Supervised and Unsupervised Subband Adaptive Denoising Frameworks with Polynomial Threshold Function

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.