Explainable bilevel optimization: An application to the Helsinki deblur challenge

IF 1.2 4区 数学 Q2 MATHEMATICS, APPLIED
Silvia Bonettini, Giorgia Franchini, Danilo Pezzi, Marco Prato
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引用次数: 2

Abstract

In this paper we present a bilevel optimization scheme for the solution of a general image deblurring problem, in which a parametric variational-like approach is encapsulated within a machine learning scheme to provide a high quality reconstructed image with automatically learned parameters. The ingredients of the variational lower level and the machine learning upper one are specifically chosen for the Helsinki Deblur Challenge 2021, in which sequences of letters are asked to be recovered from out-of-focus photographs with increasing levels of blur. Our proposed procedure for the reconstructed image consists in a fixed number of FISTA iterations applied to the minimization of an edge preserving and binarization enforcing regularized least-squares functional. The parameters defining the variational model and the optimization steps, which, unlike most deep learning approaches, all have a precise and interpretable meaning, are learned via either a similarity index or a support vector machine strategy. Numerical experiments on the test images provided by the challenge authors show significant gains with respect to a standard variational approach and performances comparable with those of some of the proposed deep learning based algorithms which require the optimization of millions of parameters.
可解释的双层优化:赫尔辛基去模糊挑战的应用程序
在本文中,我们提出了一种解决一般图像去模糊问题的双层优化方案,其中将参数变分方法封装在机器学习方案中,以提供具有自动学习参数的高质量重建图像。变分下层和机器学习上层的成分是专门为2021年赫尔辛基去模糊挑战而选择的,其中要求从模糊程度越来越高的失焦照片中恢复字母序列。我们提出的重建图像的过程包括固定次数的FISTA迭代,用于最小化边缘保持和二值化,强制正则化最小二乘函数。定义变分模型和优化步骤的参数,与大多数深度学习方法不同,它们都具有精确和可解释的含义,可以通过相似指数或支持向量机策略来学习。在挑战作者提供的测试图像上进行的数值实验表明,相对于标准变分方法,该方法取得了显著的进步,其性能可与一些提出的需要优化数百万个参数的基于深度学习的算法相媲美。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Inverse Problems and Imaging
Inverse Problems and Imaging 数学-物理:数学物理
CiteScore
2.50
自引率
0.00%
发文量
55
审稿时长
>12 weeks
期刊介绍: Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.
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