Software for Improved Imaging

Prof. Jari P. Kaipio University of Kuopio, Finland

It is often still customary to concentrate on the hardware considerations in process tomography applications. While the optimization of hardware should by no means be neglected, the computational models and software are seldom optimized and standard general purpose software is still widely used to obtain reconstructions from the measurements. The purpose of this talk is to focus on the importance of careful modelling of the underlying processes, measurement equipment and geometry.

In many applications the aim in process tomography is to monitor the processes qualitatively, that is, for example to detect unwanted air bubbles. In these cases more or less standard algorithmic implementations may prove to be adequate. These software implementations assume usually a very simple - usually 2D - geometry. However, when the geometry is not trivial or nonstandard, or stationarity of the target can not be assumed, standard software implementations are usually useless. An unfortunate outcome of this fact can be that the measurement situation has to be forced to fulfill the assumptions of the existing software. This in turn may mean the quality of the target reconstruction is unnecessarily poor due to an infeasible measurement setting. Furthermore, new algorithmic approaches may facilitate such applications which have previously been regarded as impossible.

Tomographic problems belong mathematically to the so-called inverse problems. Among the recent advances in computational inverse problems are approaches with which to handle 1) nonstationary target cases in which the target chances rapidly with respect to the measurement frame rate, 2) nonstandard information on the structural properties of the target and 3) accurate assessment of estimation errors even in cases with nongaussian measurement errors and nonlinear parameter estimation problems.

The basic ideas are illustrated by examples from our own research which has to do with nontrivial geometry problems and imaging of fast flows with electrical impedance tomography measurements. The aim is to show for example, that such notions as ”minimum identifiable object size in EIT” is irrelevant. We also discuss the reverse interrelation of hardware and software design in which the target reconstruction issues partially determine the implementation of the measurement system.

The fundamental question that can be posed is: ”To which extent can one provide general purpose software if the application-related task is to exhaust all information on the target, given the measurements?”