We implement the multiscale inversion based on the multiresolution wavelet representation. One reason is that the wavelet transform based on the Lifting Scheme has enabled the application of the 2nd generation wavelet bases in irregular, non-Euclidean manifolds. Examples of regional and global seismic tomography, detiding of the ocean current velocity fields,interpolations of Martian magnetic field and Atlantic fishery will be shown to demonstrate the merits of the multiscale regularization that screens through the non-stationary local scale hierarchy based on the locally available sampling density and construct the adequately keen resolution. Conceptual comparison with the popular kriging method will also be mentioned.