APSIPA Transactions on Signal and Information Processing > Vol 9 > Issue 1

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

Jishnu Sadasivan, Indian Institute of Science, India, Subhadip Mukherjee, KTH Royal Institute of Technology, Sweden, subhadipju@gmail.com , Chandra Sekhar Seelamantula, Indian Institute of Science, India
 
Suggested Citation
Jishnu Sadasivan, Subhadip Mukherjee and Chandra Sekhar Seelamantula (2020), "Signal denoising using the minimum-probability-of-error criterion", APSIPA Transactions on Signal and Information Processing: Vol. 9: No. 1, e3. http://dx.doi.org/10.1017/ATSIP.2019.27

Publication Date: 20 Jan 2020
© 2020 Jishnu Sadasivan, Subhadip Mukherjee and Chandra Sekhar Seelamantula
 
Subjects
 
Keywords
Minimum probability of errorShrinkage estimatorRisk estimationExpected ℓ1 distortionGaussian mixture model (GMM)
 

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In this article:
1. INTRODUCTION 
II. THE PE RISK 
III. EXPERIMENTAL RESULTS FOR MPE-BASED DENOISING 
IV. THE EXPECTED ℓ1 DISTORTION 
V. PERFORMANCE OF THE EXPECTED ℓ1 DISTORTION-BASED POINTWISE SHRINKAGE ESTIMATOR 
VI. PERFORMANCE ASSESSMENT OF MPE AND ℓ1-RISK MINIMIZATION ALGORITHMS VERSUS BENCHMARK DENOISING ALGORITHMS 
VII. CONCLUSIONS 

Abstract

We consider 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 ε-neighborhood of the true value. The underlying parameter is assumed to be deterministic. The MPE, similar to the mean-squared error (MSE), depends on the ground-truth parameter, and therefore, has to be estimated from the noisy observations. The optimum shrinkage parameter is obtained by minimizing an estimate of the MPE. When the probability of error is integrated over ε, it leads to the expected ℓ1 distortion. The proposed MPE and ℓ1 distortion formulations are applicable to various noise distributions by invoking a Gaussian mixture model approximation. Within the realm of MPE, we also develop a specific extension to subband shrinkage. The denoising performance of MPE turns out to be better than that obtained using the minimum MSE-based approaches formulated within Stein's unbiased risk estimation (SURE) framework, especially in the low signal-to-noise ratio (SNR) regime. Performance comparisons with three benchmarking algorithms carried out on electrocardiogram signals and standard test signals taken from the Wavelab toolbox show that the MPE framework results in SNR gains particularly for low input SNR.

DOI:10.1017/ATSIP.2019.27