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


Euclid: The reduced shear approximation and magnification bias for Stage IV cosmic shear experiments

Euclid: The reduced shear approximation and magnification bias for Stage IV cosmic shear experiments

Authors: A.C. Deshpande, ..., S. Casas, M. Kilbinger, V. Pettorino, S. Pires, J.-L. Starck, F. Sureau, et al.
Journal: Astronomy and Astrophysics
Year: 2020
DOI:  10.1051/0004-6361/201937323
Download:

ADS | arXiv

 


Abstract

Stage IV weak lensing experiments will offer more than an order of magnitude leap in precision. We must therefore ensure that our analyses remain accurate in this new era. Accordingly, previously ignored systematic effects must be addressed. In this work, we evaluate the impact of the reduced shear approximation and magnification bias, on the information obtained from the angular power spectrum. To first-order, the statistics of reduced shear, a combination of shear and convergence, are taken to be equal to those of shear. However, this approximation can induce a bias in the cosmological parameters that can no longer be neglected. A separate bias arises from the statistics of shear being altered by the preferential selection of galaxies and the dilution of their surface densities, in high-magnification regions. The corrections for these systematic effects take similar forms, allowing them to be treated together. We calculated the impact of neglecting these effects on the cosmological parameters that would be determined from Euclid, using cosmic shear tomography. To do so, we employed the Fisher matrix formalism, and included the impact of the super-sample covariance. We also demonstrate how the reduced shear correction can be calculated using a lognormal field forward modelling approach. These effects cause significant biases in Omega_m, sigma_8, n_s, Omega_DE, w_0, and w_a of -0.53 sigma, 0.43 sigma, -0.34 sigma, 1.36 sigma, -0.68 sigma, and 1.21 sigma, respectively. We then show that these lensing biases interact with another systematic: the intrinsic alignment of galaxies. Accordingly, we develop the formalism for an intrinsic alignment-enhanced lensing bias correction. Applying this to Euclid, we find that the additional terms introduced by this correction are sub-dominant.

Euclid preparation: VI. Verifying the Performance of Cosmic Shear Experiments

Euclid preparation: VI. Verifying the Performance of Cosmic Shear Experiments

Authors: Euclid Collaboration, P. Paykari, ..., S. Farrens, M. Kilbinger, V. Pettorino, S. Pires, J.-L. Starck, F. Sureau, et al.
Journal: Astronomy and Astrophysics
Year: 2020
DOI:  10.1051/0004-6361/201936980
Download:

ADS | arXiv

 


Abstract

Our aim is to quantify the impact of systematic effects on the inference of cosmological parameters from cosmic shear. We present an end-to-end approach that introduces sources of bias in a modelled weak lensing survey on a galaxy-by-galaxy level. Residual biases are propagated through a pipeline from galaxy properties (one end) through to cosmic shear power spectra and cosmological parameter estimates (the other end), to quantify how imperfect knowledge of the pipeline changes the maximum likelihood values of dark energy parameters. We quantify the impact of an imperfect correction for charge transfer inefficiency (CTI) and modelling uncertainties of the point spread function (PSF) for Euclid, and find that the biases introduced can be corrected to acceptable levels.

Benchmarking MRI Reconstruction Neural Networks on Large Public Datasets

Deep learning is starting to offer promising results for reconstruction in Magnetic Resonance Imaging (MRI). A lot of networks are being developed, but the comparisons remain hard because the frameworks used are not the same among studies, the networks are not properly re-trained, and the datasets used are not the same among comparisons. The recent release of a public dataset, fastMRI, consisting of raw k-space data, encouraged us to write a consistent benchmark of several deep neural networks for MR image reconstruction. This paper shows the results obtained for this benchmark, allowing to compare the networks, and links the open source implementation of all these networks in Keras. The main finding of this benchmark is that it is beneficial to perform more iterations between the image and the measurement spaces compared to having a deeper per-space network.

Reference:  Z. Ramzi, P. Ciuciu and J.-L. Starck. “Benchmarking MRI reconstruction neural networks on large public datasetsApplied Sciences, 10, 1816, 2020.  doi:10.3390/app10051816