  We propose a new acquisition geometry for electron density reconstruction in
three dimensional X-ray Compton imaging using a monochromatic source. This
leads us to a new three dimensional inverse problem where we aim to reconstruct
a real valued function $f$ (the electron density) from its integrals over
spindle tori. We prove injectivity of a generalized spindle torus transform on
the set of smooth functions compactly supported on a hollow ball. This is
obtained through the explicit inversion of a class of Volterra integral
operators, whose solutions give us an expression for the harmonic coefficients
of $f$. The polychromatic source case is later considered, and we prove
injectivity of a new spindle interior transform, apple transform and apple
interior transform on the set of smooth functions compactly supported on a
hollow ball.
  A possible physical model is suggested for both source types. We also provide
simulated density reconstructions with varying levels of added pseudo random
noise and model the systematic error due to the attenuation of the incoming and
scattered rays in our simulation.
