Adaptive kernel ridge regression for image denoising

The standard (Bayesian) methods for image denoising involve explicit (analytic) models of signal and noise. The performance of these parametric approaches critically depend on using realistic models, but accurate models may ruin analytical tractability. Recently, an alternative nonparametric method was successfully proposed in [1]. The method was based on developing stationary support vector regression (SVR) models in the wavelet domain according to prior knowledge about signal and noise features. Nevertheless, off-line analysis of the particular signal and noise statistics is required to apply it to different problems. In this work, we take a similar non-parametric approach, but we explore the ability of kernel ridge regression (KRR) to locally follow image and noise characteristics, thus trivially obtaining adaptive (non-stationary) description of the image. Making KRR adaptive alleviates the strong assumption of Gaussianity of the noise. The method is embedded in the iterative restoration framework that allows consistent parameter tuning. Promising results are obtained with a model straightforwardly formulated in the spatial domain for different noise sources.