Unveiling shapes: Shapelets for galaxy morphology and gravitational lensing studies

The shapelet basis system forms a convenient and mathematically well-established framework for describing shapes of galaxies and the telescope's point spread function (PSF). A shapelet-based image processing pipeline thus offers remarkable benefits: For weak-lensing studies, its analytic and efficient deconvolution procedure from arbitrary PSFs constitutes a significant improvement on the traditional KSB method. For complex morphologies of the lensed galaxy ensemble, it has proven to belong to the most accurate shear measurement methods available today. Furthermore, a multitude of shear estimators can be formed from the expansion coefficients, which allows cross-checking of measurements. For statistical investigation of galaxy morphologies, one profits from the significant dimensionality reduction and scale-invariance provided by the shapelet decomposition. Unfortunately, overfitting the data and unphysical high-frequency oscillations pose apparent limitations to its applicability. These problems can be remedied by minor modifications to the decomposition and deconvolution procedures.