Complex ridgelets for shift invariant characterizaion of surface topography with line singularities

A complex ridgelet transform, which provides shift invariance and good performance for line singularities, is proposed to solve the problems with existing wavelet-based methods in surface metrology by taking a dual-tree complex wavelet transform on the projections of the finite Radon transform. Numerical experiments show the efficiency of this methodology in approximation, denoising, and characterization of engineering and bioengineering surfaces with straight scratches.