A long-standing topic in artificial intelligence is the effective recognition of patterns from noisy images. In this regard, the recent data-driven paradigm considers 1) improving the representation robustness by adding noisy samples in training phase (i.e., data augmentation) or 2) pre-processing the noisy image by learning to solve the inverse problem (i.e., image denoising). However, such methods generally exhibit inefficient process and unstable result, limiting their practical applications. In this paper, we explore a non-learning paradigm that aims to derive robust representation directly from noisy images, without the denoising as pre-processing. Here, the noise-robust representation is designed as Fractional-order Moments in Radon space (FMR), with also beneficial properties of orthogonality and rotation invariance. Unlike earlier integer-order methods, our work is a more generic design taking such classical methods as special cases, and the introduced fractional-order parameter offers time-frequency analysis capability that is not available in classical methods. Formally, both implicit and explicit paths for constructing the FMR are discussed in detail. Extensive simulation experiments and an image security application are provided to demonstrate the uniqueness and usefulness of our FMR, especially for noise robustness, rotation invariance, and time-frequency discriminability.

翻译：人工智能领域长期存在的课题是如何从含噪图像中有效识别模式。当前的数据驱动范式通常采用两种策略：1）在训练阶段通过添加噪声样本来提升表示鲁棒性（即数据增强）；2）通过学习求解逆问题对含噪图像进行预处理（即图像去噪）。然而，此类方法普遍存在处理效率低下和结果不稳定等问题，限制了实际应用。本文探索一种非学习范式，旨在直接从含噪图像中生成鲁棒表示，无需预处理去噪步骤。所提出的噪声鲁棒表示被设计为Radon空间中的分数阶矩（Fractional-order Moments in Radon space, FMR），同时具有正交性和旋转不变性等有益特性。与传统的整数阶方法不同，本文工作是一种更具通用性的设计，将经典方法作为特例纳入其中，且引入的分数阶参数提供了经典方法所不具备的时频分析能力。本文从显式和隐式两条路径详细论述了FMR的构建方法。通过大量仿真实验及一项图像安全应用案例，验证了所提FMR在噪声鲁棒性、旋转不变性及时频判别能力等方面的独特性和实用性。