A new SURE approach to image denoising: interscale orthonormal wavelet thresholding

Area of Science:

• Signal Processing
• Image Processing
• Computer Vision

Background:

• Traditional wavelet image denoising often relies on statistical models for wavelet coefficients.
• Existing methods can be computationally intensive and may not achieve optimal denoising performance.
• The need for accurate mean square error (MSE) estimation without access to the clean image is a significant challenge.

Purpose of the Study:

• To introduce a new, model-free approach to orthonormal wavelet image denoising.
• To develop an efficient denoising algorithm that minimizes mean square error using Stein's unbiased risk estimate.
• To demonstrate the algorithm's performance against state-of-the-art methods and explore new wavelet-based prediction techniques.

Main Methods:

• Parametrization of the denoising process as a sum of nonlinear processes with unknown weights.
• Minimization of Stein's unbiased risk estimate (SURE) to approximate the mean square error (MSE).
• Development of an interscale orthonormal wavelet thresholding algorithm and a group-delay-based parent-child prediction method.

Main Results:

• The proposed method achieves near-optimal denoising performance in terms of image quality.
• The algorithm demonstrates competitive computational efficiency (CPU requirements) compared to existing methods.
• A novel group-delay-based parent-child prediction technique for wavelet dyadic trees was developed as a byproduct.

Conclusions:

• The model-free approach using SURE for wavelet image denoising is effective and efficient.
• This method eliminates the need for explicit statistical modeling of wavelet coefficients.
• The developed techniques offer significant improvements in orthonormal wavelet-based image denoising and analysis.