  We present a powerful and easy-to-implement algorithm for solving constrained
optimization problems that involve $L_1$/total-variation regularization terms,
and both equality and inequality constraints. We discuss the relationship of
our method to earlier works of Goldstein and Osher (2009) and Chartrand and
Wohlberg (2010), and demonstrate that our approach is a combination of the
augmented Lagrangian method with splitting and model projection. We test the
method on a geomechanical problem and invert highly compartmentalized pressure
change from noisy surface uplift observations. We conclude the paper with a
discussion of possible extension to a wide class of regularized optimization
problems with bound and equality constraints.
