Numerically robust minimal-scan reconstruction algorithms for diffraction tomography via Radon transform inversion

It is widely believed that measurements from a full angular range of 2π are generally required to exactly reconstruct a complex-valued refractive index distribution in diffraction tomography (DT). In this work, we developed a new class of minimal-scan reconstruction algorithms for DT that utilizes measurements only over the angular range 0 ≤ φ ≤ 3π/2 to perform an exact reconstruction. These algorithms, referred to as minimal-scan estimate-combination (MS-E-C) reconstruction algorithms, effectively operate by transforming the DT reconstruction problem into a conventional x-ray CT reconstruction problem that requires inversion of the Radon transform. We performed computer simulations to compare the noise and numerical properties of the MS-E-C algorithms against existing filtered backpropagation-based algorithms.