A Preconditioned Majorization‐Minimization Method for ℓ2‐ℓq Minimization

The need to minimize a linear combination of an expression that involves an (Formula presented.) -norm of a linear transformation of the computed solution and the (Formula presented.) -norm of the residual error arises in image restoration as well as in statistics. A solution method that is suited for large-scale problems is the iterative maximization-minimization method, which determines an approximate solution in a generalized Krylov subspace. This paper describes a preconditioner for accelerating the convergence of the iterative method. The design of the preconditioner is inspired by the iterated Tikhonov regularization method. Numerical examples in image deblurring and computerized tomography show that the preconditioner significantly reduces the required CPU time and gives computed solutions of about the same quality as the unpreconditioned iterative method.