Image restoration using L1-norm regularization and a gradient-based neural network with discontinuous activation functions

The problem of restoring images degraded by linear position invariant distortions and noise is solved by means of a L
₁
-norm regularization, which is equivalent to determining a L
₁
-norm solution of an overdetermined system of linear equations, which results from a data-fitting term plus a regularization term that are both in L
₁
norm. This system is solved by means of a gradient-based neural network with a discontinuous activation function, which is ensured to converge to a L
₁
-norm solution of the corresponding system of linear equations.