1 Introduction and Motivation
1.1 From Images to Catalogs
1.2 Inverse Problems and Generative Models
1.3 Measurements on Multi-Exposure Data
1.4 Ellipse-Transformed Basis Function Models
1.5 Notation

2 Bayesian Modeling of Astronomical Images
2.1.2 Calibration Parameters
2.1.3 Monte Carlo Sampling
2.2 Multiple Objects and Multiple Exposures
2.3 Handling Calibration Uncertainties
2.4 Inner Sampling and Regularization
2.5 Adaptive Importance Sampling
2.6 Algorithm

3 Multi-Scale Elliptical Shapelets
3.1 Introduction
3.2 Limitations of Standard Shapelet Techniques
3.3 Convolution of Elliptical Shapelets
3.4 Modeling with Compound Shapelets
3.5 Demonstration and Results
3.6 Summary and Future Work

4 Applications
4.1 Photometry
4.2 Astrometry
4.3 Shear Estimation
4.4 Morphology and Classification
4.5 Deblending
4.6 Public Catalogs

5 Implementation
5.1 Pipeline Overview
5.2 Scaling and Parallelization

6 Related Work
6.1 Shapelets and Sérsiclets
6.2 Lensfit
6.3 Coadd-Based Shear Estimation

7 Conclusion and Future Work