  The significance of the broken ray transform (BRT) is due to its occurrence
in a number of modalities spanning optical, x-ray, and nuclear imaging. When
data are indexed by the scatter location, the BRT is both linear and shift
invariant. Analyzing the BRT as a linear system provides a new perspective on
the inverse problem. In this framework we contrast prior inversion formulas and
identify numerical issues. This has practical benefits as well. We clarify the
extent of data required for global reconstruction by decomposing the BRT as a
linear combination of cone beam transforms. Additionally we leverage the two
dimensional Fourier transform to derive new inversion formulas that are
computationally efficient for arbitrary scatter angles. Results of numerical
simulations are presented.
