Atangana-Baleanu Regularized Wavelet Compression For Astronomical Time-Series

TL;DR

The paper tackles the challenge of compressing astronomical time-series without sacrificing faint, transient signals. It introduces a fractional AB-regularised wavelet framework that evolves wavelet coefficients via the Atangana-Baleanu Caputo derivative with a non-singular Mittag-Leffler kernel, enabling memory-aware, scale-consistent shrinkage. The method replaces classical algebraic thresholding with a proximal, memory-driven update per subband, and demonstrates competitive compression while better preserving low-amplitude transients on synthetic data and real TESS light curves. The work suggests practical benefits for large-scale time-domain archives and points to extensions for irregular sampling, 2D data, online processing, and integration with anomaly-detection pipelines.

Abstract

Astronomical light curves are noisy and irregular, so compression must reduce size without erasing weak transients. We propose a fractional wavelet compression method where wavelet coefficients are regularized via an Atangana Baleanu Caputo derivative with a nonsingular Mittag Leffler kernel. The induced long memory smoothing suppresses noise while preserving coherent transits, flares and oscillations. We give the coefficient level formulation, an efficient implementation, and comparisons with classical discrete wavelet thresholding, showing competitive compression with improved retention of low-amplitude events.

Figures (3)

• Figure 1: The image depicts a synthetic light curve that illustrates how compression impacts data. The original data is represented by a solid line, while the reconstruction of this data is shown by two different dash style lines. One of these lines represents the reconstruction using a traditional Discrete Wavelet Transform device and the other line demonstrates the proposed Atangana-Baleanu-regularisation method.
• Figure 2: When DWT-based Classical Compression Methods are compared quantitatively, it is clear that each method performs very differently based on the AB Regularised Scheme's Average Normalised MSE and Proportionate Comparison; For $\mathrm{CR}\approx 8\text{--}32$, the average MSE and PAE were lower for fractional schemes, indicating that they are producing an increase in compression from the amount of reconstructed images produced.
• Figure 3: Dependence of reconstruction quality on the fractional order $\alpha$ for the AB-regularised compressor. The curve shows the structural similarity index (SSIM) for a representative synthetic light curve at a fixed compression setting. Performance is relatively stable in the interval $0.7 \lesssim \alpha \lesssim 0.9$, with a mild maximum around $\alpha \approx 0.8$.