A secondary EWMA-based dictionary learning algorithm for polynomial phase signal denoising.

Area of Science:

• Signal Processing
• Machine Learning
• Data Denoising

Background:

• Sparse representation struggles with polynomial phase signal (PPS) denoising in Gaussian noise using conventional dictionary learning.
• Existing methods like K-SVD and RLS-DLA are limited when trained on noisy data.

Purpose of the Study:

• To develop a novel dictionary learning algorithm for effective polynomial phase signal (PPS) denoising.
• To enhance signal-to-noise ratio (SNR) and minimize mean squared error in denoised signals.

Main Methods:

• A new dictionary learning algorithm incorporating secondary exponentially weighted moving average (SEWMA) is proposed.
• Signal-to-noise ratio (SNR) estimation is used to determine the optimal weighted decline rate.
• The algorithm refines dictionary atoms using SEWMA after initial dictionary training with RLS-DLA.

Main Results:

• The proposed SEWMA-based algorithm achieves a higher SNR than K-SVD and RLS-DLA.
• Mean squared error is significantly lower with the proposed method compared to existing algorithms.
• Optimal denoising performance is achieved by setting the weighted decline rate based on estimated SNR.

Conclusions:

• The novel SEWMA-based dictionary learning algorithm offers superior performance for denoising polynomial phase signals (PPS).
• This method effectively addresses the limitations of traditional dictionary learning approaches in noisy environments.
• The proposed technique provides a robust solution for improving signal quality in applications involving polynomial phase signals.