Nested Conjugate Gradient Algorithm With Nested Preconditioning for Non-Linear Image Restoration

Skariah, Deepak G and Arigovindan, Muthuvel (2017) Nested Conjugate Gradient Algorithm With Nested Preconditioning for Non-Linear Image Restoration. In: IEEE Transactions on Image Processing, 26 (9). pp. 4471-4482. ISSN 1057-7149

PDF IEEE_tra_ima_pro_26-9_4471-4482_2017.pdf - Published Version Restricted to Registered users only Download (5MB) | Request a copy

Abstract

We develop a novel optimization algorithm, which we call nested non-linear conjugate gradient (CG) algorithm (NNCG), for image restoration based on quadratic data fitting and smooth non-quadratic regularization. The algorithm is constructed as a nesting of two conjugate gradient iterations. The outer iteration is constructed as a preconditioned non-linear CG algorithm; the preconditioning is performed by the inner CG iteration that is linear. The inner CG iteration, which performs preconditioning for outer CG iteration, itself is accelerated by an another FFT-based non-iterative preconditioner. We prove that the method converges to a stationary point for both convex and non-convex regularization functionals. We demonstrate experimentally that proposed method outperforms the well-known majorization-minimization method used for convex regularization, and a non-convex inertial-proximal method for non-convex regularization functional.

Item Type:	Journal Article
Publication:	IEEE Transactions on Image Processing
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright for this article belongs to the Institute of Electrical and Electronics Engineers Inc.
Keywords:	conjugate gradient method; convex regularization; Image restoration; nonconvex regularization; optimization; preconditioning
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	13 Jun 2022 12:03
Last Modified:	13 Jun 2022 12:03
URI:	https://eprints.iisc.ac.in/id/eprint/73411

Actions (login required)

View Item