Faster resolution of the 3-D forward problems in microwave imaging by a Partial-Block BiCGStab algorithm

In microwave image reconstruction, the biconjugate gradient stabilized (BiCGStab) algorithm is generally used to solve the 3-D forward problem. In practice, the number of forward problems that must be solved simultaneously is equal to the number of available illuminations. Here, we propose the use of a block version of the BiCGStab algorithm that can take advantage of the fact that all forward problems share the same linear operator, thereby significantly reducing the amount of computation. In order to make the technique faster and more robust, an implementation based on a partition of the illuminations into subsets is introduced. Simulations are carried out on a realistic setup for image reconstruction and reveal the superiority of the proposed algorithm over the BiCGStab method, mainly for high contrasted objects.