Image Denoising using Optimally Weighted Bilateral Filters: A Sure and Fast Approach

TL;DR

This paper introduces an optimally weighted bilateral filter that combines a modified and original filter to enhance image denoising performance across various noise levels with minimal computational cost.

Contribution

A novel weighted combination of bilateral filters is proposed, improving denoising robustness at high noise levels while maintaining efficiency.

Findings

Significant visual and PSNR improvements over the original bilateral filter.

Performance comparable to non-local means filter with lower computational cost.

Effective across different noise levels with minimal additional processing.

Abstract

The bilateral filter is known to be quite effective in denoising images corrupted with small dosages of additive Gaussian noise. The denoising performance of the filter, however, is known to degrade quickly with the increase in noise level. Several adaptations of the filter have been proposed in the literature to address this shortcoming, but often at a substantial computational overhead. In this paper, we report a simple pre-processing step that can substantially improve the denoising performance of the bilateral filter, at almost no additional cost. The modified filter is designed to be robust at large noise levels, and often tends to perform poorly below a certain noise threshold. To get the best of the original and the modified filter, we propose to combine them in a weighted fashion, where the weights are chosen to minimize (a surrogate of) the oracle mean-squared-error (MSE). The optimally-weighted filter is thus guaranteed to perform better than either of the component filters in terms of the MSE, at all noise levels. We also provide a fast algorithm for the weighted filtering. Visual and quantitative denoising results on standard test images are reported which demonstrate that the improvement over the original filter is significant both visually and in terms of PSNR. Moreover, the denoising performance of the optimally-weighted bilateral filter is competitive with the computation-intensive non-local means filter.