  We consider the problem of signal reconstruction for a system under sparse
signal corruption by a malicious agent. The reconstruction problem follows the
standard error coding problem that has been studied extensively in the
literature. We include a new challenge of robust estimation of the attack
support. The problem is then cast as a constrained optimization problem merging
promising techniques in the area of deep learning and estimation theory. A
pruning algorithm is developed to reduce the ``false positive" uncertainty of
data-driven attack localization results, thereby improving the probability of
correct signal reconstruction. Sufficient conditions for the correct
reconstruction and the associated reconstruction error bounds are obtained for
both exact and inexact attack support estimation. Moreover, a simulation of a
water distribution system is presented to validate the proposed techniques.
