Sparse + Low Rank Decomposition of Annihilating Filter-based Hankel Matrix for Impulse Noise Removal
This addresses image denoising for applications like photography or medical imaging, but it is incremental as it extends an existing ALOHA framework.
The paper tackled impulse noise removal in images by proposing a robust ALOHA method that models noise as sparse components and the underlying image as a low-rank Hankel matrix, achieving up to 8dB PSNR improvement over existing algorithms.
Recently, so called annihilating filer-based low rank Hankel matrix (ALOHA) approach was proposed as a powerful image inpainting method. Based on the observation that smoothness or textures within an image patch corresponds to 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. By extending this idea, here we propose a novel impulse noise removal algorithm using sparse + low rank decomposition of an annihilating filter-based Hankel matrix. The new approach, what we call the robust ALOHA, is motivated by the observation that an image corrupted with impulse noises has intact pixels; so the impulse noises can be modeled as sparse components, whereas the underlying image can be still modeled using a low-rank Hankel structured matrix. To solve the sparse + low rank decomposition problem, we propose an alternating direction method of multiplier (ADMM) method with initial factorized matrices coming from low rank matrix fitting (LMaFit) algorithm. To adapt the local image statistics that have distinct spectral distributions, the robust ALOHA is applied patch by patch. Experimental results from two types of impulse noises - random valued impulse noises and salt/pepper noises - for both single channel and multi-channel color images demonstrate that the robust ALOHA outperforms the existing algorithms up to 8dB in terms of the peak signal to noise ratio (PSNR).