Towards artifact-free characterization of surface topography using complex wavelets and total variation minimization

A hybrid method based on dual-tree complex wavelet transform and total variation minimization is proposed for erasure of undesirable artifacts that arise in the existing wavelet-based methods in surface metrology. The complex wavelet transform provides approximate shift invariance and good directional selectivity, and attempts to solve the weakness of real discrete wavelet methods. Reconstruct the complex wavelet coefficients using a total variation minimization principle to eliminate the wavelet-shape artifacts and the pseudo-Gibbs artifacts near the discontinuities, which are caused when thresholding small wavelet coefficients. By replacing these thresholded complex wavelet coefficients by optimal values that minimize the total variation, the method performs a close artifact-free surface characterization. Numerical experiments using a series of typical engineering and bioengineering surfaces demonstrate the remarkable potential of the methodology.