Density estimation embedded B-spline smoother for signal denoising and edge-preserving

Signal smoothing with sharp edge preserving is a very interesting area in signal and image processing. In this paper, an embedded density estimation technique and B-spline basis function based nonlinear smoother is proposed for recovering a signal with sharp edges from the observation with additive i.i.d Gaussian noise. A density estimation technique is used to estimate the empirical mean of local observations. Its performance is evaluated through a 1D signal and 2D image smoothing problem. Simulation shows that the proposed smoother has better smoothing and edge preserving capability than the Gaussian filter. And it is very easy to extend to high dimensions and is more computationally efficient.