  Recently, experiments have been reported where researchers were able to
perform high dynamic range (HDR) tomography in a heuristic fashion, by fusing
multiple tomographic projections. This approach to HDR tomography has been
inspired by HDR photography and inherits the same disadvantages. Taking a
computational imaging approach to the HDR tomography problem, we here suggest a
new model based on the Modulo Radon Transform (MRT), which we rigorously
introduce and analyze. By harnessing a joint design between hardware and
algorithms, we present a single-shot HDR tomography approach, which to our
knowledge, is the only approach that is backed by mathematical guarantees.
  On the hardware front, instead of recording the Radon Transform projections
that my potentially saturate, we propose to measure modulo values of the same.
This ensures that the HDR measurements are folded into a lower dynamic range.
On the algorithmic front, our recovery algorithms reconstruct the HDR images
from folded measurements. Beyond mathematical aspects such as injectivity and
inversion of the MRT for different scenarios including band-limited and
approximately compactly supported images, we also provide a first
proof-of-concept demonstration. To do so, we implement MRT by experimentally
folding tomographic measurements available as an open source data set using our
custom designed modulo hardware. Our reconstruction clearly shows the
advantages of our approach for experimental data. In this way, our MRT based
solution paves a path for HDR acquisition in a number of related imaging
problems.
