Optimization of Bilateral Filter Parameters via Chi-Square Unbiased Risk Estimate

Bilateral filter is an edge-preserving diffusion filter and is widely used for image denoising. The denoising quality is sensitive to the choice of the bilateral filter parameters. Here, we propose to use the Chi-Square Unbiased Risk Estimate (CURE) for optimizing bilateral filter parameters in squared magnitude MR images, which follow a non-central chi-square distribution with two degrees of freedom. CURE is an unbiased estimate of the Mean Squared Error (MSE) and it does not require any knowledge of the noise-free data. We derive explicit analytical expressions for CURE in the setting of bilateral filters and present experimental results that confirm the optimality of CURE.