Supervised and Unsupervised Subband Adaptive Denoising Frameworks with Polynomial Threshold Function

Tierui Gong,Ping Jiao,Zhijia Yang,Gengshan Wang

doi:10.1155/2017/5203214

Tierui Gong, Ping Jiao + Show 2 more

Open Access

https://doi.org/10.1155/2017/5203214

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Abstract

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.

Highlights

Signals are usually corrupted by noise in capturing and transmission stages due to environment disturbance and device error
Signal denoising has become an important research topic for a long time and a wide variety of denoising methods have been proposed. Due to their effectiveness and good performance, wavelet threshold methods have become a powerful tool for denoising problems since Donoho and several others’ fundamental works
The main purpose of these methods is to estimate a wide class of functions in some smoothness spaces from their corrupted versions [1]

Summary

Introduction

Signals are usually corrupted by noise in capturing and transmission stages due to environment disturbance and device error. Of the various wavelet threshold schemes, soft and hard based threshold methods are the most popular technologies and have been theoretically verified by Donoho and Johnstone [2]. Based on the unified flexible structure threshold function, both supervised and unsupervised subband adaptive denoising frameworks are established. Our contributions can be summarized as follows: (1) a unified linear matrix form with flexible structure for threshold function and a concrete OTRP function are proposed; (2) both supervised and unsupervised denoising frameworks are established; (3) conditions for guaranteeing optimal solution for minimizing problems are discussed and provided.

Proposed Approaches

Experiments and Results

Conclusions