Stochastic Interpolation of Sparsely Sampled Time Series via Multipoint Fractional Brownian Bridges

Area of Science:

• Physics
• Data Science
• Signal Processing

Background:

• Sparse signals present challenges in data analysis across various scientific disciplines.
• Stochastic processes offer potential for signal interpolation, but require careful parameterization.

Purpose of the Study:

• To introduce and validate a new method for interpolating sparsely sampled signals.
• To extend the fractional Brownian bridge concept for multi-point, nonequidistant interpolation.
• To determine the optimal Hurst exponent (H_opt) for accurate signal reconstruction.

Main Methods:

• Extension of the fractional Brownian bridge to include multiple intermediate points.
• Optimization of the Hurst exponent (H_opt) for signal interpolation.
• Application and validation on a fluid turbulence signal (high Reynolds number flow).

Main Results:

• Successful interpolation of sparsely sampled signals using the proposed stochastic process.
• Demonstration of the method's validity on complex, real-world data.
• Identification of the crucial role of the optimal Hurst exponent.

Conclusions:

• The developed method provides a robust approach for interpolating sparse signals.
• The technique is versatile and applicable to astrophysics, particle tracking, and surrogate data generation.
• Understanding signal characteristics, like non-self-similarity, is key for effective interpolation.