Single image inpainting and super-resolution with simultaneous uncertainty guarantees by universal reproducing kernels

Horváth, Bálint and Csáji, Balázs Csanád (2025) Single image inpainting and super-resolution with simultaneous uncertainty guarantees by universal reproducing kernels. MACHINE LEARNING, 114 (8). ISSN 0885-6125 10.1007/s10994-025-06814-0

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Abstract

The paper proposes a statistical learning approach to the problem of estimating missing pixels of images, crucial for image inpainting and super-resolution problems. One of the main novelties of the method is that it also provides uncertainty quantifications together with the estimated values. Our core assumption is that the underlying data-generating function comes from a reproducing kernel Hilbert space (RKHS). A special emphasis is put on band-limited functions, central to signal processing, which form Paley–Wiener type RKHSs. The proposed method, which we call simultaneously guaranteed kernel interpolation (SGKI), is an extension and refinement of a recently developed kernel method. An advantage of SGKI is that it not only estimates the missing pixels, but also builds non-asymptotic confidence bands for the unobserved values, which are simultaneously guaranteed for all missing pixels. We also show how to compute these bands efficiently using Schur complements, we discuss a generalization to vector-valued functions, and we present a series of numerical experiments on various datasets containing synthetically generated and benchmark images, as well.

Item Type: Article
Subjects: Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Divisions: Research Laboratory on Engineering & Management Intelligence
SWORD Depositor: MTMT Injector
Depositing User: MTMT Injector
Date Deposited: 29 Jul 2025 07:49
Last Modified: 29 Jul 2025 07:49
URI: https://eprints.sztaki.hu/id/eprint/10951

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