Addendum to ‘Electrical impedance tomography’

We present some additional references and clarifying statements to the topical review ‘Electrical impedance tomography’ (Borcea L 2002 Inverse Problems 18 R99–136). In this addendum to ‘Electrical impedance tomography’, the author would like to make some clarifying statements regarding section 7.1.2 and to direct the reader to additional references relating to sections 4.3 and 6.1. • The idea of identifying the support of an inclusion by means of the range of an operator has been introduced by Colton and Kirsch [4] and it has been justified rigorously by Kirsch [9], in the context of shape characterization of obstacles in inverse scattering. The application of these ideas to EIT is given in [3] and it is implemented by Brühl and Hanke in [2]. Independently, Ikehata [6, 8] (see also [7]) has developed noniterative approaches for finding the support of inclusions and the convex hull of inclusions from boundary measurements. The numerical implementation of the ideas in [8] is given by Ikehata and Siltanen in [10]. The reconstruction methods in [3] and [8] are compared by Brühl and Hanke in [2]. It is shown there that the two methods are somewhat related and that they can be implemented with almost the same numerical techniques. On page R119, ‘[85]’ is a typographical error and should be disregarded. • In connection with the complex exponential solutions of the Schrödinger equation (see section 4), we would like to point out Fadeev’s study [5]. Moreover, in relation to sections 4.3.2 and 4.3.3, we would like to point out the results obtained independently, by Novikov, in [13, 14]. • In relation to section 6.1, we direct the reader to the interior logarithmic stability estimates obtained in two dimensions by Liu [11] and Barceló et al [1], as well as to the proof, due to Mandache [12], of optimality of such logarithmic estimates, in two or more dimensions, for the EIT problem, rewritten in Schrödinger’s equation form. 0266-5611/03/040997+02$30.00 © 2003 IOP Publishing Ltd Printed in the UK 997