DocumentCode :
3420831
Title :
Optimal graph laplacian regularization for natural image denoising
Author :
Jiahao Pang ; Gene Cheung ; Ortega, Antonio ; Au, Oscar C.
Author_Institution :
Hong Kong Univ. of Sci. & Technol., Hong Kong, China
fYear :
2015
fDate :
19-24 April 2015
Firstpage :
2294
Lastpage :
2298
Abstract :
Image denoising is an under-determined problem, and hence it is important to define appropriate image priors for regularization. One recent popular prior is the graph Laplacian regularizer, where a given pixel patch is assumed to be smooth in the graph-signal domain. The strength and direction of the resulting graph-based filter are computed from the graph´s edge weights. In this paper, we derive the optimal edge weights for local graph-based filtering using gradient estimates from non-local pixel patches that are self-similar. To analyze the effects of the gradient estimates on the graph Laplacian regularizer, we first show theoretically that, given graph-signal hD is a set of discrete samples on continuous function h(x; y) in a closed region Ω, graph Laplacian regularizer (hD)TLhD converges to a continuous functional SΩ integrating gradient norm of h in metric space G-i.e., (∇h)TG-1(∇h)-over Ω. We then derive the optimal metric space G*: one that leads to a graph Laplacian regularizer that is discriminant when the gradient estimates are accurate, and robust when the gradient estimates are noisy. Finally, having derived G* we compute the corresponding edge weights to define the Laplacian L used for filtering. Experimental results show that our image denoising algorithm using the per-patch optimal metric space G* outperforms non-local means (NLM) by up to 1.5 dB in PSNR.
Keywords :
Laplace equations; gradient methods; graph theory; image denoising; image filtering; image resolution; NLM; PSNR; gradient estimates; graph Laplacian regularization; image priors; local graph-based filtering; natural image denoising; nonlocal means; nonlocal pixel patches; Extraterrestrial measurements; Image denoising; Image edge detection; Laplace equations; Noise; Noise measurement; graph Laplacian regularization; image denoising; inverse imaging problem; metric space;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on
Conference_Location :
South Brisbane, QLD
Type :
conf
DOI :
10.1109/ICASSP.2015.7178380
Filename :
7178380
Link To Document :
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