Regularizing active set method for nonnegatively constrained ill-posed multichannel image restoration problem.

In this paper, we consider the nonnegatively constrained multichannel image deblurring problem and propose regularizing active set methods for numerical restoration. For image deblurring problems, it is reasonable to solve a regularizing model with nonnegativity constraints because of the physical meaning of the image. We consider a general regularizing l(p)-l(q) model with nonnegativity constraints. For p and q equaling 2, the model is in a convex quadratic form, therefore, the active set method is proposed since the nonnegativity constraints are imposed naturally. For p and q not equaling 2, we present an active set method with a feasible Newton-conjugate gradient solution technique. Numerical experiments are presented for ill-posed three-channel blurred image restoration problems.