Robust Wavelet-Based Noise-Scale Estimation

Estimates the observational noise standard deviation from high-frequency wavelet coefficients using a robust median absolute deviation rule.

estimate_noise_sd(
  wavelet_object,
  detail_levels,
  supplied_sd = NULL,
  mad_levels = 1L
)

Arguments

wavelet_object

A wavelet object returned by wd.

detail_levels

A nonempty numeric or integer vector of detail levels available in wavelet_object. The finest levels are selected.

supplied_sd

Optional known positive noise standard deviation. If supplied, it is returned directly and the MAD calculation is skipped.

mad_levels

The positive integer number of finest detail levels to pool when estimating the scale. The default is 1.

Details

Unless supplied_sd is provided, the function computes $$ \widehat{\sigma} = \frac{\operatorname{median}(|d-\operatorname{median}(d)|)}{0.6745} $$ using the finest mad_levels detail levels. If the resulting value is not positive and finite, the function falls back to pooling up to the three finest available detail levels. A strictly positive machine-scale value is returned in the remaining degenerate case.

Value

A single positive numeric value giving the supplied or estimated noise standard deviation.

See also

wswavelet, wd

References

Sanyal, N. (2026). Resolution-Adaptive Compact-Support Priors for Bayesian Wavelet Denoising: A Wendland-Semicircle Slab Mixture for Low-SNR Signal Recovery. Axioms, 15(9), 678. <DOI:10.3390/axioms15090678>

Author

Nilotpal Sanyal

Examples

# \donttest{
set.seed(1)
y <- rnorm(128)
wd <- wavethresh::wd(y, filter.number = 6L, bc = "periodic")
lev <- 0:(wavethresh::nlevelsWT(wd) - 1L)
estimate_noise_sd(wd, lev)
#> [1] 0.7212277
# }