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Fig. 11

image

Singularity spectrum of the Musca 250 μm Herschel map, computed with and without edge-aware filtering. The orange curve shows the singularity spectrum computed on raw unfiltered data, while the blue curve displays the singularity spectrum computed on edge-aware filtered data using the filtering introduced in Sect. 5.2 with parameter λ = 0.7. The horizontal axis gives the h-values of the scaling exponents, and the vertical axis gives the fractal dimension (see Sect. 3.3). First, it becomes obvious that the part of the spectrum corresponding to h ≤ 0, i.e., the strongest transitions, is not accurately computed on the unfiltered data; the presence of the background noise leads to an overestimation of the multifractal spectrum. Second, the slope of the right part of the graph is poorly evaluated in the presence of noise. As a result, the singularity spectrum computed on the filtered observation map is less symmetrical with regards to the vertical axis h = 0.

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