  Recovering a signal $x^\ast \in \mathbb{R}^n$ from a sequence of linear
measurements is an important problem in areas such as computerized tomography
and compressed sensing. In this work, we consider an online setting in which
measurements are sampled one-by-one from some source distribution. We propose
solving this problem with a variant of the Kaczmarz method with an additional
heavy ball momentum term. A popular technique for solving systems of linear
equations, recent work has shown that the Kaczmarz method also enjoys linear
convergence when applied to random measurement models, however convergence may
be slowed when successive measurements are highly coherent. We demonstrate that
the addition of heavy ball momentum may accelerate the convergence of the
Kaczmarz method when data is coherent, and provide a theoretical analysis of
the method culminating in a linear convergence guarantee for a wide class of
source distributions.
