A frequency-domain formulation of the Fréchet derivative to exploit the inherent parallelism of the distorted Born iterative method

With its consideration for nonlinear scattering phenomena, the distorted Born iterative method (DBIM) is known to provide images superior to those of linear tomographic methods. However, the complexity involved with the production of superior images has prevented DBIM from overtaking simpler imaging schemes in commercial applications. The iterative process and need to solve the forward-scattering problem multiple times make DBIM a slow algorithm compared to diffraction tomography. Fortunately, as computer prices continue to decline, it is becoming easier to assemble large, distributed computer clusters from low-cost personal computer systems. These are well-suited to DBIM inversions, and offer great promise in accelerating the method. Traditional frequency-domain DBIM formulations produce an image by inverting the Fréchet derivative. If the derivative is treated as a matrix, it is costly to construct and awkward to invert on distributed computer systems. This paper presents an interpretation of the Fréchet derivative that is ideal for parallel-computing applications. As a bonus, this formulation reduces the storage requirements of DBIM implementations, making it possible to invert larger problems on a fixed system.