arXiv subjects

Jérôme Idier

Publications and source records attributed to Jérôme Idier.

At least 19 recordsLinked to original sources

arXiv2024

Ultrasound Image Enhancement with the Variance of Diffusion Models

Ultrasound imaging, despite its widespread use in medicine, often suffers from various sources of noise and artifacts that impact the signal-to-noise ratio and overall image quality. Enhancing ultrasound images requires a delicate balance between contrast, resolution, and speckle preservation. This paper introduces a novel approach that integrates adaptive beamforming with denoising diffusion-based variance imaging to address this challenge. By applying Eigenspace-Based Minimum Variance (EBMV) beamforming and employing a denoising diffusion model fine-tuned on ultrasound data, our method computes the variance across multiple diffusion-denoised samples to produce high-quality despeckled images. This approach leverages both the inherent multiplicative noise of ultrasound and the stochastic nature of diffusion models. Experimental results on a publicly available dataset demonstrate the effectiveness of our method in achieving superior image reconstructions from single plane-wave acquisitions. The code is available at: https://github.com/Yuxin-Zhang-Jasmine/IUS2024_Diffusion.

cs.CV↗

arXiv2024

Ultrasound Imaging based on the Variance of a Diffusion Restoration Model

Despite today's prevalence of ultrasound imaging in medicine, ultrasound signal-to-noise ratio is still affected by several sources of noise and artefacts. Moreover, enhancing ultrasound image quality involves balancing concurrent factors like contrast, resolution, and speckle preservation. Recently, there has been progress in both model-based and learning-based approaches addressing the problem of ultrasound image reconstruction. Bringing the best from both worlds, we propose a hybrid reconstruction method combining an ultrasound linear direct model with a learning-based prior coming from a generative Denoising Diffusion model. More specifically, we rely on the unsupervised fine-tuning of a pre-trained Denoising Diffusion Restoration Model (DDRM). Given the nature of multiplicative noise inherent to ultrasound, this paper proposes an empirical model to characterize the stochasticity of diffusion reconstruction of ultrasound images, and shows the interest of its variance as an echogenicity map estimator. We conduct experiments on synthetic, in-vitro, and in-vivo data, demonstrating the efficacy of our variance imaging approach in achieving high-quality image reconstructions from single plane-wave acquisitions and in comparison to state-of-the-art methods. The code is available at: https://github.com/Yuxin-Zhang-Jasmine/DRUSvar

eess.IV↗

arXiv2023

Super-resolution capacity of variance-based stochastic fluorescence microscopy

Improving the resolution of fluorescence microscopy beyond the diffraction limit can be achievedby acquiring and processing multiple images of the sample under different illumination conditions.One of the simplest techniques, Random Illumination Microscopy (RIM), forms the super-resolvedimage from the variance of images obtained with random speckled illuminations. However, thevalidity of this process has not been fully theorized. In this work, we characterize mathematicallythe sample information contained in the variance of diffraction-limited speckled images as a functionof the statistical properties of the illuminations. We show that an unambiguous two-fold resolutiongain is obtained when the speckle correlation length coincides with the width of the observationpoint spread function. Last, we analyze the difference between the variance-based techniques usingrandom speckled illuminations (as in RIM) and those obtained using random fluorophore activation(as in Super-resolution Optical Fluctuation Imaging, SOFI).

physics.optics↗

arXiv2023

Diffusion Reconstruction of Ultrasound Images with Informative Uncertainty

Despite its wide use in medicine, ultrasound imaging faces several challenges related to its poor signal-to-noise ratio and several sources of noise and artefacts. Enhancing ultrasound image quality involves balancing concurrent factors like contrast, resolution, and speckle preservation. In recent years, there has been progress both in model-based and learning-based approaches to improve ultrasound image reconstruction. Bringing the best from both worlds, we propose a hybrid approach leveraging advances in diffusion models. To this end, we adapt Denoising Diffusion Restoration Models (DDRM) to incorporate ultrasound physics through a linear direct model and an unsupervised fine-tuning of the prior diffusion model. We conduct comprehensive experiments on simulated, in-vitro, and in-vivo data, demonstrating the efficacy of our approach in achieving high-quality image reconstructions from a single plane wave input and in comparison to state-of-the-art methods. Finally, given the stochastic nature of the method, we analyse in depth the statistical properties of single and multiple-sample reconstructions, experimentally show the informativeness of their variance, and provide an empirical model relating this behaviour to speckle noise. The code and data are available at: (upon acceptance).

cs.CV↗

arXiv2023

Reconstruction multiclasse pour l'imagerie TEP 3-photons

This contribution addresses the problem of image reconstruction of radioactivity distribution for which the available information arises from several classes of data, each associated with a specific combination of detections. We introduce a theoretical framework to measure the amount of information brought by each class and we develop an iterative algorithm dedicated to multi-class reconstruction based on maximum likelihood.We apply our approach to the XEMIS2 camera, a preclinical prototype of a Compton telescope dedicated to 3-photon PET imaging for which four distinct classes of partial detections coexist with the full detection class.Based on Monte Carlo simulations, we present the first elements of our model.

stat.AP↗

arXiv2023

Ultrasound Image Reconstruction with Denoising Diffusion Restoration Models

Ultrasound image reconstruction can be approximately cast as a linear inverse problem that has traditionally been solved with penalized optimization using the $l_1$ or $l_2$ norm, or wavelet-based terms. However, such regularization functions often struggle to balance the sparsity and the smoothness. A promising alternative is using learned priors to make the prior knowledge closer to reality. In this paper, we rely on learned priors under the framework of Denoising Diffusion Restoration Models (DDRM), initially conceived for restoration tasks with natural images. We propose and test two adaptions of DDRM to ultrasound inverse problem models, DRUS and WDRUS. Our experiments on synthetic and PICMUS data show that from a single plane wave our method can achieve image quality comparable to or better than DAS and state-of-the-art methods. The code is available at: https://github.com/Yuxin-Zhang-Jasmine/DRUS-v1.

cs.CV↗

arXiv2022

Multiplicative Updates for NMF with $β$-Divergences under Disjoint Equality Constraints

Nonnegative matrix factorization (NMF) is the problem of approximating an input nonnegative matrix, $V$, as the product of two smaller nonnegative matrices, $W$ and $H$. In this paper, we introduce a general framework to design multiplicative updates (MU) for NMF based on $β$-divergences ($β$-NMF) with disjoint equality constraints, and with penalty terms in the objective function. By disjoint, we mean that each variable appears in at most one equality constraint. Our MU satisfy the set of constraints after each update of the variables during the optimization process, while guaranteeing that the objective function decreases monotonically. We showcase this framework on three NMF models, and show that it competes favorably the state of the art: (1)~$β$-NMF with sum-to-one constraints on the columns of $H$, (2) minimum-volume $β$-NMF with sum-to-one constraints on the columns of $W$, and (3) sparse $β$-NMF with $\ell_2$-norm constraints on the columns of $W$.

cs.LG↗

arXiv2021

SLS (Single $\ell_1$ Selection): a new greedy algorithm with an $\ell_1$-norm selection rule

In this paper, we propose a new greedy algorithm for sparse approximation, called SLS for Single L_1 Selection. SLS essentially consists of a greedy forward strategy, where the selection rule of a new component at each iteration is based on solving a least-squares optimization problem, penalized by the L_1 norm of the remaining variables. Then, the component with maximum amplitude is selected. Simulation results on difficult sparse deconvolution problems involving a highly correlated dictionary reveal the efficiency of the method, which outperforms popular greedy algorithms and Basis Pursuit Denoising when the solution is sparse.

math.OC↗

arXiv2021

A Partially Collapsed Sampler for Unsupervised Nonnegative Spike Train Restoration

In this paper the problem of restoration of non-negative sparse signals is addressed in the Bayesian framework. We introduce a new probabilistic hierarchical prior, based on the Generalized Hyperbolic (GH) distribution, which explicitly accounts for sparsity. This new prior allows on the one hand, to take into account the non-negativity. And on the other hand, thanks to the decomposition of GH distributions as continuous Gaussian mean-variance mixture, allows us to propose a partially collapsed Gibbs sampler (PCGS), which is shown to be more efficient in terms of convergence time than the classical Gibbs sampler.

eess.SP↗

arXiv2021

Uniqueness of the Random Illumination Microscopy Variance Equation

Recently, it has been shown theoretically that fluorescence microscopy using random illuminations (RIM) yields a doubled lateral resolution and an improved optical sectioning. Moreover, an algorithm called algoRIM, based on variance matching, has been successfully validated on numerous biological applications. Here, we propose a proof of uniqueness of the RIM variance equation, which corresponds to a first theoretical validation of algoRIM.

physics.data-an↗

arXiv2020

Local-mean preserving post-processing step for non-negativity enforcement in PET imaging: application to $^{90}$Y-PET

In a low-statistics PET imaging context, the positive bias in regions of low activity is a burning issue. To overcome this problem, algorithms without the built-in non-negativity constraint may be used. They allow negative voxels in the image to reduce, or even to cancel the bias. However, such algorithms increase the variance and are difficult to interpret, since negative radioactive concentrations have no physical meaning. Here, we propose a post-processing strategy to remove negative intensities while preserving the local mean activities. Our idea is to transfer the negative intensities to neighboring voxels, so that the mean of the image is preserved. The proposed post-processing algorithm solves a linear programming problem with a specific symmetric structure, and the solution can be computed in a very efficient way. Acquired data from an yttrium-90 phantom show that on images produced by a non-constrained algorithm, a much lower variance in the cold area is obtained after the post-processing step.

eess.IV↗

arXiv2017

On the super-resolution capacity of imagers using unknown speckle illuminations

Speckle based imaging consists of forming a super-resolved reconstruction of an unknown sample from low-resolution images obtained under random inhomogeneous illuminations (speckles). In a blind context where the illuminations are unknown, we study the intrinsic capacity of speckle-based imagers to recover spatial frequencies outside the frequency support of the data, with minimal assumptions about the sample. We demonstrate that, under physically realistic conditions, the covariance of the data has a super-resolution power corresponding to the squared magnitude of the imager point spread function. This theoretical result is important for many practical imaging systems such as acoustic and electromagnetic tomographs, fluorescence and photoacoustic microscopes, or synthetic aperture radar imaging. A numerical validation is presented in the case of fluorescence microscopy.

physics.data-an↗

arXiv2017

Joint reconstruction strategy for structured illumination microscopy with unknown illuminations

The blind structured illumination microscopy (SIM) strategy proposed in (Mudry et al., 1992) is fully re-founded in this paper, unveiling the central role of the sparsity of the illumination patterns in the mechanism that drives super-resolution in the method. A numerical analysis shows that the resolving power of the method can be further enhanced with optimized one-photon or two-photon speckle illuminations. A much improved numerical implementation is provided for the reconstruction problem under the image positivity constraint. This algorithm rests on a new preconditioned proximal iteration faster than existing solutions, paving the way to 3D and real-time 2D reconstruction

physics.data-an↗

arXiv2015

Homotopy based algorithms for $\ell_0$-regularized least-squares

Sparse signal restoration is usually formulated as the minimization of a quadratic cost function $\|y-Ax\|_2^2$, where A is a dictionary and x is an unknown sparse vector. It is well-known that imposing an $\ell_0$ constraint leads to an NP-hard minimization problem. The convex relaxation approach has received considerable attention, where the $\ell_0$-norm is replaced by the $\ell_1$-norm. Among the many efficient $\ell_1$ solvers, the homotopy algorithm minimizes $\|y-Ax\|_2^2+λ\|x\|_1$ with respect to x for a continuum of $λ$'s. It is inspired by the piecewise regularity of the $\ell_1$-regularization path, also referred to as the homotopy path. In this paper, we address the minimization problem $\|y-Ax\|_2^2+λ\|x\|_0$ for a continuum of $λ$'s and propose two heuristic search algorithms for $\ell_0$-homotopy. Continuation Single Best Replacement is a forward-backward greedy strategy extending the Single Best Replacement algorithm, previously proposed for $\ell_0$-minimization at a given $λ$. The adaptive search of the $λ$-values is inspired by $\ell_1$-homotopy. $\ell_0$ Regularization Path Descent is a more complex algorithm exploiting the structural properties of the $\ell_0$-regularization path, which is piecewise constant with respect to $λ$. Both algorithms are empirically evaluated for difficult inverse problems involving ill-conditioned dictionaries. Finally, we show that they can be easily coupled with usual methods of model order selection.

math.NA↗

arXiv2014

Efficient Gaussian Sampling for Solving Large-Scale Inverse Problems using MCMC Methods

The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky factorization, induce an excessive numerical complexity and memory requirement, sequential coordinate sampling methods present a low rate of convergence. Based on the reversible jump Markov chain framework, this paper proposes an efficient Gaussian sampling algorithm having a reduced computation cost and memory usage. The main feature of the algorithm is to perform an approximate resolution of a linear system with a truncation level adjusted using a self-tuning adaptive scheme allowing to achieve the minimal computation cost. The connection between this algorithm and some existing strategies is discussed and its efficiency is illustrated on a linear inverse problem of image resolution enhancement.

stat.ME↗

arXiv2012

Joint k-step analysis of Orthogonal Matching Pursuit and Orthogonal Least Squares

Tropp's analysis of Orthogonal Matching Pursuit (OMP) using the Exact Recovery Condition (ERC) is extended to a first exact recovery analysis of Orthogonal Least Squares (OLS). We show that when the ERC is met, OLS is guaranteed to exactly recover the unknown support in at most k iterations. Moreover, we provide a closer look at the analysis of both OMP and OLS when the ERC is not fulfilled. The existence of dictionaries for which some subsets are never recovered by OMP is proved. This phenomenon also appears with basis pursuit where support recovery depends on the sign patterns, but it does not occur for OLS. Finally, numerical experiments show that none of the considered algorithms is uniformly better than the other but for correlated dictionaries, guaranteed exact recovery may be obtained after fewer iterations for OLS than for OMP.

stat.CO↗

arXiv2011

Algorithms for nonnegative matrix factorization with the beta-divergence

This paper describes algorithms for nonnegative matrix factorization (NMF) with the beta-divergence (beta-NMF). The beta-divergence is a family of cost functions parametrized by a single shape parameter beta that takes the Euclidean distance, the Kullback-Leibler divergence and the Itakura-Saito divergence as special cases (beta = 2,1,0, respectively). The proposed algorithms are based on a surrogate auxiliary function (a local majorization of the criterion function). We first describe a majorization-minimization (MM) algorithm that leads to multiplicative updates, which differ from standard heuristic multiplicative updates by a beta-dependent power exponent. The monotonicity of the heuristic algorithm can however be proven for beta in (0,1) using the proposed auxiliary function. Then we introduce the concept of majorization-equalization (ME) algorithm which produces updates that move along constant level sets of the auxiliary function and lead to larger steps than MM. Simulations on synthetic and real data illustrate the faster convergence of the ME approach. The paper also describes how the proposed algorithms can be adapted to two common variants of NMF : penalized NMF (i.e., when a penalty function of the factors is added to the criterion function) and convex-NMF (when the dictionary is assumed to belong to a known subspace).

cs.LG↗

arXiv2010

Régularisation et optimisation pour l'imagerie sismique des fondations de pylônes

This research report summarizes the progress of work carried out jointly by the IRCCyN and the École Polytechnique de Montréal about the resolution of the inverse problem for the seismic imaging of transmission overhead line structure foundations. Several methods aimed at mapping the underground medium are considered. More particularly, we focus on methods based on a bilinear formulation of the forward problem on one hand (CSI, modified gradient, etc.) and on methods based on a "primal" formulation on the other hand. The performances of these methods are compared using synthetic data. This work was partially funded by RTE (Réseau de Transport d'Électricité), which has initiated the project, and was carried out in collaboration with EDF R&D (Électricité de France - Recherche et Développement).

cs.CE↗