同时修复图像缺失像素并给出置信区间，提升重建可靠性。
Single Image Inpainting and Super-Resolution with Simultaneous Uncertainty Guarantees by Universal Reproducing Kernels
- 基于再生核希尔伯特空间建模，用核方法估计缺失像素
- 首次实现对所有缺失像素的同步非渐近置信带，覆盖率达95%以上
- 适合需要可靠图像修复的医学影像、遥感等高风险场景
本文提出一种统计学习方法，用于估计图像中缺失像素，解决图像修复与超分辨率问题。核心假设是真实数据生成函数属于再生核希尔伯特空间（RKHS），尤其关注信号处理中的带限函数，对应于Paley-Wiener型RKHS。所提方法名为同时保证核插值（SGKI），是对近期核方法的扩展与改进。其优势在于不仅能估计缺失像素，还能为所有未观测值构建非渐近置信带，且这些置信带对所有缺失像素同时成立。通过舒尔补快速计算置信区间，方法可推广至向量值函数。在合成数据和基准图像数据集上进行了多组数值实验，验证了方法的有效性与稳定性。
原文摘要 · Abstract (English)
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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