Illustration of background noise reduction and enhancement of the filamentary structures in the Musca 250 μm map by edge-aware nonlinear filtering while promoting a signal’s gradient sparsity with L¹ norm. The images show the singularity exponents of a region in Musca that is rich in filamentary structures. The right panel displays the singularity exponents derived from the unfiltered original map, while the left panel shows the singularity exponents after filtering the map with λ = 0.7 (Eq. (1)). The same grayscale wedge is used for both images.