[Maximal entropy principle wavelet denoising]

Area of Science:

• Signal Processing
• Information Theory
• Statistical Analysis

Context:

• Determining the optimal threshold for wavelet coefficients is crucial in wavelet denoising to distinguish between signal and noise.
• Existing methods face challenges in accurately setting these thresholds, impacting denoising performance.

Purpose:

• To develop a wavelet denoising method that accurately determines the threshold for wavelet coefficients using the maximal entropy principle (MEP).
• To establish a statistically optimal threshold that differentiates signal from noise based on probabilistic distributions.

Summary:

• The proposed method leverages information theory's MEP, deducing that detailed wavelet coefficients of random noise follow a normal distribution.
• An optimal threshold is derived using MEP, ensuring coefficients below this value adhere to a normal probabilistic distribution, effectively separating signal and noise.
• Simulation analysis confirms this threshold optimally distinguishes signal and noise coefficients from a statistical standpoint.

Impact:

• The method significantly improves the signal-to-noise ratio (SNR) compared to other wavelet denoising techniques.
• The performance of this MEP-based thresholding demonstrates minimal sensitivity to variations in the signal-to-noise ratio.
• This approach offers a statistically robust and effective solution for wavelet-based signal denoising applications.