Abstract: Systems and methods are disclosed for enhancing digital signals. In one implementation, a digital signal that has undergone a non-linear distortion can be received. The non-linear distortion can be reformulated as one or more linear operators that yield a statistical connection between a first signal and a second signal and one or more convex constraints on the first signal and/or the second signal. A convex minimization problem can be formulated in view of the first signal, the second signal, and the one or more convex constraints. The digital signal can be processed to solve the convex minimization problem, thereby generating an enhanced digital signal.