arXiv subjects

Audrey Repetti

Publications and source records attributed to Audrey Repetti.

32 records · Page 2Linked to original sources

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↗

arXiv2021

A practical preconditioner for wide-field continuum imaging of radio interferometric data

The celebrated CLEAN algorithm has been the cornerstone of deconvolution algorithms in radio interferometry almost since its conception in the 1970s. For all its faults, CLEAN is remarkably fast, robust to calibration artefacts and in its ability to model point sources. We demonstrate how the same assumptions that afford CLEAN its speed can be used to accelerate more sophisticated deconvolution algorithms.

astro-ph.IM↗

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

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↗

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

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

Non-convex optimization for self-calibration of direction-dependent effects in radio interferometric imaging

Radio interferometric imaging aims to estimate an unknown sky intensity image from degraded observations, acquired through an antenna array. In the theoretical case of a perfectly calibrated array, it has been shown that solving the corresponding imaging problem by iterative algorithms based on convex optimization and compressive sensing theory can be competitive with classical algorithms such as CLEAN. However, in practice, antenna-based gains are unknown and have to be calibrated. Future radio telescopes, such as the SKA, aim at improving imaging resolution and sensitivity by orders of magnitude. At this precision level, the direction-dependency of the gains must be accounted for, and radio interferometric imaging can be understood as a blind deconvolution problem. In this context, the underlying minimization problem is non-convex, and adapted techniques have to be designed. In this work, leveraging recent developments in non-convex optimization, we propose the first joint calibration and imaging method in radio interferometry, with proven convergence guarantees. Our approach, based on a block-coordinate forward-backward algorithm, jointly accounts for visibilities and suitable priors on both the image and the direction-dependent effects (DDEs). As demonstrated in recent works, sparsity remains the prior of choice for the image, while DDEs are modelled as smooth functions of the sky, i.e. spatially band-limited. Finally, we show through simulations the efficiency of our method, for the reconstruction of both images of point sources and complex extended sources. MATLAB code is available on GitHub.

astro-ph.IM↗

arXiv2017

A regularized tri-linear approach for optical interferometric imaging

In the context of optical interferometry, only undersampled power spectrum and bispectrum data are accessible. It poses an ill-posed inverse problem for image recovery. Recently, a tri-linear model was proposed for monochromatic imaging, leading to an alternated minimization problem. In that work, only a positivity constraint was considered, and the problem was solved by an approximated Gauss-Seidel method. In this paper, we propose to improve the approach on three fundamental aspects. Firstly, we define the estimated image as a solution of a regularized minimization problem, promoting sparsity in a fixed dictionary using either an $\ell_1$ or a weighted-$\ell_1$ regularization term. Secondly, we solve the resultant non-convex minimization problem using a block-coordinate forward-backward algorithm. This algorithm is able to deal both with smooth and non-smooth functions, and benefits from convergence guarantees even in a non-convex context. Finally, we generalize our model and algorithm to the hyperspectral case, promoting a joint sparsity prior through an $\ell_{2,1}$ regularization term. We present simulation results, both for monochromatic and hyperspectral cases, to validate the proposed approach.

astro-ph.IM↗

arXiv2016

Scalable splitting algorithms for big-data interferometric imaging in the SKA era

In the context of next generation radio telescopes, like the Square Kilometre Array, the efficient processing of large-scale datasets is extremely important. Convex optimisation tasks under the compressive sensing framework have recently emerged and provide both enhanced image reconstruction quality and scalability to increasingly larger data sets. We focus herein mainly on scalability and propose two new convex optimisation algorithmic structures able to solve the convex optimisation tasks arising in radio-interferometric imaging. They rely on proximal splitting and forward-backward iterations and can be seen, by analogy with the CLEAN major-minor cycle, as running sophisticated CLEAN-like iterations in parallel in multiple data, prior, and image spaces. Both methods support any convex regularisation function, in particular the well studied l1 priors promoting image sparsity in an adequate domain. Tailored for big-data, they employ parallel and distributed computations to achieve scalability, in terms of memory and computational requirements. One of them also exploits randomisation, over data blocks at each iteration, offering further flexibility. We present simulation results showing the feasibility of the proposed methods as well as their advantages compared to state-of-the-art algorithmic solvers. Our Matlab code is available online on GitHub.

astro-ph.IM↗

arXiv2014

Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed l1/l2 Regularization

The l1/l2 ratio regularization function has shown good performance for retrieving sparse signals in a number of recent works, in the context of blind deconvolution. Indeed, it benefits from a scale invariance property much desirable in the blind context. However, the l1/l2 function raises some difficulties when solving the nonconvex and nonsmooth minimization problems resulting from the use of such a penalty term in current restoration methods. In this paper, we propose a new penalty based on a smooth approximation to the l1/l2 function. In addition, we develop a proximal-based algorithm to solve variational problems involving this function and we derive theoretical convergence results. We demonstrate the effectiveness of our method through a comparison with a recent alternating optimization strategy dealing with the exact l1/l2 term, on an application to seismic data blind deconvolution.

math.OC↗

arXiv2014

A Class of Randomized Primal-Dual Algorithms for Distributed Optimization

Based on a preconditioned version of the randomized block-coordinate forward-backward algorithm recently proposed in [Combettes,Pesquet,2014], several variants of block-coordinate primal-dual algorithms are designed in order to solve a wide array of monotone inclusion problems. These methods rely on a sweep of blocks of variables which are activated at each iteration according to a random rule, and they allow stochastic errors in the evaluation of the involved operators. Then, this framework is employed to derive block-coordinate primal-dual proximal algorithms for solving composite convex variational problems. The resulting algorithm implementations may be useful for reducing computational complexity and memory requirements. Furthermore, we show that the proposed approach can be used to develop novel asynchronous distributed primal-dual algorithms in a multi-agent context.

math.OC↗