- Subject:
- Neuroscience, Techniques, History of Neuroscience

This chapter considers the so-called four-shell model of the brain and assumes that a continuously distributed primary neuronal current is supported either within the cerebral cortex or only on the ... More