A fusion of principal component analysis and singular value decomposition based multivariate denoising algorithm for...

Area of Science:

• Geophysics
• Signal Processing
• Data Analysis

Background:

• Accurate measurement of time-dependent geomagnetic fields relies on free induction decay (FID) transversal data.
• Noise reduction and signal preservation in FID data are challenging due to limitations of existing filtering techniques.
• Efficiently reducing noise without prior information or stationary data assumptions remains a critical issue.

Purpose of the Study:

• To introduce a novel multivariate algorithm, principal component analysis and decomposition (PCAD), for noise reduction and interference cancellation in FID transversal data.
• To enhance the accuracy of geomagnetic field measurements by improving signal-to-noise ratio in FID data.
• To develop a method that balances denoising efficiency with the preservation of pure FID data.

Main Methods:

• Developed a new algorithm, PCAD, integrating principal component analysis (PCA) and singular value decomposition (SVD).
• Utilized PCA to identify dominant components of FID signals and noise floors, selecting optimal subspaces via cumulative variance.
• Combined PCA with SVD filtering, identifying and nulling singular values corresponding to interferences for noise suppression.

Main Results:

• The PCAD algorithm demonstrated superior performance in noise suppression compared to widely used filter methods.
• Extensive experiments on synthetic and real FID data showed PCAD preserves FID transversal data more effectively.
• Significant improvements in noise reduction were observed across various noise levels.

Conclusions:

• The PCAD algorithm offers an effective solution for noise reduction and interference cancellation in FID transversal data.
• This method provides an optimal trade-off between preserving data integrity and achieving high denoising efficiency.
• PCAD enhances the accuracy of time-dependent geomagnetic field measurements by improving FID data quality.