Signal denoising using the minimum-probability-of-error criterion

Abstract

We address the problem of signal denoising via transform-domain shrinkage based on a novel risk criterion called the minimum probability of error (MPE), which measures the probability that the estimated parameter lies outside an -neighborhood of the actual value. However, the MPE, similar to the meansquared error (MSE), depends on the ground-truth parameter, and has to be estimated from the noisy observations. We consider linear shrinkage-based denoising functions, wherein the optimum shrinkage parameter is obtained by minimizing an estimate of the MPE. When the probability of error is integrated over , it leads to the expected 1 distortion. The proposed MPE and 1 distortion formulations are applicable to various noise distributions by invoking a Gaussian mixture model approximation. Within the realm of MPE, we also develop an extension of the transform-domain shrinkage by grouping transform coefficients, resulting in subband shrinkage. The denoising performance obtained within the proposed framework is shown to be better than that obtained using the minimum MSEbased approaches formulated within Stein's unbiased risk estimation (SURE) framework, especially in the low measurement signal-tonoise ratio (SNR) regime. Performance comparison with three stateof-the-art denoising algorithms, carried out on electrocardiogram signals and two test signals taken from the Wavelab toolbox, exhibits that the MPE framework results in consistent SNR gains for input SNRs below 5 dB.Index Terms-Minimum probability of error, shrinkage estimator, risk estimation, transform-domain shrinkage, subband shrinkage, expected 1 distortion, Gaussian mixture model.