A distribution-independent risk estimator for image denoising

We address the problem of image denoising for an additive white noise model without placing any restrictions on the statistical distribution of noise. We assume knowledge of only the first- and second-order noise statistics. In the recent mean-square error (MSE) minimization approaches for image denoising, one considers a particular noise distribution and derives an expression for the unbiased risk estimate of the MSE. For additive white Gaussian noise, an unbiased estimate of the MSE is Stein's unbiased risk estimate (SURE), which relies on Stein's lemma. We derive an unbiased risk estimate without using Stein's lemma or its counterparts for additive white noise model irrespective of the noise distribution. We refer to the MSE estimate as the generic risk estimate (GenRE). We demonstrate the effectiveness of GenRE using shrinkage in the undecimated Haar wavelet transform domain as the denoising function. The estimated peak-signal-to-noise-ratio (PSNR) using GenRE is typically within 1% of the PSNR obtained when optimizing with the oracle MSE. The performance of the proposed method is on par with SURE for Gaussian noise distribution, and better than SURE-based methods for other noise distributions such as uniform and Laplacian distribution in terms of both PSNR and structural similarity (SSIM).