Sparse and Low-Rank Decomposition of a Hankel Structured Matrix for Impulse Noise Removal - 2018


Recently, the annihilating filter-primarily based low-rank Hankel matrix (ALOHA) approach was proposed as a powerful image inpainting technique. Based mostly on the observation that smoothness or textures within a picture patch correspond to sparse spectral parts within the frequency domain, ALOHA exploits the existence of annihilating filters and therefore the associated rank-deficient Hankel matrices in a picture domain to estimate any missing pixels. By extending this idea, we propose a unique impulse-noise removal algorithm that uses the sparse and low-rank decomposition of a Hankel structured matrix. This technique, known as the sturdy ALOHA, relies on the observation that a picture corrupted with the impulse noise has intact pixels; consequently, the impulse noise will be modeled as sparse components, whereas the underlying image can still be modeled employing a low-rank Hankel structured matrix. To solve the sparse and low-rank matrix decomposition problem, we tend to propose an alternating direction methodology of multiplier approach, with initial factorized matrices coming from a coffee-rank matrix-fitting algorithm. To adapt native image statistics that have distinct spectral distributions, the sturdy ALOHA is applied during a patch-by-patch manner. Experimental results from impulse noise for each single-channel and multichannel color images demonstrate that the sturdy ALOHA is superior to existing approaches, particularly throughout the reconstruction of complex texture patterns.

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