A geometric approach to the filtered backpropagation algorithm

We show how the filtered backpropagation algorithm [1] for parallel-beam diffraction tomography can be implemented geometrically by weighted straight-line projections. The resulting algorithm is formally equivalent to the original approach using Fourier transforms [2], but reorganizes the calculations to separately backpropagate each plane-wave component of the filtered data. In principle, at least, the projection method also suggests the design of an ultrasound scanner that records the wavefield with line detectors.