t. This paper surveys some of the work our group has done in electrical impedance tomography.

Electrical Impedance Tomography

There has been tremendous advances in our ability to produce images of human brain function. Applications of functional brain imaging extend from improving our understanding of the basic mechanisms of cognitive processes to better characterization of pathologies that impair normal function. Magnetoencephalography (MEG) and electroencephalography (EEG) (MEG/EEG) localize neural electrical activity using noninvasive measurements of external electromagnetic signals. Among the available functional imaging techniques, MEG and EEG uniquely have temporal resolutions below 100 ms. This temporal precision allows us to explore the timing of basic neural processes at the level of cell assemblies. MEG/EEG source localization draws on a wide range of signal processing techniques including digital filtering, three-dimensional image analysis, array signal processing, image modeling and reconstruction, and, blind source separation and phase synchrony estimation. We describe the underlying models currently used in MEG/EEG source estimation and describe the various signal processing steps required to compute these sources. In particular we describe methods for computing the forward fields for known source distributions and parametric and imaging-based approaches to the inverse problem.

Electromagnetic brain mapping

The subject of inverse problems in differential equations is of enormous practical importance, and has also generated substantial mathematical and computational innovation. Typically some form of regularization is required to ameliorate ill-posed behaviour. In this article we review the Bayesian approach to regularization, developing a function space viewpoint on the subject. This approach allows for a full characterization of all possible solutions, and their relative probabilities, whilst simultaneously forcing significant modelling issues to be addressed in a clear and precise fashion. Although expensive to implement, this approach is starting to lie within the range of the available computational resources in many application areas. It also allows for the quantification of uncertainty and risk, something which is increasingly demanded by these applications. Furthermore, the approach is conceptually important for the understanding of simpler, computationally expedient approaches to inverse problems.

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Inverse problems: A Bayesian perspective

Now in its second edition, this accessible text presents a unified Bayesian treatment of state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models. The book focuses on discrete-time state space models and carefully introduces fundamental aspects related to optimal filtering and smoothing. In particular, it covers a range of efficient non-linear Gaussian filtering and smoothing algorithms, as well as Monte Carlo-based algorithms. This updated edition features new chapters on constructing state space models of practical systems, the discretization of continuous-time state space models, Gaussian filtering by enabling approximations, posterior linearization filtering, and the corresponding smoothers. Coverage of key topics is expanded, including extended Kalman filtering and smoothing, and parameter estimation. The book's practical, algorithmic approach assumes only modest mathematical prerequisites, suitable for graduate and advanced undergraduate students. Many examples are included, with Matlab and Python code available online, enabling readers to implement algorithms in their own projects.

Bayesian Filtering and Smoothing

A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology.

Statistical inversion of aerosol size distribution data

The present invention describes a method, apparatus and computer program for detecting the locations of boundaries between different materials in a desired measurement volume. The apparatus uses at least one measuring probe, the electrodes of which are characterized in that they together form an assembly that differs from a straight line. In addition, a volume at a further distance from the assembly can also be observed by the assembly, so that measurements can be conducted remotely and, on the other hand, the apparatus stays unbroken in diverse measurement situations. By using the EIT-measurement and applying for example a so-called 1D-σ-method or methods of machine learning, electrical conductivity distributions in the measured volume are detected. As a result, the locations of the possible boundaries between different materials or for example thicknesses of different material layers are detected.

A probe indicating intermaterial boundaries

This paper deals with the solution of an inverse heat conduction problem, aiming at the identification of contact failures in composites formed by layers of different materials. The inverse problem is solved within the Bayesian framework, with a Markov chain Monte Carlo method. The effects of the prior models, for the unknown contact conductance at the interface of a plate with two layers, are examined. The solution of the inverse problem is performed with simulated temperature measurements.Copyright © 2011 by ASME

Identification of Contact Failures in Multi-Layered Composites

Modeling errors due to Timoshenko approximation in damage identification

When an ultrasound wave is focused in biological tissue, a part of the energy of the wave is absorbed and turned into heat. This phenomena is used as a distributed heat source in ultrasound surgery, in which the aim is to destroy cancerous tissue by causing thermal damage. The main advantages of the ultrasound surgery are that it is noninvasive, there are no harmful side effects and spatial accuracy is good. The main disadvantage is that the treatment time is long for large cancer volumes when current treatment techniques are used. This is due to the undesired temperature rise in healthy tissue during the treatment. The interest for optimization of ultrasound surgery has been increased recently. With proper mathematical models and optimization algorithms the treatment time can be shortened and temperature rise in tissues can be better localized. In this study, two alternative control procedures for thermal dose optimization during ultrasound surgery are presented. In the first method, the scanning path between individual foci is optimized in order to decrease the treatment time. This method uses the prefocused ultrasound fields and predetermined focus locations. In the second method, combined feedforward and feedback controls are used to produce desired thermal dose in tissue. In the feedforward part, the phase and amplitude of the ultrasound transducers are changed as a function of time to produce the desired thermal dose distribution in tissue. The foci locations do not need to be predetermined. In addition, inequality constraint approximations for maximum input amplitude and maximum temperature can be used with the proposed method. The feedforward control is further expanded with a feedback controller which can be used during the treatment to compensate the modeling errors. All of the proposed control methods are tested with numerical simulations in 2D or 3D.

Jari P. Kaipio

Papers

Statistical inversion of aerosol size distribution data

A probe indicating intermaterial boundaries

Identification of Contact Failures in Multi-Layered Composites

Modeling errors due to Timoshenko approximation in damage identification

Optimal control in high intensity focused ultrasound surgery