Nested Conjugate Gradient Algorithm With Nested Preconditioning for Non-Linear Image Restoration | IEEE Journals & Magazine | IEEE Xplore

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


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...Show More

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.
Published in: IEEE Transactions on Image Processing ( Volume: 26, Issue: 9, September 2017)
Page(s): 4471 - 4482
Date of Publication: 19 June 2017

ISSN Information:

PubMed ID: 28641260

Funding Agency:


References

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