Using Steins Unbiased Risk Estimate to Optimize Level of Decomposition in Stationary Wavelet Transform Denoising

TL;DR

This paper introduces a method using Stein's Unbiased Risk Estimate to automatically determine the optimal decomposition level in stationary wavelet transform denoising, improving accuracy without prior knowledge of the clean signal.

Contribution

It presents a novel approach to select the optimal wavelet decomposition level based on risk estimation, applicable even when the clean signal is unknown.

Findings

SURE risk reaches minimum at the same level as the sum square error

Method works with known or estimated noise variance

Automatically determines optimal decomposition level

Abstract

A method of determining the optimum number of levels of decomposition in soft-thresholding wavelet denoising using Stationary Wavelet Transform is presented here. The method calculates the risk at each level of decomposition using Steins Unbiased Risk Estimate, analogous to calculating the sum square error of the denoising process. The SURE risk is found to reach minimum at the same level of decomposition as the sum square error. The advantage of this method is that the clean signal need not be known a priori. The method can be used with either a priori known noise variance or an estimate of the noise variance. This allows the determination of the optimum level of decomposition for wavelet denoising of an unknown signal so long as the noise variance can be estimated.