On Kernel Selection of Multivariate Local Polynomial Modelling and its Application to Image Smoothing and Reconstruction

This paper studies the problem of adaptive kernel selection for multivariate local polynomial regression (LPR) and its application to smoothing and reconstruction of noisy images. In multivariate LPR, the multidimensional signals are modeled locally by a polynomial using least-squares (LS) criterion with a kernel controlled by a certain bandwidth matrix. Based on the traditional intersection confidence intervals (ICI) method, a new refined ICI (RICI) adaptive scale selector for symmetric kernel is developed to achieve a better bias-variance tradeoff. The method is further extended to steering kernel with local orientation to adapt better to local characteristics of multidimensional signals. The resulting multivariate LPR method called the steering-kernel-based LPR with refined ICI method (SK-LPR-RICI) is applied to the smoothing and reconstruction problems in noisy images. Simulation results show that the proposed SK-LPR-RICI method has a better PSNR and visual performance than conventional LPR-based methods in image processing.