A new iterative method for a class of linear system arising from image restoration problems

Abstract

In this paper, by utilizing the matrix properties arising from the image restoration model, a new iterative method for solving the corresponding augmented linear system is proposed. Theoretical results about the convergence properties and computational advantage of the new method are studied in detail, showing that it just involves a matrix–vector product, which can be implemented by fast Fourier transform (FFT) or discrete Cosine transform (DCT) algorithms and can save much computation cost. Numerical experiments are provided, further confirm that our theoretical results is reliable and our method is feasible and effective.

Keywords

• Image restoration
• Boundary conditions
• Iterative method
• Convergence
• Spectral properties