Hybrid wavelet denoising procedure of discontinuous surfaces

In this study, the authors propose a method for recovering a two-dimensional surface (image) from noisy observations containing significant jumps and discontinuities. The proposed procedure, termed as the segmented polynomial wavelet regression (SPWR) algorithm, combines wavelet regression with polynomial extrapolation and segmentation procedures. The bias that might occur on the discontinuous surface is alleviated through a segmentation process, and at the same time, inhomogeneous multi-scale features of the surface are efficiently treated by wavelet regression. The SPWR algorithm enjoys all the benefits of wavelet regression by implicitly detecting the discontinuities, and it is fast and easy to implement. Through a simulation study, it is demonstrated that the proposed method can produce substantially effective results.