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

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 oute...

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Veröffentlicht in:IEEE transactions on image processing Jg. 26; H. 9; S. 4471 - 4482
Hauptverfasser: Skariah, Deepak G., Arigovindan, Muthuvel
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States IEEE 01.09.2017
Schlagworte:
conjugate gradient method
Convergence
convex regularization
Cost function
Gradient methods
Image restoration
Minimization
Noise measurement
nonconvex regularization
optimization
preconditioning
ISSN:1057-7149, 1941-0042, 1941-0042
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Zusammenfassung: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.
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ISSN:1057-7149
1941-0042
1941-0042
DOI:10.1109/TIP.2017.2717182