Checking scale invariance: local correlation measure. Top left and right: visualization of the singularity exponents computed with the local correlation measure described in Eqs. (B.7) and (B.5), respectively, on the Musca 250 μm Herschel flux map presented in Sect. 2. The two images correspond to two consecutive downscaled wavelet projections of the original signal using a discrete wavelet projection. Bottom: resulting mappings h ↦ D(h) using the singularity exponents computed on the two consecutive scales (red: one-half scale of the original Musca Herschel map; green: one-fourth scale of the original Musca Herschel map). The two mappings coincide much better than with the exponents computed from log -regression and displayed in Fig. 5. Consequently, the local correlation measure algorithm exhibits the scaling in a much betterway.
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