Neural Kernel Regression for Consistent Monte Carlo Denoising

Unbiased Monte Carlo path tracing that is extensively used in realistic rendering produces undesirable noise, especially with low samples per pixel (spp). Recently, several methods have coped with this problem by importing unbiased noisy images and auxiliary features to neural networks to either predict a fixed-sized kernel for convolution or directly predict the denoised result. Since it is impossible to produce arbitrarily high spp images as the training dataset, the network-based denoising fails to produce high-quality images under high spp. More specifically, network-based denoising is inconsistent and does not converge to the ground truth as the sampling rate increases. On the other hand, the post-correction estimators yield a blending coefficient for a pair of biased and unbiased images influenced by image errors or variances to ensure the consistency of the denoised image. As the sampling rate increases, the blending coefficient of the unbiased image converges to 1, that is, using the unbiased image as the denoised results. However, these estimators usually produce artifacts due to the difficulty of accurately predicting image errors or variances with low spp. To address the above problems, we take advantage of both kernel-predicting methods and post-correction denoisers. A novel kernel-based denoiser is proposed based on distribution-free kernel regression consistency theory, which does not explicitly combine the biased and unbiased results but constrain the kernel bandwidth to produce consistent results under high spp. Meanwhile, our kernel regression method explores bandwidth optimization in the robust auxiliary feature space instead of the noisy image space. This leads to consistent high-quality denoising at both low and high spp. Experiment results demonstrate that our method outperforms existing denoisers in accuracy and consistency.