Faint Object Detection in Multidimensional Astronomical Data

This thesis addresses the challenges of detecting faint objects in modern astronomical surveys like LSST and Euclid, which produce vast, complex, multi-wavelength datasets. Traditional pixel-based analysis methods struggle with crowded fields, overlapping sources, and variable backgrounds, leading to missed detections and biased measurements.

The core innovation is a paradigm shift from pixel-based to hierarchical, structure-aware analysis using the max-tree data structure. This framework organizes an image into nested components based on intensity, preserving topological relationships and the intrinsic geometry of astronomical emissions.

Three key contributions are presented. First, a novel method called Multi-band Max-Tree Objects (MMTO) is introduced for multi-spectral source segmentation. It accurately (98%) identifies correlated sources across wavelengths with a 31x computational speed-up, enabling scalable analysis of petabyte-scale surveys. Second, a morphological background model is developed that uses the max-tree to distinguish background light from source emission, yielding more accurate flux measurements than standard tools. Third, a hierarchical deblending algorithm operates on the max-tree to separate overlapping sources without parametric shape assumptions, preserving faint, nested structures.

Beyond astronomy, these techniques offer a versatile framework for analyzing complex, multi-scale data in fields like medical imaging and remote sensing. Future work may integrate deep learning and extend the methods for larger datasets. Ultimately, this thesis bridges the gap between data acquisition and discovery by providing robust, scalable tools to explore the faint universe, ensuring scientific rigor in the era of big-data astronomy.