arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2004.09434stat.MLcs.LGmath.OC

Automated data-driven selection of the hyperparameters for Total-Variation based texture segmentation

Univ Lyon(里昂大学);ENS de Lyon(里昂高等师范学院);Univ Lyon 1(里昂第一大学);CNRS(法国国家科学研究中心);Université de Bourgogne Franche-Comté(勃艮第-弗朗什-孔泰大学)

Barbara Pascal, Samuel Vaiter, Nelly Pustelnik, Patrice Abry

英文摘要:

Penalized Least Squares are widely used in signal and image processing. Yet, it suffers from a major limitation since it requires fine-tuning of the regularization parameters. Under assumptions on the noise probability distribution, Stein-based approaches provide unbiased estimator of the quadratic risk. The Generalized Stein Unbiased Risk Estimator is revisited to handle correlated Gaussian noise without requiring to invert the covariance matrix. Then, in order to avoid expansive grid search, it is necessary to design algorithmic scheme minimizing the quadratic risk with respect to regularization parameters. This work extends the Stein's Unbiased GrAdient estimator of the Risk of Deledalle et al. to the case of correlated Gaussian noise, deriving a general automatic tuning of regularization parameters. First, the theoretical asymptotic unbiasedness of the gradient estimator is demonstrated in the case of general correlated Gaussian noise. Then, the proposed parameter selection strategy is particularized to fractal texture segmentation, where problem formulation naturally entails inter-scale and spatially correlated noise. Numerical assessment is provided, as well as discussion of the practical issues.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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