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Full Space and Subspace Methods for Large Scale Image Restoration

In: Optimization and Regularization for Computational Inverse Problems and Applications

Author

Listed:
  • Yanfei Wang

    (Chinese Academy of Sciences, Institute of Geology and Geophysics)

  • Shiqian Ma

    (Columbia University, Department of Industrial Engineering and Operations Research)

  • Qinghua Ma

    (Renmin University of China, School of Information
    Beijing Union University, College of Art and Science)

Abstract

In this chapter, we discuss about the full space and subspace methods for ill-posed image restoration problems. Image restoration refers to minimizing the degradation which is caused by sensing environment, say CCD camera misfocus, nonuniform motion, atmospheric aerosols and atmospheric turbulence. For image restoration problems, a key matter is to solve a quadratic programming problem. We study numerical solution methods in full space by limited memory of BFGS method and the subspace trust region method. We develop a novel approach for reducing the cost of sparse matrix-vector multiplication when applying the full space and subspace methods to atmospheric image restoration. Also the projection technique for the regularized convex quadratic functional is developed in the iteration for ensuring nonnegativity. Numerical experiments indicate that these methods are useful for large-scale image restoration problems.

Suggested Citation

  • Yanfei Wang & Shiqian Ma & Qinghua Ma, 2010. "Full Space and Subspace Methods for Large Scale Image Restoration," Springer Books, in: Yanfei Wang & Changchun Yang & Anatoly G. Yagola (ed.), Optimization and Regularization for Computational Inverse Problems and Applications, chapter 0, pages 183-201, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-13742-6_9
    DOI: 10.1007/978-3-642-13742-6_9
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