  It is well known that a band-limited signal can be reconstructed from its
uniformly spaced samples if the sampling rate is sufficiently high. More
recently, it has been proved that one can reconstruct a 1D band-limited signal
even if the exact sample locations are unknown, but given just the distribution
of the sample locations and their ordering in 1D. In this work, we extend the
analytical bounds on the reconstruction error in such scenarios for
quasi-bandlimited signals. We also prove that the method for such a
reconstruction is resilient to a certain proportion of errors in the
specification of the sample location ordering. We then express the problem of
tomographic reconstruction of 2D images from 1D Radon projections under unknown
angles with known angle distribution, as a special case for reconstruction of
quasi-bandlimited signals from samples at unknown locations with known
distribution. Building upon our theoretical background, we present asymptotic
bounds for 2D quasi-bandlimited image reconstruction from 1D Radon projections
in the unknown angles setting, which commonly occurs in cryo-electron
microscopy (cryo-EM). To the best of our knowledge, this is the first piece of
work to perform such an analysis for 2D cryo-EM, even though the associated
reconstruction algorithms have been known for a long time.
