Spectra of Variance-Stabilized Correlated Noise: Modeling and Efficient Computation

Abstract

Variance-stabilizing transformations (VSTs) are established statistical tools for tackling heteroskedasticity. They are commonly utilized as a preprocessing module within signal-processing pipelines, enabling one to use off-the-shelf methods designed for data corrupted by noise of constant variance on data that is otherwise corrupted by noise with signal-dependent variance. Being univariate mappings, VSTs are agnostic to possible correlation in the data. However, contrary to common assumptions, applying VSTs not only stabilizes the noise variance, but can also significantly perturb the noise correlation hence distorting the noise spectrum. As the accurate knowledge of the noise spectrum is essential to many applications such as filtering and coding, any unpredictable distortion of the noise spectrum is detrimental. In this paper, we propose a method to compute the distorted noise spectrum of the variance-stabilized data. The proposed method is efficient and accurate, extending the scope of reliable application of VSTs to data corrupted by correlated noise.