Separation of stationary and non-stationary sources with a generalized eigenvalue problem

Area of Science:

• Signal Processing
• Data Analysis
• Geophysics

Background:

• Real-world data often contains mixtures of stationary and non-stationary signals, challenging direct analysis.
• Separating these signal types is crucial for understanding underlying data-generating mechanisms, as seen in EEG and geophysical data.
• Existing Stationary Subspace Analysis (SSA) methods can be computationally intensive and lack closed-form solutions.

Purpose of the Study:

• To develop the first Stationary Subspace Analysis (SSA) algorithm with a closed-form solution.
• To introduce a faster, more stable, and potentially optimal method for separating mixed signal sources.
• To demonstrate the efficacy of the new method on simulated and real-world geophysical data.

Main Methods:

• Development of Analytic Stationary Subspace Analysis (ASSA), a novel algorithm providing a closed-form solution for SSA.
• Performance evaluation through numerical simulations across diverse settings, comparing ASSA with state-of-the-art methods.
• Application of ASSA to geophysical data, specifically analyzing Pi 2 pulsations in the geomagnetic field.

Main Results:

• ASSA achieves a significant speed improvement, exceeding 100 times faster than current state-of-the-art methods.
• The method demonstrates numerical stability and optimality under time-constant covariance conditions between stationary and non-stationary sources.
• ASSA yields superior results in simulations, even with time-varying group-wise covariance, and extracts meaningful components from geophysical data.

Conclusions:

• Analytic Stationary Subspace Analysis (ASSA) provides a computationally efficient and stable approach to signal separation.
• The closed-form solution of ASSA offers a significant advancement over existing SSA techniques.
• ASSA's application to geophysical data reveals new insights into geomagnetic field pulsations, highlighting its practical utility.