arXiv subjects

Yves Wiaux

Publications and source records attributed to Yves Wiaux.

At least 37 records · Page 2Linked to original sources

arXiv2023

First AI for deep super-resolution wide-field imaging in radio astronomy: unveiling structure in ESO 137--006

We introduce the first AI-based framework for deep, super-resolution, wide-field radio-interferometric imaging, and demonstrate it on observations of the ESO~137-006 radio galaxy. The algorithmic framework to solve the inverse problem for image reconstruction builds on a recent ``plug-and-play'' scheme whereby a denoising operator is injected as an image regulariser in an optimisation algorithm, which alternates until convergence between denoising steps and gradient-descent data-fidelity steps. We investigate handcrafted and learned variants of high-resolution high-dynamic range denoisers. We propose a parallel algorithm implementation relying on automated decompositions of the image into facets and the measurement operator into sparse low-dimensional blocks, enabling scalability to large data and image dimensions. We validate our framework for image formation at a wide field of view containing ESO~137-006, from 19 gigabytes of MeerKAT data at 1053 and 1399 MHz. The recovered maps exhibit significantly more resolution and dynamic range than CLEAN, revealing collimated synchrotron threads close to the galactic core.

astro-ph.IM↗

arXiv2022

Image reconstruction algorithms in radio interferometry: from handcrafted to learned regularization denoisers

We introduce a new class of iterative image reconstruction algorithms for radio interferometry, at the interface of convex optimization and deep learning, inspired by plug-and-play methods. The approach consists in learning a prior image model by training a deep neural network (DNN) as a denoiser, and substituting it for the handcrafted proximal regularization operator of an optimization algorithm. The proposed AIRI (``AI for Regularization in radio-interferometric Imaging'') framework, for imaging complex intensity structure with diffuse and faint emission from visibility data, inherits the robustness and interpretability of optimization, and the learning power and speed of networks. Our approach relies on three steps. Firstly, we design a low dynamic range training database from optical intensity images. Secondly, we train a DNN denoiser at a noise level inferred from the signal-to-noise ratio of the data. We use training losses enhanced with a nonexpansiveness term ensuring algorithm convergence, and including on-the-fly database dynamic range enhancement via exponentiation. Thirdly, we plug the learned denoiser into the forward-backward optimization algorithm, resulting in a simple iterative structure alternating a denoising step with a gradient-descent data-fidelity step. We have validated AIRI against CLEAN, optimization algorithms of the SARA family, and a DNN trained to reconstruct the image directly from visibility data. Simulation results show that AIRI is competitive in imaging quality with SARA and its unconstrained forward-backward-based version uSARA, while providing significant acceleration. CLEAN remains faster but offers lower quality. The end-to-end DNN offers further acceleration, but with far lower quality than AIRI.

eess.IV↗

arXiv2021

Fast Fiber Orientation Estimation in Diffusion MRI from kq-Space Sampling and Anatomical Priors

High spatio-angular resolution diffusion MRI (dMRI) has been shown to provide accurate identification of complex neuronal fiber configurations, albeit, at the cost of long acquisition times. We propose a method to recover intra-voxel fiber configurations at high spatio-angular resolution relying on a 3D kq-space under-sampling scheme to enable accelerated acquisitions. Simulations and real data analysis suggest that accurate FOD mapping can be achieved from severe kq-space under-sampling regimes potentially enabling high spatio-angular resolution dMRI in the clinical setting.

eess.IV↗

arXiv2021

Cygnus A jointly calibrated and imaged via non-convex optimisation from VLA data

Radio interferometric (RI) data are noisy under-sampled spatial Fourier components of the unknown radio sky affected by direction-dependent antenna gains. Failure to model these antenna gains accurately results in a radio sky estimate with limited fidelity and resolution. The RI inverse problem has been recently addressed via a joint calibration and imaging approach which consists in solving a non-convex minimisation task, involving suitable priors for the DDEs, namely temporal and spatial smoothness, and sparsity for the unknown radio map via an $\ell_1$-norm prior, in the context of realistic RI simulations. Building on these developments, we propose to promote sparsity of the radio map via a log-sum prior, enforcing sparsity more strongly than the $\ell_1$-norm. The resulting minimisation task is addressed via a sequence of non-convex minimisation tasks composed of re-weighted $\ell_1$ image priors, which are solved approximately. We demonstrate the efficiency of the approach on RI observations of the celebrated radio galaxy Cygnus~A obtained with the Karl G. Jansky Very Large Array at X, C, and S bands. More precisely, we showcase that the approach enhances data fidelity significantly while achieving high resolution high dynamic range radio maps, confirming the suitability of the priors considered for the unknown DDEs and radio image. As a clear qualitative indication of the high fidelity achieved by the data and the proposed approach, we report the detection of three background sources in the vicinity of Cyg~A, at S band.

astro-ph.IM↗

arXiv2021

Learning Maximally Monotone Operators for Image Recovery

We introduce a new paradigm for solving regularized variational problems. These are typically formulated to address ill-posed inverse problems encountered in signal and image processing. The objective function is traditionally defined by adding a regularization function to a data fit term, which is subsequently minimized by using iterative optimization algorithms. Recently, several works have proposed to replace the operator related to the regularization by a more sophisticated denoiser. These approaches, known as plug-and-play (PnP) methods, have shown excellent performance. Although it has been noticed that, under some Lipschitz properties on the denoisers, the convergence of the resulting algorithm is guaranteed, little is known about characterizing the asymptotically delivered solution. In the current article, we propose to address this limitation. More specifically, instead of employing a functional regularization, we perform an operator regularization, where a maximally monotone operator (MMO) is learned in a supervised manner. This formulation is flexible as it allows the solution to be characterized through a broad range of variational inequalities, and it includes convex regularizations as special cases. From an algorithmic standpoint, the proposed approach consists in replacing the resolvent of the MMO by a neural network (NN). We present a universal approximation theorem proving that nonexpansive NNs are suitable models for the resolvent of a wide class of MMOs. The proposed approach thus provides a sound theoretical framework for analyzing the asymptotic behavior of first-order PnP algorithms. In addition, we propose a numerical strategy to train NNs corresponding to resolvents of MMOs. We apply our approach to image restoration problems and demonstrate its validity in terms of both convergence and quality.

math.OC↗

arXiv2021

Variable Metric Forward-Backward Algorithm for Composite Minimization Problems

We present a forward-backward-based algorithm to minimize a sum of a differentiable function and a nonsmooth function, both being possibly nonconvex. The main contribution of this work is to consider the challenging case where the nonsmooth function corresponds to a sum of non-convex functions, resulting from composition between a strictly increasing, concave, differentiable function and a convex nonsmooth function. The proposed variable metric Composite Function Forward-Backward algorithm (C2FB) circumvents the explicit, and often challenging, computation of the proximity operator of the composite functions through a majorize-minimize approach. Precisely, each composite function is majorized using a linear approximation of the differentiable function, which allows one to apply the proximity step only to the sum of the nonsmooth functions. We prove the convergence of the algorithm iterates to a critical point of the objective function leveraging the Kurdyka-Łojasiewicz inequality. The convergence is guaranteed even if the proximity operators are computed inexactly, considering relative errors. We show that the proposed approach is a generalization of reweighting methods, with convergence guarantees. In particular, applied to the log-sum function, our algorithm reduces to a generalized version of the celebrated reweighted $\ell_1$ method. Finally, we show through simulations on an image processing problem that the proposed C2FB algorithm necessitates less iterations to converge and leads to better critical points compared with traditional reweighting methods and classic forward-backward algorithms.

math.OC↗

arXiv2020

Computational time-of-flight diffuse optical tomography

Imaging through a strongly diffusive medium remains an outstanding challenge in particular in association with applications in biological and medical imaging. Here we propose a method based on a single-photon time-of-flight camera that allows, in combination with computational processing of the spatial and full temporal photon distribution data, to image an object embedded inside a strongly diffusive medium over more than 80 transport mean free paths. The technique is contactless and requires one second acquisition times thus allowing Hz frame rate imaging. The imaging depth corresponds to several cm of human tissue and allows one to perform deep-body imaging, here demonstrated as a proof-of-principle.

physics.optics↗

arXiv2019

Wideband Super-resolution Imaging in Radio Interferometry via Low Rankness and Joint Average Sparsity Models (HyperSARA)

We propose a new approach within the versatile framework of convex optimization to solve the radio-interferometric wideband imaging problem. Our approach, dubbed HyperSARA, solves a sequence of weighted nuclear norm and l21 minimization problems promoting low rankness and joint average sparsity of the wideband model cube. On the one hand, enforcing low rankness enhances the overall resolution of the reconstructed model cube by exploiting the correlation between the different channels. On the other hand, promoting joint average sparsity improves the overall sensitivity by rejecting artefacts present on the different channels. An adaptive Preconditioned Primal-Dual algorithm is adopted to solve the minimization problem. The algorithmic structure is highly scalable to large data sets and allows for imaging in the presence of unknown noise levels and calibration errors. We showcase the superior performance of the proposed approach, reflected in high-resolution images on simulations and real VLA observations with respect to single channel imaging and the CLEAN-based wideband imaging algorithm in the WSCLEAN software. Our MATLAB code is available online on GITHUB.

eess.IV↗

arXiv2019

Polca SARA - Full polarization, direction-dependent calibration and sparse imaging for radio interferometry

New generation of radio interferometers are envisaged to produce high quality, high dynamic range Stokes images of the observed sky from the corresponding under-sampled Fourier domain measurements. In practice, these measurements are contaminated by the instrumental and atmospheric effects that are well represented by Jones matrices, and are most often varying with observation direction and time. These effects, usually unknown, act as a limiting factor in achieving the required imaging performance and thus, their calibration is crucial. To address this issue, we develop a global algorithm, named Polca SARA, aiming to perform full polarization, direction-dependent calibration and sparse imaging by employing a non-convex optimization technique. In contrast with the existing approaches, the proposed method offers global convergence guarantees and flexibility to incorporate sophisticated priors to regularize the imaging as well as the calibration problem. Thus, we adapt a polarimetric imaging specific method, enforcing the physical polarization constraint along with a sparsity prior for the sought images. We perform extensive simulation studies of the proposed algorithm. While indicating the superior performance of polarization constraint based imaging, the obtained results also highlight the importance of calibrating for direction-dependent effects as well as for off-diagonal terms (denoting polarization leakage) in the associated Jones matrices, without inclusion of which the imaging quality deteriorates.

astro-ph.IM↗

arXiv2019

Compressive optical imaging with a photonic lantern

The thin and flexible nature of optical fibres often makes them the ideal technology to view biological processes in-vivo, but current microendoscopic approaches are limited in spatial resolution. Here, we demonstrate a new route to high resolution microendoscopy using a multicore fibre (MCF) with an adiabatic multimode-to-singlemode photonic lantern transition formed at the distal end by tapering. We show that distinct multimode patterns of light can be projected from the output of the lantern by individually exciting the single-mode MCF cores, and that these patterns are highly stable to fibre movement. This capability is then exploited to demonstrate a form of single-pixel imaging, where a single pixel detector is used to detect the fraction of light transmitted through the object for each multimode pattern. A custom compressive imaging algorithm we call SARA-COIL is used to reconstruct the object using only the pre-measured multimode patterns themselves and the detector signals.

physics.optics↗

arXiv2018

Greedy Approximate Projection for Magnetic Resonance Fingerprinting with Partial Volumes

In quantitative Magnetic Resonance Imaging, traditional methods suffer from the so-called Partial Volume Effect (PVE) due to spatial resolution limitations. As a consequence of PVE, the parameters of the voxels containing more than one tissue are not correctly estimated. Magnetic Resonance Fingerprinting (MRF) is not an exception. The existing methods addressing PVE are neither scalable nor accurate. We propose to formulate the recovery of multiple tissues per voxel as a nonconvex constrained least-squares minimisation problem. To solve this problem, we develop a memory efficient, greedy approximate projected gradient descent algorithm, dubbed GAP-MRF. Our method adaptively finds the regions of interest on the manifold of fingerprints defined by the MRF sequence. We generalise our method to compensate for phase errors appearing in the model, using an alternating minimisation approach. We show, through simulations on synthetic data with PVE, that our algorithm outperforms state-of-the-art methods. Our approach is validated on the EUROSPIN phantom and on in vivo datasets.

eess.IV↗

arXiv2018

Scalable Bayesian uncertainty quantification in imaging inverse problems via convex optimization

We propose a Bayesian uncertainty quantification method for large-scale imaging inverse problems. Our method applies to all Bayesian models that are log-concave, where maximum-a-posteriori (MAP) estimation is a convex optimization problem. The method is a framework to analyse the confidence in specific structures observed in MAP estimates (e.g., lesions in medical imaging, celestial sources in astronomical imaging), to enable using them as evidence to inform decisions and conclusions. Precisely, following Bayesian decision theory, we seek to assert the structures under scrutiny by performing a Bayesian hypothesis test that proceeds as follows: firstly, it postulates that the structures are not present in the true image, and then seeks to use the data and prior knowledge to reject this null hypothesis with high probability. Computing such tests for imaging problems is generally very difficult because of the high dimensionality involved. A main feature of this work is to leverage probability concentration phenomena and the underlying convex geometry to formulate the Bayesian hypothesis test as a convex problem, that we then efficiently solve by using scalable optimization algorithms. This allows scaling to high-resolution and high-sensitivity imaging problems that are computationally unaffordable for other Bayesian computation approaches. We illustrate our methodology, dubbed BUQO (Bayesian Uncertainty Quantification by Optimization), on a range of challenging Fourier imaging problems arising in astronomy and medicine.

stat.ME↗

arXiv2018

CoverBLIP: accelerated and scalable iterative matched-filtering for Magnetic Resonance Fingerprint reconstruction

Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are bottlenecked by the heavy computations of a matched-filtering step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. We address this shortcoming by arranging dictionary atoms in the form of cover tree structures and adopt the corresponding fast approximate nearest neighbour searches to accelerate matched-filtering. For datasets belonging to smooth low-dimensional manifolds cover trees offer search complexities logarithmic in terms of data population. With this motivation we propose an iterative reconstruction algorithm, named CoverBLIP, to address large-size MRF problems where the fingerprint dictionary i.e. discrete manifold of Bloch responses, encodes several intrinsic NMR parameters. We study different forms of convergence for this algorithm and we show that provided with a notion of embedding, the inexact and non-convex iterations of CoverBLIP linearly convergence toward a near-global solution with the same order of accuracy as using exact brute-force searches. Our further examinations on both synthetic and real-world datasets and using different sampling strategies, indicates between 2 to 3 orders of magnitude reduction in total search computations. Cover trees are robust against the curse-of-dimensionality and therefore CoverBLIP provides a notion of scalability -- a consistent gain in time-accuracy performance-- for searching high-dimensional atoms which may not be easily preprocessed (i.e. for dimensionality reduction) due to the increasing degrees of non-linearities appearing in the emerging multi-parametric MRF dictionaries.

cs.CV↗

arXiv2018

Cover Tree Compressed Sensing for Fast MR Fingerprint Recovery

We adopt data structure in the form of cover trees and iteratively apply approximate nearest neighbour (ANN) searches for fast compressed sensing reconstruction of signals living on discrete smooth manifolds. Levering on the recent stability results for the inexact Iterative Projected Gradient (IPG) algorithm and by using the cover tree's ANN searches, we decrease the projection cost of the IPG algorithm to be logarithmically growing with data population for low dimensional smooth manifolds. We apply our results to quantitative MRI compressed sensing and in particular within the Magnetic Resonance Fingerprinting (MRF) framework. For a similar (or sometimes better) reconstruction accuracy, we report 2-3 orders of magnitude reduction in computations compared to the standard iterative method which uses brute-force searches.

stat.ML↗

arXiv2018

CoverBLIP: scalable iterative matched filtering for MR Fingerprint recovery

Current proposed solutions for the high dimensionality of the MRF reconstruction problem rely on a linear compression step to reduce the matching computations and boost the efficiency of fast but non-scalable searching schemes such as the KD-trees. However such methodologies often introduce an unfavourable compromise in the estimation accuracy when applied to nonlinear data structures such as the manifold of Bloch responses with possible increased dynamic complexity and growth in data population. To address this shortcoming we propose an inexact iterative reconstruction method, dubbed as the Cover BLoch response Iterative Projection (CoverBLIP). Iterative methods improve the accuracy of their non-iterative counterparts and are additionally robust against certain accelerated approximate updates, without compromising their final accuracy. Leveraging on these results, we accelerate matched-filtering using an ANNS algorithm based on Cover trees with a robustness feature against the curse of dimensionality.

q-bio.QM↗

arXiv2018

Cygnus A super-resolved via convex optimisation from VLA data

We leverage the Sparsity Averaging Reweighted Analysis (SARA) approach for interferometric imaging, that is based on convex optimisation, for the super-resolution of Cyg A from observations at the frequencies 8.422GHz and 6.678GHz with the Karl G. Jansky Very Large Array (VLA). The associated average sparsity and positivity priors enable image reconstruction beyond instrumental resolution. An adaptive Preconditioned Primal-Dual algorithmic structure is developed for imaging in the presence of unknown noise levels and calibration errors. We demonstrate the superior performance of the algorithm with respect to the conventional CLEAN-based methods, reflected in super-resolved images with high fidelity. The high resolution features of the recovered images are validated by referring to maps of Cyg A at higher frequencies, more precisely 17.324GHz and 14.252GHz. We also confirm the recent discovery of a radio transient in Cyg A, revealed in the recovered images of the investigated data sets. Our matlab code is available online on GitHub.

astro-ph.IM↗

arXiv2018

Sparse interferometric Stokes imaging under polarization constraint (Polarized SARA)

We develop a novel algorithm for sparse Stokes parameters imaging in radio interferometry under the polarization constraint. The latter is a physical non-linear relation between the Stokes parameters, imposing that the polarization intensity is a lower bound on the total intensity. To solve the joint inverse Stokes imaging problem including this bound, we leverage epigraphical projection techniques in convex optimization and design a primal-dual method offering a highly flexible and parallelizable structure. In addition, we propose to regularize each Stokes parameter map through an average sparsity prior in the context of a reweighted analysis approach (SARA). The resulting approach is dubbed Polarized SARA. We demonstrate on simulated observations of M87 with the Event Horizon Telescope that imposing the polarization constraint leads to superior image quality. The results also confirm that the performance of the average sparsity prior surpasses the alternative state-of-the-art priors for polarimetric imaging.

astro-ph.IM↗

arXiv2017

Robust sparse image reconstruction of radio interferometric observations with purify

Next-generation radio interferometers, such as the Square Kilometre Array (SKA), will revolutionise our understanding of the universe through their unprecedented sensitivity and resolution. However, to realise these goals significant challenges in image and data processing need to be overcome. The standard methods in radio interferometry for reconstructing images, such as CLEAN, have served the community well over the last few decades and have survived largely because they are pragmatic. However, they produce reconstructed inter\-ferometric images that are limited in quality and scalability for big data. In this work we apply and evaluate alternative interferometric reconstruction methods that make use of state-of-the-art sparse image reconstruction algorithms motivated by compressive sensing, which have been implemented in the PURIFY software package. In particular, we implement and apply the proximal alternating direction method of multipliers (P-ADMM) algorithm presented in a recent article. First, we assess the impact of the interpolation kernel used to perform gridding and degridding on sparse image reconstruction. We find that the Kaiser-Bessel interpolation kernel performs as well as prolate spheroidal wave functions, while providing a computational saving and an analytic form. Second, we apply PURIFY to real interferometric observations from the Very Large Array (VLA) and the Australia Telescope Compact Array (ATCA) and find images recovered by PURIFY are higher quality than those recovered by CLEAN. Third, we discuss how PURIFY reconstructions exhibit additional advantages over those recovered by CLEAN. The latest version of PURIFY, with developments presented in this work, is made publicly available.

astro-ph.IM↗