The purpose of this paper is to investigate the achievable improvement in reconstruction accuracy in electrical tomography through the incorporation of physical bound constraints as prior knowledge in the inverse problem solution.
The structure of the nonlinear least squares inverse problem formulation and the importance of prior knowledge are addressed. Several different methods for the incorporation of bound constraints are discussed. The methods are compared by means of reconstructions from simulated and measured data and the computational demands.
The inclusion of bound constraints on the material values in the inverse problem solution results in a considerable improvement of the reconstructions. The occurrence of artefacts and blurring can be reduced. Among the investigated constraint handling methods, the logarithmic parameter reconstruction approach can be implemented with minimal additional computational effort.
The study is performed with discrete two‐phase material distributions as occurring in industrial problems. A further step would be the extension to multiple phases.
The logarithmic transform method is a novel approach for the incorporation of bound constraints in tomography. It outperforms other constraint handling approaches and may be of interest for electrical tomography systems in various applications.
