Million Points of Light (MPoL)

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MPoL is a Python framework for Regularized Maximum Likelihood (RML) imaging. It is built on top of PyTorch, which provides state of the art auto-differentiation capabilities and optimizers. We focus on supporting continuum and spectral line observations from interferometers like the Atacama Large Millimeter/Submillimeter Array (ALMA) and the Karl G. Jansky Very Large Array (VLA). There is potential to extend the package to work on other Fourier reconstruction problems like sparse aperture masking and other forms of optical interferometry.

To get a sense of how MPoL works, please take a look at the Introduction to Regularized Maximum Likelihood Imaging and then the tutorials down below. If you have any questions, please join us on our Github discussions page.

If you’d like to help build the MPoL package, please check out the Developer Documentation to get started. For more information about the constellation of packages supporting RML imaging and modeling, check out the MPoL-dev organization website and github repository hosting the source code.

If you use MPoL in your research, please cite us! See MPoL-dev/MPoL for the citation.

User Guide

• Introduction to Regularized Maximum Likelihood Imaging
  • Introduction to Likelihood functions
  • Data in the Fourier domain
  • Likelihood functions for Fourier data
  • RML images as non-parametric models
  • The MPoL package for Regularized Maximum Likelihood imaging
• MPoL Installation
  • Using pip
  • From source
  • Upgrading
  • Documentation
  • Using CUDA acceleration
• Units and Conventions
  • Fourier transform conventions
  • Continuous representation of interferometry
  • Discretized representation
• Developer Documentation
  • Release model
  • Setting up your development environment
  • Testing
  • Documentation
  • Contributing
  • Releasing a new version of MPoL
• API
  • Utilities
  • Coordinates
  • Geometry
  • Gridding
  • Datasets
  • Images
  • Fourier
  • Precomposed Modules
  • Losses
  • Training and testing
  • Cross-validation
  • Analysis
  • Plotting

Tutorials

• Introduction to PyTorch: Tensors and Gradient Descent
  • Introduction to Tensors
  • Calculating Gradients
  • Optimizing a Function with Gradient Descent
  • Additional Resources
• Gridding and diagnostic images
  • Importing data
  • Plotting the data
  • The GridCoords object
  • Making images with DirtyImager
  • Averaging and exporting data with DataAverager
  • Checking data weights
• Intro to RML with MPoL
  • Gridding recap
  • The PyTorch dataset
  • Building an image model
  • Breaking down the training loop
  • Loss functions
  • Gradient descent
  • Iterating the training Loop
  • Visualizing the image
  • Visualizing the residuals
• Likelihood functions and model visibilities
  • Mock image
  • The mpol.fourier.NuFFT object
  • Compared to the mpol.gridding.DataAverager object
  • Image-plane forward model
  • Producing model visibilities
  • Evaluating a likelihood function
  • Normalized negative log likelihood loss function
• Cross validation
  • Setup
  • K-fold cross validation
  • Choosing the K-folds
  • The cross validation loop
  • Results
• GPU Acceleration
  • Installation and Configuration
  • Why use the GPU?
  • Using the GPU as part of PyTorch and MPoL
• Initializing with the Dirty Image
  • Image Setup
  • Model and Optimization Setup
  • Loss Function
  • Training Loop
  • Saving the Model
  • Loading the Model
  • Conclusion
• HD143006 Tutorial Part 1
  • Viewing the CLEAN image
  • Plotting the Baselines
  • The mpol.gridding.DirtyImager Object
  • Making diagnostic dirty images
  • Comparing Dirty and CLEANed Images
• HD143006 Tutorial Part 2
  • Loading Data
  • Getting the Dirty Image and Creating the Model
  • Initializing Model with the Dirty Image
  • Visualization utilities
  • Training loop
  • Cross Validation
• Making a Mock Dataset
  • Choosing a mock sky brightness distribution
  • Using Pillow to greyscale, apodize, pad, and resize
  • Exporting to a Numpy array and setting flux scale
  • Initializing ImageCube
  • Obtaining \(u,v\) baseline and weight distributions
  • Making the mock dataset
  • Verifying the mock dataset
• Parametric Inference with Pyro
  • MPoL and models
  • DSHARP AS 209 dataset
  • Introduction to Probabilistic Programming Languages
  • Building a parametric disk model
  • Parameter inference with Stochastic Variational Inference (SVI)
  • SVI with a AutoMultivariateNormal Model
  • Parameter inference with MCMC

• Index

• Changelog