Infinite-dimensional multilayer perceptrons.

In this paper a new multilayer perceptron (MLP) structure is introduced to simulate nonlinear transformations on infinite-dimensional function spaces. This extension is achieved by replacing discrete neurons by a continuum of neurons, summations by integrations and weight matrices by kernels of integral transforms. Variational techniques have been employed for the analysis and training of the infinite-dimensional MLP (IDMLP). The training problem of IDMLP is solved by the Lagrange multiplier technique yielding the coupled state and adjoint state integro-difference equations. A steepest descent-like algorithm is used to construct the required kernel and threshold functions. Finally, some results are presented to show the performance of the new IDMLP.

A method for comparative evaluation of EIT algorithms using a standard data set.

The point spread function (PSF) is the most widely used tool for quantifying the spatial resolution of imaging systems. However, prerequisites for the proper use of this tool are linearity and space invariance. Because EIT is non-linear it is only possible to compare different reconstruction algorithms using a standard data set. In this study, the FEM is used to generate simulation data, which are used to investigate the non-linear behaviour of EIT, the space dependence of its PSF and its capability of resolving nearby objects. It is found that for the case of iterative backprojection (IterB), the full width half maximum (FWHM) values of single-object perturbations for central, intermediate and peripheral high-contrast objects are 27%, 18% and 14% of the imaging region diameter respectively. For the method based on singular value decomposition of the Geselowitz lead sensitivity matrix (GS-SVD), the FWHM is not space dependent and is 12% of the imaging region diameter. Conclusions obtained using single-object PSF studies must also be checked with double-object or more complex perturbations because EIT is non-linear. For example, the GS-SVD method fails to detect two widely separated objects unless the truncation level of SVD is carefully adjusted. With more truncation, however, the resolution of the method is worsened. Based on these and similar observations a set of simulation data, which is proposed for comparative evaluation of different EIT algorithms, is specified and explained in the conclusion section.

A fast image reconstruction algorithm for electrical impedance tomography.

In this paper, we propose a fast algorithm for the reconstruction of the conductivity perturbation delta sigma about a known conductivity variation sigma omicron. The method is based on the minimization of a quadratic functional subject to linear constraints, where the existence of a unique solution is guaranteed. The algorithm developed for this purpose is iterative and each iteration is composed of a simple matrix multiplication. The validity of this method is illustrated with several examples.