A New Steplength Selection for Scaled Gradient Methods with Application to Image Deblurring

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• 作者：Federica Porta ; Marco Prato ; Luca Zanni
• 关键词：Image deconvolution ; Constrained optimization ; Scaled gradient projection methods ; Ritz values ; 65K05 ; 65R32 ; 68U10 ; 90C06
• 刊名：Journal of Scientific Computing
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：65
• 期：3
• 页码：895-919
• 全文大小：2,497 KB
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• 作者单位：Federica Porta (1)
  Marco Prato (1)
  Luca Zanni (1)
  
  1. Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Universit脿 degli Studi di Modena e Reggio Emilia, Via Campi 213/b, 41125, Modena, Italy
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algorithms
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Mathematical and Computational Physics
  
• 出版者：Springer Netherlands
• ISSN：1573-7691

文摘

Gradient methods are frequently used in large scale image deblurring problems since they avoid the onerous computation of the Hessian matrix of the objective function. Second order information is typically sought by a clever choice of the steplength parameter defining the descent direction, as in the case of the well-known Barzilai and Borwein rules. In a recent paper, a strategy for the steplength selection approximating the inverse of some eigenvalues of the Hessian matrix has been proposed for gradient methods applied to unconstrained minimization problems. In the quadratic case, this approach is based on a Lanczos process applied every \(m\) iterations to the matrix of the gradients computed in the previous \(m\) iterations, but the idea can be extended to a general objective function. In this paper we extend this rule to the case of scaled gradient projection methods applied to constrained minimization problems, and we test the effectiveness of the proposed strategy in image deblurring problems in both the presence and the absence of an explicit edge-preserving regularization term. Keywords Image deconvolution Constrained optimization Scaled gradient projection methods Ritz values