Fast blockwise SURE shrinkage for image denoising

• We derive the closed-form optimal blockwise SURE shrinkage for image denoising.
• We propose an adaptive and fast blockwise shrinkage algorithm with a constant-time complexity.
• We demonstrate this shrinkage solution is effective to a wide collection of image denoising methods.

In this paper, we investigate the shrinkage problem of image denoising for various methods under the additive white Gaussian noise (AWGN) model. Our main contribution is to derive the closed-form of the optimal shrinkage that minimizes the Stein's unbiased risk estimator (SURE) and thus allows direct blockwise shrinkage without additional optimizations. Simulation results show that the proposed method boosts the denoising performance for a variety of image denoising techniques including the moving average filter, the median filter, the wiener filter, the bilateral filter, the probabilistic non-local means, and the block matching 3D filter in terms of higher pixel signal noise ratio (PSNR) and structural similarity index (SSIM). We also case study the proposed shrinkage solution with respect to the classic NLM denoising, whose shrinkage solutions and equivalent forms have been widely researched, and further confirm its superiority. The proposed shrinkage solution can be used to improve arbitrary image denoising methods under the AWGN model, and it serves as a good remedy to save badly denoised images due to inappropriate parameters.