A new analysis suggests that a wavelet-based method can separate Galactic dust from the mottled cosmic infrared background in Planck maps, even in a patch where the signal was weak. Across three high-Galactic-latitude regions, the method recovered dust without detecting significant leakage between the dust and background components.
The approach uses Wavelet Phase Harmonics, or WPH: statistics designed to capture patterns in an image across different angular scales. The study treated the task as a component-separation problem, trying to extract the Milky Way’s dust emission from a mixed 353 GHz intensity map while retaining the statistical properties of the cosmic infrared background anisotropies.
A difficult test in three small windows
The researchers analyzed the Planck Public Release 3 SMICA CMB-subtracted 353 GHz intensity map alongside low- and intermediate-velocity hydrogen maps from HI4PI. They focused on three square, high-latitude patches, each covering 222 square degrees and measuring 14.9 degrees on a side, with 256 by 256 pixels. The regions ranged from a signal-to-noise ratio of 0.9 to 4.6, putting the method through low-, intermediate- and high-signal conditions.
To characterize the background component, the algorithm used 100 synthetic contamination maps. Their mean standard deviation was 9.0 kilojanskys per steradian, with an estimated 1-sigma variation of 0.4 kilojanskys per steradian. During the reconstruction, the researchers minimized a combined loss in pixel space with L-BFGS optimization, repeatedly estimating the expected contamination statistics from the synthetic maps.
A mock version of the lowest-signal region provided a benchmark with a known input correlation. In that simulation, with a signal-to-noise ratio of 1, the recovered dust–hydrogen correlation was 0.90, close to the value built into the mock data. That result supports the method’s performance in the test case, but it does not provide a direct ground-truth accuracy estimate for the real Planck sky.
The separation held up across scales
The recovered contamination spectra matched the synthetic ensemble in all three regions, and the study found no statistically significant correlation between the recovered contamination and the hydrogen maps within its 1-sigma Gaussian uncertainties. The result is consistent with negligible detected dust leakage into the contamination map, although it does not show that leakage is exactly zero.
A comparison in the lowest-signal region found that the WPH dust map agreed with the available template-fit dust reference while preserving the reference contamination’s phase structure at multipoles above 100, the scales where contamination dominated. Unlike the template fit, which used a fixed 1.8-degree correlation scale at Nside 32, WPH recovered structures on both large and small angular scales.
The dust power spectra were described by power laws across multipoles from 25 to 625. The fitted slopes were −2.66 ± 0.08 in the low-signal region, −2.33 ± 0.17 in the intermediate region and −2.66 ± 0.12 in the high-signal region. The dust and contamination spectra crossed at multipoles 100, 225 and 425, respectively, showing that the balance between the two components changed from patch to patch.
The recovered contamination maps also showed the expected overall distributions. Gaussian fits gave standard deviations of 8.1, 8.8 and 8.8 kilojanskys per steradian across the three regions, while the maps’ Minkowski functionals, measures of map structure, agreed with those from the 100 synthetic realizations.
Dust tracked one hydrogen component more closely
The recovered dust was strongly associated with low-velocity hydrogen emission, with a Pearson correlation of at least 0.7 in each region. Its relationship with intermediate-velocity hydrogen was much weaker: about 0.2 in the intermediate- and high-signal patches, and −0.33 in the low-signal patch.
The scale of the relationship mattered. The ratio of the dust–hydrogen cross-power to the corresponding auto-power was close to one at large angular scales and declined at smaller scales. Spatially varying-emissivity models reproduced that pattern using power-spectrum slopes of −2.2 for the intermediate-signal region and −2.4 for the high-signal region; the models were run 100 times.
After local changes in dust emissivity were accounted for, the mean residual moved toward zero as the assumed emissivity-correlation scale decreased and showed no dependence on hydrogen column density. The residual spread, however, increased approximately with hydrogen column density raised to the power 0.7. In template-fit reference maps, residual variation stayed well below 3 sigma in the first two regions, while about 24% of measurements in the third lay above that threshold and followed an increasing trend.
What the test does not settle
This was a map-level test in three square high-latitude patches, not a full-sky demonstration. The known-input comparison was performed on a mock version of the lowest-signal patch, where the recovered dust–hydrogen correlation was 0.90; the real-map result is instead based on agreement with synthetic contamination statistics and the absence of statistically significant detected leakage.
The declining small-scale correlation and the residual-scaling pattern were reproduced by spatially varying-emissivity models, but these map-level results do not by themselves identify the physical source of the variation. Whether the same behavior holds across broader sky coverage or other frequencies remains open.
Paper data and sources
Original title: Revealing Galactic dust beneath the cosmic infrared background anisotropies with Wavelet Phase Harmonics
Authors: Srijita Sinha, Tuhin Ghosh, Erwan Allys et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
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