A SURE based sub-band adaptive denoising method

Abstract

This paper introduces a different approach to wavelet denoising. Unlike traditional soft or hard thresholding based wavelet domain schemes, we employ an odd-term reserving polynomial function with flexible coefficients as the noisy signal estimator. Meanwhile we adopt Stein's Unbiased Risk Estimate (SURE) to give an unbiased estimate of the mean-squared error (MSE) between clean and denoised signal. The polynomial function coefficients are determined by minimizing the Stein's unbiased risk estimate. This SURE based property makes our approach only depend on the noisy signal, not on the clean one. Furthermore, the polynomial function structure makes coefficients solving a linear minimization problem, which is more efficient and easy to solve comparing with gradient based minimization problem. We test the proposed approach on a set of signals and the simulation results show our approach performs better than those soft and hard thresholding based methods (e.g. SureShrink, MiniMaxShrink and VisuShrink) in both MSE and signal-to-noise ratio (SNR) sense.