  We consider in this paper the problem of estimating a parameter matrix from
observations which are affected by two types of noise components: (i) a sparse
noise sequence which, whenever nonzero can have arbitrarily large amplitude
(ii) and a dense and bounded noise sequence of "moderate" amount. This is
termed a robust regression problem. To tackle it, a quite general
optimization-based framework is proposed and analyzed. When only the sparse
noise is present, a sufficient bound is derived on the number of nonzero
elements in the sparse noise sequence that can be accommodated by the estimator
while still returning the true parameter matrix. While almost all the
restricted isometry-based bounds from the literature are not verifiable, our
bound can be easily computed through solving a convex optimization problem.
Moreover, empirical evidence tends to suggest that it is generally tight. If in
addition to the sparse noise sequence, the training data are affected by a
bounded dense noise, we derive an upper bound on the estimation error.
