Multi-CCD Point Spread Function Modelling

Context. Galaxy imaging surveys observe a vast number of objects that are affected by the instrument’s Point Spread Function (PSF). Weak lensing missions, in particular, aim at measuring the shape of galaxies, and PSF effects represent an important source of systematic errors which must be handled appropriately. This demands a high accuracy in the modelling as well as the estimation of the PSF at galaxy positions.

Aims. Sometimes referred to as non-parametric PSF estimation, the goal of this paper is to estimate a PSF at galaxy positions, starting from a set of noisy star image observations distributed over the focal plane. To accomplish this, we need our model to first of all, precisely capture the PSF field variations over the Field of View (FoV), and then to recover the PSF at the selected positions. Methods. This paper proposes a new method, coined MCCD (Multi-CCD PSF modelling), that creates, simultaneously, a PSF field model over all of the instrument’s focal plane. This allows to capture global as well as local PSF features through the use of two complementary models which enforce different spatial constraints. Most existing non-parametric models build one model per Charge-Coupled Device (CCD), which can lead to difficulties in capturing global ellipticity patterns.

Results. We first test our method on a realistic simulated dataset comparing it with two state-of-the-art PSF modelling methods (PSFEx and RCA). We outperform both of them with our proposed method. Then we contrast our approach with PSFEx on real data from CFIS (Canada-France Imaging Survey) that uses the CFHT (Canada-France-Hawaii Telescope). We show that our PSF model is less noisy and achieves a ~ 22% gain on pixel Root Mean Squared Error (RMSE) with respect to PSFEx.

Conclusions. We present, and share the code of, a new PSF modelling algorithm that models the PSF field on all the focal plane that is mature enough to handle real data.

Reference: Tobias Liaudat, Jérôme Bonnin,  Jean-Luc Starck, Morgan A. Schmitz, Axel Guinot, Martin Kilbinger and Stephen D. J. Gwyn. “Multi-CCD Point Spread Function Modelling, submitted 2020.

arXiv, code.

Probabilistic Mapping of Dark Matter by Neural Score Matching


The Dark Matter present in the Large-Scale Structure of the Universe is invisible, but its presence can be inferred through the small gravitational lensing effect it has on the images of far away galaxies. By measuring this lensing effect on a large number of galaxies it is possible to reconstruct maps of the Dark Matter distribution on the sky. This, however, represents an extremely challenging inverse problem due to missing data and noise dominated measurements. In this work, we present a novel methodology for addressing such inverse problems by combining elements of Bayesian statistics, analytic physical theory, and a recent class of Deep Generative Models based on Neural Score Matching. This approach allows to do the following: (1) make full use of analytic cosmological theory to constrain the 2pt statistics of the solution, (2) learn from cosmological simulations any differences between this analytic prior and full simulations, and (3) obtain samples from the full Bayesian posterior of the problem for robust Uncertainty Quantification. We present an application of this methodology on the first deep-learning-assisted Dark Matter map reconstruction of the Hubble Space Telescope COSMOS field.

Reference: Benjamin Remy, François Lanusse, Zaccharie Ramzi, Jia Liu, Niall Jeffrey and Jean-Luc Starck. “Probabilistic Mapping of Dark Matter by Neural Score Matching, Machine Learning and the Physical Sciences Workshop, NeurIPS 2020.

arXiv, code.

XPDNet for MRI Reconstruction: an Application to the fastMRI 2020 Brain Challenge

We present a modular cross-domain neural network the XPDNet and its application to the MRI reconstruction task. This approach consists in unrolling the PDHG algorithm as well as learning the acceleration scheme between steps. We also adopt state-of-the-art techniques specific to Deep Learning for MRI reconstruction. At the time of writing, this approach is the best performer in PSNR on the fastMRI leaderboards for both knee and brain at acceleration factor 4.

Reference:  Z. Ramzi,  P. Ciuciu and J.-L. Starck . “XPDNet for MRI Reconstruction: an Application to the fastMRI 2020 Brain Challenge.

 

This network was used to submit reconstructions to the 2020 fastMRI Brain reconstruction challenge. Results are to be announced on December 6th 2020.

Denoising Score-Matching for Uncertainty Quantification in Inverse Problems

Deep neural networks have proven extremely efficient at solving a wide range of inverse problems, but most often the uncertainty on the solution they provide is hard to quantify. In this work, we propose a generic Bayesian framework for solving inverse problems, in which we limit the use of deep neural networks to learning a prior distribution on the signals to recover. We adopt recent denoising score matching techniques to learn this prior from data, and subsequently use it as part of an annealed Hamiltonian Monte-Carlo scheme to sample the full posterior of image inverse problems. We apply this framework to Magnetic Resonance Image (MRI) reconstruction and illustrate how this approach not only yields high quality reconstructions but can also be used to assess the uncertainty on particular features of a reconstructed image.

Reference:  Z. Ramzi,  Benjamin Remy, François Lanusse, J.-L. Starck and P. Ciuciu. “Denoising Score-Matching for Uncertainty Quantification in Inverse Problems, Deep Learning and Inverse Problems Workshop NeurIPS, 2020.

Wavelets in the Deep Learning Era

Sparsity based methods, such as wavelets, have been state-of-the-art for more than 20 years for inverse problems before being overtaken by neural networks.
In particular, U-nets have proven to be extremely effective.
Their main ingredients are a highly non-linear processing, a massive learning made possible by the flourishing of optimization algorithms with the power of computers (GPU) and the use of large available data sets for training.
While the many stages of non-linearity are intrinsic to deep learning, the usage of learning with training data could also be exploited by sparsity based approaches.
The aim of our study is to push the limits of sparsity with learning, and comparing the results with U-nets.
We present a new network architecture, which conserves the properties of sparsity based methods such as exact reconstruction and good generalization properties, while fostering the power of neural networks for learning and fast calculation.
We evaluate the model on image denoising tasks and show it is competitive with learning-based models.

Reference:  Z. Ramzi,  J.-L. Starck and P. Ciuciu. “Wavelets in the Deep Learning Era, Eusipco, 2020.

Benchmarking Deep Nets MRI Reconstruction Models on the FastMRI Publicly Available Dataset

 

The MRI reconstruction field lacked a proper data set that allowed for reproducible results on real raw data (i.e. complex-valued), especially when it comes to deep learning (DL) methods as this kind of approaches require much more data than classical Compressed Sensing~(CS) reconstruction. This lack is now filled by the fastMRI data set, and it is needed to evaluate recent DL models on this benchmark. Besides, these networks are written in different frameworks and repositories (if publicly available), it is therefore needed to have a common tool, publicly available, allowing a reproducible benchmark of the different methods and ease of building new models. We provide such a tool that allows the benchmark of different reconstruction deep learning models.

Reference:  Z. Ramzi, P. Ciuciu and J.-L. Starck. “Benchmarking Deep Nets MRI Reconstruction Models on the FastMRI Publicly Available Dataset, ISBI, 2020.

Semi-supervised dictionary learning with graph regularization and active points

 

Authors: Khanh-Hung TranFred-Maurice Ngole-Mboula, J-L. Starck
Journal: SIAM Journal on Imaging Sciences
Year: 2020
DOI: 10.1137/19M1285469
Download: arXiv


Abstract

Supervised Dictionary Learning has gained much interest in the recent decade and has shown significant performance improvements in image classification. However, in general, supervised learning needs a large number of labelled samples per class to achieve an acceptable result. In order to deal with databases which have just a few labelled samples per class, semi-supervised learning, which also exploits unlabelled samples in training phase is used. Indeed, unlabelled samples can help to regularize the learning model, yielding an improvement of classification accuracy. In this paper, we propose a new semi-supervised dictionary learning method based on two pillars: on one hand, we enforce manifold structure preservation from the original data into sparse code space using Locally Linear Embedding, which can be considered a regularization of sparse code; on the other hand, we train a semi-supervised classifier in sparse code space. We show that our approach provides an improvement over state-of-the-art semi-supervised dictionary learning methods
.

Deep Learning for space-variant deconvolution in galaxy surveys

 

Authors: Florent Sureau, Alexis Lechat, J-L. Starck
Journal: Astronomy and Astrophysics
Year: 2020
DOI: 10.1051/0004-6361/201937039
Download: ADS | arXiv


Abstract

The deconvolution of large survey images with millions of galaxies requires developing a new generation of methods that can take a space-variant point spread function into account. These methods have also to be accurate and fast. We investigate how deep learning might be used to perform this task. We employed a U-net deep neural network architecture to learn parameters that were adapted for galaxy image processing in a supervised setting and studied two deconvolution strategies. The first approach is a post-processing of a mere Tikhonov deconvolution with closed-form solution, and the second approach is an iterative deconvolution framework based on the alternating direction method of multipliers (ADMM). Our numerical results based on GREAT3 simulations with realistic galaxy images and point spread functions show that our two approaches outperform standard techniques that are based on convex optimization, whether assessed in galaxy image reconstruction or shape recovery. The approach based on a Tikhonov deconvolution leads to the most accurate results, except for ellipticity errors at high signal-to-noise ratio. The ADMM approach performs slightly better in this case. Considering that the Tikhonov approach is also more computation-time efficient in processing a large number of galaxies, we recommend this approach in this scenario.

In the spirit of reproducible research, the codes will be made freely available on the CosmoStat website (http://www.cosmostat.org). The testing datasets will also be provided to repeat the experiments performed in this paper.

PySAP: Python Sparse Data Analysis Package for Multidisciplinary Image Processing

 

Authors: S. Farrens, A. Grigis, L. El Gueddari, Z. Ramzi, Chaithya G. R., S. Starck, B. Sarthou, H. Cherkaoui, P.Ciuciu, J-L. Starck
Journal: Astronomy and Computing
Year: 2020
DOI: 10.1016/j.ascom.2020.100402
Download: ADS | arXiv


Abstract

We present the open-source image processing software package PySAP (Python Sparse data Analysis Package) developed for the COmpressed Sensing for Magnetic resonance Imaging and Cosmology (COSMIC) project. This package provides a set of flexible tools that can be applied to a variety of compressed sensing and image reconstruction problems in various research domains. In particular, PySAP offers fast wavelet transforms and a range of integrated optimisation algorithms. In this paper we present the features available in PySAP and provide practical demonstrations on astrophysical and magnetic resonance imaging data.


Code

PySAP Code