Cartesian projection of the denoised thermal dust maps centered at the intersection of four faces. From left to right and top to bottom panels: denoising each face independently using α-shearlets with α = 1, restoration via the rotation-based approach, patchwork approach with α = 1, dictionary learning with patch width of 12. The colorscale has been stretched to visualize the artifacts seen as a cross-shape discontinuity at the boundaries of the four HEALPix faces in the upper left panel. All of our proposed approaches are free from these artifacts. Units are in μK.