Solving regularized linear least-squares problems by alternating direction methods with applications to image restoration

We present and analyze ways to apply the Alternating Direction Method (ADM) to bound-constrained quadratic problems including ℓ1 and ℓ2 regularized linear least-squares problems. The resulting ADM schemes require the solution of two subproblems at each iteration: the first one is a linear system, the second one is a boundconstrained optimization problem with closed-form solution. Numerical results on image deblurring problems are provided and comparisons are made with a Newton-based method and a first-order method for bound-constrained optimization.