Janne M. J. Huttunen

Approximation error analysis in nonlinear state estimation with an application to state-space identification

Nonstationary inverse problems are usually cast in the state-space formalism. The complete statistics of linear Gaussian problems can be computed with the Kalman filters and smoothers. Nonlinear non-Gaussian problems would necessitate the adoption of particle filters or similar computationally very heavy approaches. The so-called extended Kalman filters often provide suboptimal but feasible estimates for the nonlinear problems. Several applications which lead to nonstationary inverse problems are time critical, such as process tomography and many biomedical problems. In such applications, there is typically a need to use reduced-order models which may heavily compromise the computational accuracy that is usually required for inverse problems. One approach to overcome the model reduction problem is to use the approximation error analysis. In this paper, we derive the equations for the extended Kalman filter for nonlinear state estimation problems in which the approximation error models are taken into account. We consider the approximation errors that are due to both state reduction and time stepping. As an example, we consider the identification of the coefficients of the heat equation. Our main result is that, also in nonlinear problems, approximation error analysis allows us to obtain accurate estimates and uncertainties of the parameters in reduced-order models that are suitable for fast calculation.

Determination of heterogeneous thermal parameters using ultrasound induced heating and MR thermal mapping

In this paper, a method for the determination of spatially varying thermal conductivity and perfusion coefficients of tissue is proposed. The temperature evolution in tissue is modelled with the Pennes bioheat equation. The main motivation here is a model-based optimal control for ultrasound surgery, in which the tissue properties are needed when the treatment is planned. The overview of the method is as follows. The same ultrasound transducers, which are eventually used for the treatment, are used to inflict small temperature changes in tissue. This temperature evolution is monitored using MR thermal imaging, and the tissue properties are then estimated on the basis of these measurements. Furthermore, an approach to choose transducer excitations for the determination procedure is also considered. The purpose of this paper is to introduce a method and therefore simulations are used to verify the method. Furthermore, computations are accomplished in a 2D spatial domain.

MRI contrasts in high rank rotating frames

MRI relaxation measurements are performed in the presence of a fictitious magnetic field in the recently described technique known as RAFF (Relaxation Along a Fictitious Field). This method operates in the 2nd rotating frame (rank n = 2) by using a nonadiabatic sweep of the radiofrequency effective field to generate the fictitious magnetic field. In the present study, the RAFF method is extended for generating MRI contrasts in rotating frames of ranks 1 ≤ n ≤ 5. The developed method is entitled RAFF in rotating frame of rank n (RAFFn).

Correction of Model Reduction Errors in Simulations

In simulations of complex physical phenomena, model reductions are often required to decrease the computation time of the simulation model to a feasible level. Model reduction is often obtained by using a reduced model, which may be based on a reduced numerical approximation and simplifications of the underlying accurate model. The use of a reduced model, however, induces errors to the simulation results. In this paper, we describe and evaluate a novel approach for the correction of the approximation errors in reduced simulation models. The key idea is to model the approximation error between the accurate and reduced simulation model as an additive noise term to the reduced model and construct a low-cost predictor model for the approximation error based on statistical learning. In this paper, the approximation error approach is evaluated with the following problems: correction of spatial and temporal discretization errors in a time-varying heat equation--based evolution model, correction of spatial discre...

Thermal Tomography Using Experimental Measurement Data

Experimental measurement data is used to test the feasibility of thermal tomography. The 3D distributed thermal conductivity, heat capacity and surface heat transfer coefficient of a mortar target containing an air hole are estimated using measurement data obtained with a prototype thermal tomography measurement device.Copyright