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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 5203214, 12 pages
Research Article

Supervised and Unsupervised Subband Adaptive Denoising Frameworks with Polynomial Threshold Function

1Department of Industrial Control Networks and Systems, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China
2University of Chinese Academy of Sciences, Beijing 100049, China

Correspondence should be addressed to Tierui Gong

Received 18 September 2016; Revised 28 December 2016; Accepted 22 January 2017; Published 9 March 2017

Academic Editor: Barak Fishbain

Copyright © 2017 Tierui Gong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Unlike inflexible structure of soft and hard threshold function, a unified linear matrix form with flexible structure for threshold function is proposed. Based on the unified linear flexible structure threshold function, both supervised and unsupervised subband adaptive denoising frameworks are established. To determine flexible coefficients, a direct mean-square error (MSE) minimization is conducted in supervised denoising while Stein’s unbiased risk estimate as a MSE estimate is minimized in unsupervised denoising. The SURE rule requires no hypotheses or a priori knowledge about clean signals. Furthermore, we discuss conditions to obtain optimal coefficients for both supervised and unsupervised subband adaptive denoising frameworks. Applying an Odd-Term Reserving Polynomial (OTRP) function as concrete threshold function, simulations for polynomial order, denoising performance, and noise effect are conducted. Proper polynomial order and noise effect are analyzed. Both proposed methods are compared with soft and hard based denoising technologies—VisuShrink, SureShrink, MiniMaxShrink, and BayesShrink—in denoising performance simulation. Results show that the proposed approaches perform better in both MSE and signal-to-noise ratio (SNR) sense.