Gaussian Lifting for Fast Bilateral and Nonlocal Means Filtering

Area of Science:

• Image Processing
• Computer Vision
• Signal Processing

Background:

• Existing fast implementations for bilateral and nonlocal filters in high dimensions face inefficiencies due to complex resampling or filtering processes.
• Accurate filter implementation is crucial for image processing and bilateral-regularized inverse problems.

Purpose of the Study:

• To propose the Gaussian lifting framework for efficient and accurate bilateral and nonlocal means filtering.
• To leverage similarities between separable wavelet transforms and Gaussian pyramids for signal processing.
• To explore adaptive lifting schemes for enhanced filtering.

Main Methods:

• Scalar resampling of high-dimensional signals after decorrelation.
• Application of multi-rate signal processing techniques.
• Development of the Gaussian lifting framework inspired by wavelet transforms and Gaussian pyramids.

Main Results:

• The Gaussian lifting approach demonstrates more accurate and efficient image filtering across multiple scales.
• The framework offers an alternative to complex resampling methods in high-dimensional filtering.
• Adaptive lifting schemes show potential for further optimization.

Conclusions:

• Gaussian lifting provides an efficient and accurate method for bilateral and nonlocal means filtering.
• This framework enhances the performance of image processing and inverse problem solutions.
• The approach is adaptable and shows promise for future research in signal processing.