Minimal-scan reconstruction algorithms for fan-beam diffraction tomography and their analogy to halfscan fan-beam CT

In fan-beam diffraction tomography (DT), a scattering object is interrogated using a cylindrical acoustical or electromagnetic wavefield, and the scattered wavefield around the object is measured and used to reconstruct the refractive index distribution of the scattering object. Recently, there has been a strong interest in developing ultrasound-, microwave- and photon density-based DT systems as medical imaging modalities. In conventional fan-beam computed tomography (CT), it is possible to reduce the scanning time by use of the so-called minimal-scan approach (also referred to as the halfscan approach) in which one acquires the minimal-scan fan-beam sinogram at projection angles from zero to π plus the fan angle. It is widely believed that in fan-beam DT, measurements from a full angular range of 2π around the scattering object are generally required to exactly reconstruct a complex-valued refractive index distribution. In this work we reveal that to perform an exact reconstruction, one needs measurements only over the angular range 0 ≤ φ ≤ φ_min, where π < φ_min ≤ 3π/2 is a specified function describing the fan-beam DT geometry. Based on this observation, we develop minimal-scan reconstruction algorithms for fan-beam DT. We also present a discussion of the conceptual similarities between the minimal-scan fan-beam DT and CT reconstruction problems.