An image-reconstruction algorithm based on Landweber's iteration method for electrical-capacitance tomography

Abstract

Electrical capacitance tomography (ECT) is a so-called 'soft-field' tomography technique. The linear back-projection (LBP) method is used widely for image reconstruction in ECT systems. It is numerically simple and computationally fast because it involves only a single matrix-vector multiplication. However, the images produced by the LBP algorithm are generally qualitative rather than quantitative. This paper presents an image-reconstruction algorithm based on a modified Landweber iteration method that can greatly enhance the quality of the image when two distinct phases are present. In this algorithm a simple constraint is used as a regularization for computing a stabilized solution, with a better immunity to noise and faster convergence. Experimental results are presented.

An Image Reconstruction Algorithm for Electrical Impedance Tomography Using Adaptive Group Sparsity Constraint

“…The first method is Landweber iteration [27]. The updating form of Landweber iteration for EIT is expressed by 1 T ( )…”

Improved Landweber Algorithm Based on Correlation

“…According to the two standards of the image error and image correlation coefficient, a further comparison is made [17]: Î mage error ε ε ε − = (13) ( ) ( ) ( ) …”

The reconstruction problem

“…Often supported by the fallacious arguments, in particular that it is fast (it is no faster than the application of any precomputed regularized inverse) and that it is commonly used (only by those who know no better). In an interesting development the application of a normalised adjoint to the residual voltage error for the linearised problem was suggested for ECT, and later recognised as yet another reinvention of the well known Landweber iterative method [162]. Although there is no good reason to use pure linear iteration schemes directly on problems with such small a number of parameters as they can be applied much faster using the SVD, an interesting variation is to use such a slowly converging linear solution together with projection on to a constraint set; a method which has been shown to work well in ECT [30].…”