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arXiv · 2506.23221

Single Image Inpainting and Super-Resolution with Simultaneous Uncertainty Guarantees by Universal Reproducing Kernels

Bálint Horváth·Balázs Csanád Csáji
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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.

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Bálint Horváth, Balázs Csanád Csáji. 2025-06-29. Single Image Inpainting and Super-Resolution with Simultaneous Uncertainty Guarantees by Universal Reproducing Kernels. https://arxiv.org/abs/2506.23221

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