Estimate noise scale from singular values with linear tail extrapolation

This function estimates a characteristic scale from a vector of singular values by fitting a linear model to the tail and extrapolating to length n. The median of the extrapolated values is returned as the estimate. If no sufficiently linear tail is detected (based on min_r2) or the extrapolation produces negative values, a fallback estimate is returned using the 75\

Usage

getScaleFromSVs(sv, n, min_r2 = 0.95)

Arguments

sv

Numeric vector of singular values sorted in decreasing order.

n

Integer, total length to which the linear tail is extrapolated.

min_r2

Numeric, minimum R-squared value required for accepting the linear tail fit. Defaults to 0.95.

Value

A numeric scalar giving the estimated scale. If linear extrapolation is unreliable, returns sv[ceiling(0.75 * length(sv))].

Examples

sv <- exp(-seq(0, 5, length.out = 50)) + rnorm(50, 0, 0.01)
getScaleFromSVs(sv, n = 100)
#> $scale
#> [1] 0.01510799
#>