Real order total variation with applications to the loss functions in learning schemes

04/10/2022

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by   Pan Liu, et al.

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Loss function are an essential part in modern data-driven approach, such as bi-level training scheme and machine learnings. In this paper we propose a loss function consisting of a r-order (an)-isotropic total variation semi-norms TV^r, r∈ℝ^+, defined via the Riemann-Liouville (R-L) fractional derivative. We focus on studying key theoretical properties, such as the lower semi-continuity and compactness with respect to both the function and the order of derivative r, of such loss functions.