Restricted guided filter with SURE-LET-based parameter optimization

Guided image filtering has recently emerged as an effective technique for noise reduction and edge-preserving smoothing operation due to its appealing properties. It outperforms conventional bilateral filtering in a variety of applications in terms of both quality and computational cost. However, the combination of smoothing parameters (ε and Ω_s) that delivers optimal results has not yet been reported, and the contrast of the filtered output is considerably reduced. In this paper, we present a restricted version of guided filtering that has better contrast-preserving characteristics, and use Stein´s unbiased risk estimate (SURE) with an exhaustive search or a linear expansion of threshold (LET) to optimally tune the two above parameters. With SURE, the mean squared error (MSE) can be unbiasedly estimated without the requirement of the noise-free image. Experiments verified the accuracy of the SURE derivation and its effectiveness with respect to providing a better trade off between two interrelated objectives - noise reduction and edge-preservation.