Table 2 Comparison of discussed methods for addressing heteroscedastic noise

No scaling

-

-

Overweights higher intensity peaks relative to lower intensity ones by an amount proportional to their difference (unbounded).

Heuristic

Variance scaling

The noise variance vector is estimated as the sample variance.

The sample variance includes systematic spatial variation, which is erroneously treated as noise. It underestimates the significance of high-intensity over-dispersed peaks.

Pareto scaling

The noise variance vector is estimated as the sample standard deviation.

The sample standard deviation includes systematic spatial variation, which is erroneously treated as noise. It underestimates the significance of low-intensity/censored peaks.

Root-mean scaling

The noise variance is assumed to equal the global mean spectrum (i.e., the sample mean).

Overestimates the significance of low-intensity/censored peaks relative to high-intensity ones by an amount bounded by a constant factor.

Log transform

Takes the logarithm of intensities in each spectrum.

From a noise equalisation standpoint, assumes noise variance is an exponential function of the signal. It is mathematically problematic for sparse datasets with a high fraction of zeros.

Square-root transform

Takes the square-root of intensities in each spectrum.

Prone to overfitting the noise since each data element is assigned an individual estimate of its variance. These estimates can be exceedingly poor for low-intensity signals.

Machine learning-based

PFA

Directly estimates the uncorrelated noise variance vector as part of an iterative matrix factorization algorithm.

Erroneously characterises uncorrelated systematic variation as noise, can be very time consuming to compute, is susceptible to outliers.

Model-based(proposed in this work)

WSoR

The noise variance vector is computed based on a weighted-sum-of-Ricians statistical model.