Table 2
Summary of statistical methods for structural analysis of Galactic cirrus.
| Method | Diagnosticsa | Scales Probed | Anomaly Insensitive?b | Non-Gaussian Information?c | Invariant Across Field?d | Complexitye |
|---|---|---|---|---|---|---|
| Local Intensity Statistics | Moments PDF distance | Local (tunable r) | × | ✓ | × | Moderate to high |
| Power spectrum | Low | |||||
| Δ-Variance | Power-law slope | Global (all k or L) | ✓ | × | ✓ | Moderate |
| Cross-power spectrum | Low | |||||
| Wavelet Scattering Transform | Scattering coeff. Summary statistics | Global (all J) | ✓ | ✓ | ✓ | Moderate to high |
Notes. (a)Diagnostics used in this work for morphological characterization and comparison across dust tracers. (b)Is the diagnostic robust against local anomalies such as residuals of source removal? (c)Does the method retain non-Gaussian or equivalent local intermittency information? (d)Is the diagnostic invariant across the field? (e)Relative computation cost of each method, with the exact overhead depending on the setup. Note that computation for local intensity statistics scales with image size by 𝒪(N) and therefore is inefficient for high resolution wide fields, while computation for WST scales by 𝒪(N log N) and can be accelerated by GPU. Although it appears that WST is preferred over other methods, physical interpretation of the abundant (102 ~ 103) coefficients is not straightforward, and so benefits accrue from complementary insights from other methods.
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