Feature-preserving filtering for micro-structured surfaces using combined sparse regularizers

Micro-structured components have been widely used in modern opto-electronics systems, but effective characterization methods for structured surfaces are still of lack. Reliable filtering is required to separate the salient structural features and micro-textures, so that the characteristic parameters of the geometrical features can be obtained accurately. Conventional filtering methods cannot preserve sharp features very well. In this paper, a feature-preserving filtering method is proposed using the combined sparse regularizers. In addition to the fidelity term, two regularization terms involving the first order and second order derivatives respectively are taken in the optimization objective function, so that the filtered data can be divided into a piecewise constant part and a piecewise smooth part. Taking the advantage of sparsity of ℓp-norm (0 < p < 1), the regularized filtering method can achieve good balance between feature preserving and noise removal. An iterative reweighted algorithm is used to solve the complex objective function. Numerical experiments and comparisons are presented to show that the proposed method is capable of preserving features like sharp edges and corners and suitable for a wide variety of surface shapes.