2015/10/19 by Kyong Hwan Jin, Jong Chul Ye, Jin, Kyong Hwan +1
Computer Science · Engineering · Mathematics · #Advanced Image Fusion Techniques #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Image and Signal Denoising Methods #Sparse and Compressive Sensing Techniques #Statistical and numerical algorithms #cs.CV
paper · pdf · doi:10.48550/arxiv.1510.05559
arxiv created 2015/10/19 · openalex publication_date 2015/10/19 · arxiv updated 2015/10/20 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28
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).