arXiv subjects

Matthieu Terris

Publications and source records attributed to Matthieu Terris.

13 recordsLinked to original sources

arXiv2025

DeepInverse: A Python package for solving imaging inverse problems with deep learning

DeepInverse is an open-source PyTorch-based library for solving imaging inverse problems. The library covers all crucial steps in image reconstruction from the efficient implementation of forward operators (e.g., optics, MRI, tomography), to the definition and resolution of variational problems and the design and training of advanced neural network architectures. In this paper, we describe the main functionality of the library and discuss the main design choices.

eess.IV↗

arXiv2025

From Score Matching to Diffusion: A Fine-Grained Error Analysis in the Gaussian Setting

Sampling from an unknown distribution, accessible only through discrete samples, is a fundamental problem at the core of generative AI. The current state-of-the-art methods follow a two-step process: first, estimating the score function (the gradient of a smoothed log-distribution) and then applying a diffusion-based sampling algorithm -- such as Langevin or Diffusion models. The resulting distribution's correctness can be impacted by four major factors: the generalization and optimization errors in score matching, and the discretization and minimal noise amplitude in the diffusion. In this paper, we make the sampling error explicit when using a diffusion sampler in the Gaussian setting. We provide a sharp analysis of the Wasserstein sampling error that arises from these four error sources. This allows us to rigorously track how the anisotropy of the data distribution (encoded by its power spectrum) interacts with key parameters of the end-to-end sampling method, including the number of initial samples, the stepsizes in both score matching and diffusion, and the noise amplitude. Notably, we show that the Wasserstein sampling error can be expressed as a kernel-type norm of the data power spectrum, where the specific kernel depends on the method parameters. This result provides a foundation for further analysis of the tradeoffs involved in optimizing sampling accuracy.

cs.LG↗

arXiv2025

Reconstruct Anything Model: a lightweight general model for computational imaging

Most existing learning-based methods for solving imaging inverse problems can be roughly divided into two classes: iterative algorithms, such as plug-and-play and diffusion methods leveraging pretrained denoisers, and unrolled architectures that are trained end-to-end for specific imaging problems. Iterative methods in the first class are computationally costly and often yield suboptimal reconstruction performance, whereas unrolled architectures are generally problem-specific and require expensive training. In this work, we propose a novel non-iterative, lightweight architecture that incorporates knowledge about the forward operator (acquisition physics and noise parameters) without relying on unrolling. Our model is trained to solve a wide range of inverse problems, such as deblurring, magnetic resonance imaging, computed tomography, inpainting, and super-resolution, and handles arbitrary image sizes and channels, such as grayscale, complex, and color data. The proposed model can be easily adapted to unseen inverse problems or datasets with a few fine-tuning steps (up to a few images) in a self-supervised way, without ground-truth references. Throughout a series of experiments, we demonstrate state-of-the-art performance from medical imaging to low-photon imaging and microscopy. Our code is available at https://github.com/matthieutrs/ram.

eess.IV↗

arXiv2024

FiRe: Fixed-points of Restoration Priors for Solving Inverse Problems

Selecting an appropriate prior to compensate for information loss due to the measurement operator is a fundamental challenge in imaging inverse problems. Implicit priors based on denoising neural networks have become central to widely-used frameworks such as Plug-and-Play (PnP) algorithms. In this work, we introduce Fixed-points of Restoration (FiRe) priors as a new framework for expanding the notion of priors in PnP to general restoration models beyond traditional denoising models. The key insight behind FiRe is that smooth images emerge as fixed points of the composition of a degradation operator with the corresponding restoration model. This enables us to derive an explicit formula for our implicit prior by quantifying invariance of images under this composite operation. Adopting this fixed-point perspective, we show how various restoration networks can effectively serve as priors for solving inverse problems. The FiRe framework further enables ensemble-like combinations of multiple restoration models as well as acquisition-informed restoration networks, all within a unified optimization approach. Experimental results validate the effectiveness of FiRe across various inverse problems, establishing a new paradigm for incorporating pretrained restoration models into PnP-like algorithms. Code available at https://github.com/matthieutrs/fire.

eess.IV↗

arXiv2024

Robust plug-and-play methods for highly accelerated non-Cartesian MRI reconstruction

Achieving high-quality Magnetic Resonance Imaging (MRI) reconstruction at accelerated acquisition rates remains challenging due to the inherent ill-posed nature of the inverse problem. Traditional Compressed Sensing (CS) methods, while robust across varying acquisition settings, struggle to maintain good reconstruction quality at high acceleration factors ($\ge$ 8). Recent advances in deep learning have improved reconstruction quality, but purely data-driven methods are prone to overfitting and hallucination effects, notably when the acquisition setting is varying. Plug-and-Play (PnP) approaches have been proposed to mitigate the pitfalls of both frameworks. In a nutshell, PnP algorithms amount to replacing suboptimal handcrafted CS priors with powerful denoising deep neural network (DNNs). However, in MRI reconstruction, existing PnP methods often yield suboptimal results due to instabilities in the proximal gradient descent (PGD) schemes and the lack of curated, noiseless datasets for training robust denoisers. In this work, we propose a fully unsupervised preprocessing pipeline to generate clean, noiseless complex MRI signals from multicoil data, enabling training of a high-performance denoising DNN. Furthermore, we introduce an annealed Half-Quadratic Splitting (HQS) algorithm to address the instability issues, leading to significant improvements over existing PnP algorithms. When combined with preconditioning techniques, our approach achieves state-of-the-art results, providing a robust and efficient solution for high-quality MRI reconstruction.

eess.IV↗

arXiv2023

The AIRI plug-and-play algorithm for image reconstruction in radio-interferometry: variations and robustness

Plug-and-Play (PnP) algorithms are appealing alternatives to proximal algorithms when solving inverse imaging problems. By learning a Deep Neural Network (DNN) denoiser behaving as a proximal operator, one waives the computational complexity of optimisation algorithms induced by sophisticated image priors, and the sub-optimality of handcrafted priors compared to DNNs. Such features are highly desirable in radio-interferometric (RI) imaging, where precision and scalability of the image reconstruction process are key. In previous work, we introduced AIRI, PnP counterpart to the unconstrained variant of the SARA optimisation algorithm, relying on a forward-backward algorithmic backbone. Here, we introduce variations of AIRI towards a more general and robust PnP paradigm in RI imaging. Firstly, we show that the AIRI denoisers can be used without any alteration to instantiate a PnP counterpart to the constrained SARA optimisation algorithm itself, relying on a primal-dual forward-backward algorithmic backbone, thus extending the remit of the AIRI paradigm. Secondly, we show that AIRI algorithms are robust to strong variations in the nature of the training dataset, with denoisers trained on medical images yielding similar reconstruction quality to those trained on astronomical images. Thirdly, we develop a functionality to quantify the model uncertainty introduced by the randomness in the training process. We validate the image reconstruction and uncertainty quantification functionality of AIRI algorithms against the SARA family and CLEAN, both in simulation and on real data of the ESO 137-006 galaxy acquired with the MeerKAT telescope. AIRI code is available in the BASPLib code library on GitHub.

eess.IV↗

arXiv2023

Equivariant plug-and-play image reconstruction

Plug-and-play algorithms constitute a popular framework for solving inverse imaging problems that rely on the implicit definition of an image prior via a denoiser. These algorithms can leverage powerful pre-trained denoisers to solve a wide range of imaging tasks, circumventing the necessity to train models on a per-task basis. Unfortunately, plug-and-play methods often show unstable behaviors, hampering their promise of versatility and leading to suboptimal quality of reconstructed images. In this work, we show that enforcing equivariance to certain groups of transformations (rotations, reflections, and/or translations) on the denoiser strongly improves the stability of the algorithm as well as its reconstruction quality. We provide a theoretical analysis that illustrates the role of equivariance on better performance and stability. We present a simple algorithm that enforces equivariance on any existing denoiser by simply applying a random transformation to the input of the denoiser and the inverse transformation to the output at each iteration of the algorithm. Experiments on multiple imaging modalities and denoising networks show that the equivariant plug-and-play algorithm improves both the reconstruction performance and the stability compared to their non-equivariant counterparts.

eess.IV↗

arXiv2023

Meta-Prior: Meta learning for Adaptive Inverse Problem Solvers

Deep neural networks have become a foundational tool for addressing imaging inverse problems. They are typically trained for a specific task, with a supervised loss to learn a mapping from the observations to the image to recover. However, real-world imaging challenges often lack ground truth data, rendering traditional supervised approaches ineffective. Moreover, for each new imaging task, a new model needs to be trained from scratch, wasting time and resources. To overcome these limitations, we introduce a novel approach based on meta-learning. Our method trains a meta-model on a diverse set of imaging tasks that allows the model to be efficiently fine-tuned for specific tasks with few fine-tuning steps. We show that the proposed method extends to the unsupervised setting, where no ground truth data is available. In its bilevel formulation, the outer level uses a supervised loss, that evaluates how well the fine-tuned model performs, while the inner loss can be either supervised or unsupervised, relying only on the measurement operator. This allows the meta-model to leverage a few ground truth samples for each task while being able to generalize to new imaging tasks. We show that in simple settings, this approach recovers the Bayes optimal estimator, illustrating the soundness of our approach. We also demonstrate our method's effectiveness on various tasks, including image processing and magnetic resonance imaging.

cs.CV↗

arXiv2023

Scalable precision wide-field imaging in radio interferometry: II. AIRI validated on ASKAP data

Accompanying Part I, this sequel delineates a validation of the recently proposed AI for Regularisation in radio-interferometric Imaging (AIRI) algorithm on observations from the Australian Square Kilometre Array Pathfinder (ASKAP). The monochromatic AIRI-ASKAP images showcased in this work are formed using the same parallelised and automated imaging framework described in Part I: ``uSARA validated on ASKAP data''. Using a Plug-and-Play approach, AIRI differs from uSARA by substituting a trained denoising deep neural network (DNN) for the proximal operator in the regularisation step of the forward-backward algorithm during deconvolution. We build a trained shelf of DNN denoisers which target the estimated image-dynamic-ranges of our selected data. Furthermore, we quantify variations of AIRI reconstructions when selecting the nearest DNN on the shelf versus using a universal DNN with the highest dynamic range, opening the door to a more complete framework that not only delivers image estimation but also quantifies epistemic model uncertainty. We continue our comparative analysis of source structure, diffuse flux measurements, and spectral index maps of selected target sources as imaged by AIRI and the algorithms in Part I -- uSARA and WSClean. Overall we see an improvement over uSARA and WSClean in the reconstruction of diffuse components in AIRI images. The scientific potential delivered by AIRI is evident in further imaging precision, more accurate spectral index maps, and a significant acceleration in deconvolution time, whereby AIRI is four times faster than its sub-iterative sparsity-based counterpart uSARA.

astro-ph.IM↗

arXiv2022

Deep network series for large-scale high-dynamic range imaging

We propose a new approach for large-scale high-dynamic range computational imaging. Deep Neural Networks (DNNs) trained end-to-end can solve linear inverse imaging problems almost instantaneously. While unfolded architectures provide robustness to measurement setting variations, embedding large-scale measurement operators in DNN architectures is impractical. Alternative Plug-and-Play (PnP) approaches, where the denoising DNNs are blind to the measurement setting, have proven effective to address scalability and high-dynamic range challenges, but rely on highly iterative algorithms. We propose a residual DNN series approach, also interpretable as a learned version of matching pursuit, where the reconstructed image is a sum of residual images progressively increasing the dynamic range, and estimated iteratively by DNNs taking the back-projected data residual of the previous iteration as input. We demonstrate on radio-astronomical imaging simulations that a series of only few terms provides a reconstruction quality competitive with PnP, at a fraction of the cost.

astro-ph.IM↗

arXiv2022

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↗

arXiv2020

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↗