Random impulse noise removal using sparse and low rank decomposition of annihilating filter-based Hankel matrix

Annihilating filer-based low rank Hankel matrix (ALOHA) approach was recently proposed as an intrinsic image model for image inpainting estimation. Based on the observation that smoothness or textures within an image patch are represented as sparse spectral components in the frequency domain, ALOHA exploits the existence of annihilating filters and the associated rank-deficient Hankel matrices in the image domain to estimate the missing pixels. As a extension, here we propose a novel impulse noise removal algorithm using sparse + low rank decomposition of an annihilating filter-based Hankel matrix. This novel approach, what we call robust ALOHA, is inspired by the observation that an image corrupted with impulse noises has intact pixels; so the impulse noises can be modeled as sparse outliers, whereas the underlying image can be still modeled using a low-rank Hankel structured matrix. Numerical results confirm that robust ALOHA has significant performance improvements compared to the state-of-the-art impulse removal algorithms.