  We consider the imaging of cosmic strings by using Cosmic Microwave
Background (CMB) data. Mathematically, we study the inversion of an X-ray
transform in Lorentzian geometry, called the light ray transform. The inverse
problem is highly ill-posed, with additional complexities of being large-scale
and dynamic, with unknown parameters that represent multidimensional objects.
This presents significant computational challenges for the numerical
reconstruction of images that have high spatial and temporal resolution. In
this paper, we begin with a microlocal stability analysis for inverting the
light ray transform using the Landweber iteration. Next, we discretize the
spatiotemporal object and light ray transform and consider iterative
computational methods for solving the resulting inverse problem. We provide a
numerical investigation and comparison of some advanced iterative methods for
regularization including Tikhonov and sparsity-promoting regularizers for
various example scalar functions with conormal type singularities.
