D-bar Methods for EIT

This chapter focuses on the D-bar method for EIT, which is really one method in a family of direct reconstruction methods based on complex geometrical optics (CGO), which generally lead to a D-bar equation to be solved as part of the method. By “direct” reconstruction methods, we refer to algorithms that are not based on improving a reconstructed conductivity iteratively step by step, as is done for example in variational regularization, but rather calculate a regularized reconstruction directly from the data. One of the advantages of direct methods is that there is often no need for a forward problem solver, or it is only invoked once to compute a simulated reference state. Furthermore, many of the methods are trivially parallelizable.