Bilateral filter evaluation based on exponential kernels

The well-known bilateral filter is used to smooth noisy images while keeping their edges. This filter is commonly used with Gaussian kernel functions without real justification. The choice of the kernel functions has a major effect on the filter behavior. We propose to use exponential kernels with L
¹
distances instead of Gaussian ones. We derive Stein's Unbiased Risk Estimate to find the optimal parameters of the new filter and compare its performance with the conventional one. We show that this new choice of the kernels has a comparable smoothing effect but with sharper edges due to the faster, smoothly decaying kernels.