用张量函数实现精准图像增强与去噪，适用于非线性场景。
Mapping-Based Image Diffusion
- 基于张量构建可定制的图像优化函数，融合应用需求与上下文信息。
- 在伽马校正和目标范围滤波中表现优于传统方法，去噪性能媲美先进PDE模型。
- 适合需要高精度控制的图像处理任务，如医学影像或工业检测。
本文提出一种新型张量基函数，用于定向图像增强与去噪。通过显式正则化，该函数利用基本原理融入应用相关与上下文信息，填补了现有文献中同时建模应用依赖性与上下文知识的空白。我们证明了最小值的存在性，并分析了张量对称性约束、凸性及几何解释。实验表明，该框架在存在非线性函数的场景（如伽马校正、目标值域滤波）中表现优异；在通用去噪任务中，性能与专用的基于偏微分方程的先进方法相当。
原文摘要 · Abstract (English)
In this work, we introduce a novel tensor-based functional for targeted image enhancement and denoising. Via explicit regularization, our formulation incorporates application dependent and contextual information using first principles. Few works in literature treat variational models that describe both application dependent information and contextual knowledge of the denoising problem. We prove the existence of a minimizer and present results on tensor symmetry constraints, convexity, and geometric interpretation of the proposed functional. We show that our framework excels in applications where nonlinear functions are present such as in gamma correction and targeted value range filtering. We also study general denoising performance where we show comparable results to dedicated PDE-based state of the art methods.
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