NDLI: Sure-optimal two-dimensional Savitzky-Golay filters for image denoising

Content Provider	IEEE Xplore Digital Library
Author	Menon, S.V. Seelamantula, C.S.
Copyright Year	2013
Description	Author affiliation: Dept. of Electr. Eng., Indian Inst. of Sci., Bangalore, India (Menon, S.V.; Seelamantula, C.S.)
Abstract	Savitzky-Golay (SG) filters are linear, shift-invariant lowpass filters employed for data smoothing. In their pathbreaking paper published in Analytical Chemistry, Savitzky and Golay mathematically established that polynomial regression of data over local intervals and evaluation of their values at the center of the approximation window is equivalent to convolution with a finite impulse response filter. In this paper, we expound SURE (Stein's unbiased risk estimate) based adaptive SG filters for image denoising. Our goal is to optimally choose SG filter parameters, namely, order and window length, the optimality defined in terms of the mean squared error (MSE). In practical scenarios, only a single realization of the noisy image is available and the ground truth is inaccessible. Hence, we propose SURE, which is an unbiased estimate of MSE, to solve the parameter selection problem. It is observed that bandwidth of the minimum MSE (MMSE)-optimum SG filter is small at relatively slowly varying portions of the underlying image, and vice versa at abrupt transitions, thereby enabling us to trade off bias and variance to obtain near-optimal performance. The denoising results obtained exhibit considerable peak signal-to-noise-ratio (PSNR) improvement. At low SNRs, the filter performance is further enhanced by using a regularized cost function.
Starting Page	459
Ending Page	463
File Size	1320952
Page Count	5
File Format	PDF
ISBN	9781479923410
DOI	10.1109/ICIP.2013.6738095
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-09-15
Publisher Place	Australia
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	PSNR Polynomials Noise reduction Noise measurement Bandwidth Approximation methods Finite impulse response filters Stein's unbiased risk estimator (SURE) Polynomial regression Minimum mean-squared error
Content Type	Text
Resource Type	Article

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