Supervised and Unsupervised Subband Adaptive Denoising Frameworks with Polynomial Threshold Function

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 esta...

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Bibliographic Details
Published in:Mathematical problems in engineering 2017-01, Vol.2017 (2017), p.1-12
Main Authors: Jiao, Ping, Wang, Gengshan, Yang, Zhijia, Gong, Tierui
Format: Article
Language:English
Subjects:
Engineering
Estimates
Flexible structures
Functions (mathematics)
Mathematical analysis
Methods
Noise
Noise reduction
Noise threshold
Optimization
Polynomials
Probability distribution
Signal to noise ratio
Simulation
Thresholds
Wavelet transforms
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2017/5203214