Preconditioned linearized Bregman method with Golub-Kahan bidiagonalization for frame-based image deblurring

Abstract

A preconditioned linearized Bregman method with Golub-Kahan bidiagonalization is proposed for solving frame-based image deblurring problems suffering from ill-posedness, where the constructed preconditioner is general and independent of the specific structure of the coefficient matrix. The convergence theorem of the proposed method is established based on its connection with the gradient descent method through the dual objective function. Numerical experiments further demonstrate the computational efficiency of the proposed method in terms of the iteration steps and the elapsed time.