  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.
