Jérôme Idier

French National Centre for Scientific Research | CNRS · Laboratoire des Sciences du Numériques de Nantes

The ultimate aim of fluorescence microscopy is to achieve high-resolution imaging of increasingly larger biological samples. Extended depth of field presents a potential solution to accelerate imaging of large samples when compression of information along the optical axis is not detrimental to the interpretation of images. We have implemented an ex...

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...

Improving the resolution of fluorescence microscopy beyond the diffraction limit can be achieved by acquiring and processing multiple images of the sample under different illumination patterns (periodic grids, focused beams, or more generally speckles). When the illuminations are known, the superresolved reconstruction is generally formed from a li...

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 pri...

Random Illumination Microscopy (RIM) usually forms a super-resolved reconstruction of the sample from the statistics of hundreds of images obtained under speckled illuminations. We show that RIM approach is also effective when a few specific light grids are used for illuminating the sample. This combination improves the temporal resolution of RIM w...

Random Illumination Microscopy (RIM) requires capturing around 200 fluorescence images with speckle illuminations. Implementing Pseudo-Random Illuminations reduces this number by a factor of 10, enabling robust real-time super-resolution imaging of biological specimens. Our study explore the trade-off between the robustness and speed in pseudo-RIM.

We describe the basic principles of super-resolved Random Illumination Microscopy (RIM) and present different applications in fluorescence and non-linear imaging.

Random Illumination Microscopy (RIM) is a recent super-resolved fluorescence imaging technique in which the sample is recovered iteratively by matching the empirical variance of low-resolution images obtained from random speckle illuminations, with the expected variance model. RIM was shown theoretically to achieve a two-fold resolution gain and it...

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...

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...

A benefit of random illumination microscopy (RIM) is that it improves the resolution and linearity of the brightness of structured illumination microscopy using minimally controlled speckled illumination. Here, we implemented RIM in the total internal reflection fluorescence (TIRF) configuration for imaging biological processes close to the coversl...

The L-curve is a popular heuristic to tune Tikhonov regularization in linear inverse problems. This paper shows how it naturally arises when the problem is solved from a Bayesian perspective. Specifically, it establishes that the L-curve is a graphical way of searching for the maximum aposteriori solution after marginalization over the priors. The...

Intrinsically disordered proteins (IDP) are at the center of numerous biological processes, and attract consequently extreme interest in structural biology. Numerous approaches have been developed for generating sets of IDP conformations verifying a given set of experimental measurements. We propose here to perform a systematic enumeration of prote...

Civilian nuclear power is a low carbon energy source having high security requirements. Many components of nuclear power plants such as primary cooling circuit or pressure vessels have to be regularly inspected to ensure the safety of the installation. These parts are generally thick and only accessible from the external surface whereas defects suc...

Ultrasonic inspection of coarse-grained steels is a common challenge in various industrial fields. This task is often difficult because of acoustic scattering that creates structural noise in the ultrasonic signals and images. Therefore, inspections usually use low-frequency probes, which achieve poor resolution with standard delay-and-sum (DAS) im...

Inverse polynomial models are a class of models whose estimation is mildly non linear. Different methods allow linearisation of this problem in order to obtain a direct estimator. We propose a formalism to analyse these methods within a family of weighted least square estimators. Based on their theoretical study, we propose a new estimator with bet...

Remote sensing pushbroom-type imaging systems acquire entire columns of an image with a single detector. As a consequence, the miss-calibration of the detectors produces stripes on the image. In this context, this article introduces a new self-calibration destriping method based on an affine response model for the detectors, called statistical affi...

This paper introduces a new family of prior models called Bernoulli-Gaussian-Mixtures (BGM), with a view to efficiently address sparse linear inverse problems or sparse linear regression, in the Bayesian framework. The BGM family is based on continuous Location and Scale Mixtures of Gaussians (LSMG), which includes a wide range of symmetric and a...

The popularity of yttrium-90 ( <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">90</sup> Y) PET is growing. However, due to the very low branching ratio of <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">90</sup> Y ( $3.2\times 10^{-5}$ ), images reconstr...

In this paper, we present a generic performance model able to evaluate the accuracy of depth estimation using depth from defocus (DFD). This model only requires the sensor point spread function at a given depth to evaluate the theoretical accuracy of depth estimation. Hence, it can be used for any (un)conventional system, using either one or severa...

This paper addresses high-resolution ultrasonic image reconstruction from Full Matrix Capture (FMC) data in the context of nondestructive testing (NDT). In order to reduce the numerical complexity, the time-domain data and ultrasonic model are projected into the image domain through a linear beamforming procedure. The resulting model is interpreted...

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

This paper proposes an exact recovery analysis of greedy algorithms for non-negative sparse representations. Orthogonal greedy algorithms such as Orthogonal Matching Pursuit (OMP) and Orthogonal Least Squares (OLS) consist of gradually increasing the solution support and updating the nonzero coefficients in the least squares sense. From a theoretic...

Current super-resolution microscopy (SRM) methods suffer from an intrinsic complexity that might curtail their routine use in cell biology. We describe here random illumination microscopy (RIM) for live-cell imaging at super-resolutions matching that of 3D structured illumination microscopy, in a robust fashion. Based on speckled illumination and s...

Wall Shear Stress (WSS) has been demonstrated to be a biomarker of the development of atherosclerosis. In vivo assessment of WSS is still challenging, but 4D Flow MRI represents a promising tool to provide 3D velocity data from which WSS can be calculated. In this study, a system based on Laser Doppler Velocimetry (LDV) was developed to validate ne...

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...

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...

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...

The optimization problem encountered in protein structure determination is undergoing a change of perspective due to the larger importance in biology taken by the disordered regions of biomolecules. In such cases, the convergence criterion is more difficult to set up; moreover, the enormous size of the space makes it difficult to achieve a complete...

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...

It is well-known that Orthogonal Matching Pursuit (OMP) recovers the exact support of K-sparse signals under the condition µ < 1/(2K − 1) where µ denotes the mutual coherence of the dictionary. In this communication, we show that under the same condition and if the unknown K-sparse signal is non-negative, the weights of the atoms selected by OMP ar...

This paper considers the microwave imaging reconstruction problem, based on additive penalization and gradient-based optimization. Each evaluation of the cost function and of its gradient requires the resolution of as many high-dimensional linear systems as the number of incident fields, which represents a large amount of computations. Since all su...

Wall shear stress (WSS) is a relevant hemodynamic indicator of the local stress applied on the endothelium surface. More specifically, its spatiotemporal distribution reveals crucial in the evolution of many pathologies such as aneurysm, stenosis, and atherosclerosis. This paper introduces a new solution, called PaLMA, to quantify the WSS from 4D F...

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...

In the context of nondestructive testing (NDT), this paper proposes an inverse problem approach for the reconstruction of high-resolution ultrasonic images from full matrix capture (FMC) datasets. We build a linear model that links the FMC data, i.e. the signals collected from all transmitter-receiver pairs of an ultrasonic array, to the discretize...

Super-resolution fluorescence microscopy has been instrumental to progress in biology. Yet, the photo-induced toxicity, the loss of resolution into scattering samples or the complexity of the experimental setups curtail its general use for functional cell imaging. Here, we describe a new technology for tissue imaging reaching a 114nm/8Hz resolution...

Multi-element probes are widely used in Non-Destructive Testing (NDT) for their ability to produce images. Full Matrix Capture (FMC) is a standard acquisition process that consists in acquiring all inter-element responses. The common reconstruction procedure, namely the Total Focusing Method (TFM), is a linear reconstruction technique that does not...

Orthogonal greedy algorithms are popular sparse signal reconstruction algorithms. Their principle is to select atoms one by one. A series of unconstrained least-square subproblems of gradually increasing size is solved to compute the approximation coefficients, which is efficiently performed using a fast recursive update scheme. When dealing with n...

Nous proposons une méthode de reconstruction d’images ultrasonores à partir de données issues de sondes multi-éléments, composées des réponses de chaque couple émetteur-récepteur (Full Matrix Capture, FMC), typiquement utilisées pour le contrôle non destructif des matériaux. Afin de réduire la taille du problème, nous proposons une approche où les...

Cette communication concerne la conception, l'implémentation et l'analyse d'algorithmes gloutons pour la reconstruction parci-monieuse sous contrainte de positivité. Ces algorithmes, conçus pour minimiser un critère quadratique sous contraintes de parcimonie et de positivité, généralisent les algorithmes Orthogonal Matching Pursuit et Orthogonal Le...

Sparse approximation arises in many applications and often leads to a constrained or penalized L0 minimization problem, which was proved to be NP-hard. This paper proposes a revision of existing analyses of NP-hardness of the penalized L0 minimization problem and it introduces a new proof adapted from Natarajan's construction (1995). Moreover, we p...

This paper proposes a method to enhance the resolution of images computed from Full Matrix Capture (FMC) datasets widely used in Non-Destructive Evaluation (NDE). The resolution of standard techniques such as Total Focusing Method (TFM) that do not account for the impulse response of transducers is limited. The proposed model exploits the instrumen...

It is well-known that Orthogonal Matching Pursuit (OMP) recovers the exact support of K-sparse signals under the condition µ < 1/(2K − 1) where µ denotes the mutual coherence of the dictionary. In this communication, we show that under the same condition and if the unknown K-sparse signal is non-negative, the weights of the atoms selected by OMP ar...

Orthogonal greedy algorithms are popular sparse signal reconstruction algorithms. Their principle is to select atoms one by one. A series of unconstrained least-squares subproblems of gradually increasing size is solved to compute the approximation coefficients, which is efficiently performed using a fast recursive update scheme. When dealing with...

We propose a joint least squares and least absolute deviations (JOLESALAD) model, show that the proposed model can cover LASSO and two of its variants, namely the generalized LASSO (gLASSO) and the constrained LASSO (cLASSO), and prove that under a full rank condition the JOLESALAD can be transformed into cLASSO. Based on this equivalency, rich too...

We bring a contribution to the exact recovery theory of a K-sparse vector in the noiseless setting under the standard condition µ < 1/(2K − 1), where µ denotes the mutual coherence. While it is known that Orthogonal Matching Pursuit (OMP) and Orthogonal Least Squares (OLS) identify the true support in K iterations, we prove that the weights of the...

Piecewise signals appear in many application fields. Here, we propose a framework for segmenting such signals based on the modeling of each piece using a parametric probability distribution. The proposed framework first models the segmentation as an optimization problem with sparsity regularization. Then, an algorithm based on dynamic programming i...

The total focusing method (TFM) becomes a common approach in order to process full matrix capture data in nondestructive testing. This method consists in transmitting an unfocused beam and performing focusing in reception at each point of a reconstruction grid. The quality of TFM images is generally better than conventional phased array focusing th...

Purpose: The purpose of this study was to assess the precision of four-dimensional (4D) phase-contrast magnetic resonance imaging (PCMRI) to measure mean flow and peak velocity (Vmax) in a pulsatile flow phantom and to test its sensitivity to spatial resolution and Venc. Material and methods: The pulsatile flow phantom consisted of a straight tu...

We present a numerical study of a microscopy setup in which the sample is illuminated with uncontrolled speckle patterns and the two-photon excitation fluorescence is collected on a camera. We show that, using a simple deconvolution algorithm for processing the speckle low-resolution images, this wide-field imaging technique exhibits resolution sig...

Multi-tissue partial volume estimation in MRI images is investigated with a viewpoint related to spectral unmixing as used in hyperspectral imaging. The main contribution of this paper is twofold. It firstly proposes a theoretical analysis of the statistical optimality conditions of the proportion estimation problem, which in the context of multi-c...

Speckle based imaging consists of forming a super- resolved reconstruction of an unknown sample from low- resolution images obtained under random inhomogeneous illu- minations (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 freque...

This article addresses least-squares minimization under sparsity and non-negativity constraints. We propose a recursive implementation of Non-Negative Orthogonal Matching Pursuit (NNOMP) based on the active set method for solving least-squares subproblems. We further propose an improvement of NNOMP, named support-Shrinkage NNOMP (SNNOMP), based on...

The blind structured illumination microscopy (SIM) strategy proposed in [1] 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 o...

The Blind-SIM strategy proposed in Mudry, Emeric, et al. "Structured illumination microscopy using unknown speckle patterns." Nature Photonics (2012) is drastically revisited and a Preconditioned Primal-Dual splitting (PPDS) strategy is introduced to provide a very fast reconstruction algorithm.

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...

We consider a fluorescence microscope in which several three-dimensional images of a sample are recorded for different speckle illuminations. We show, on synthetic data, that by summing the positive deconvolution of each speckle image, one obtains a sample reconstruction with axial and transverse resolutions that compare favorably to that of an ide...

This paper studies the intrinsic connection between a generalized LASSO and a basic LASSO formulation. The former is the extended version of the latter by introducing a regularization matrix to the coefficients. We show that when the regularization matrix is even- or under-determined with full rank conditions, the generalized LASSO can be transform...

In this communication, a fast reconstruction algorithm is proposed for fluorescence blind structured illumination microscopy (SIM) under the sample positivity constraint. This new algorithm is by far simpler and faster than existing solu- tions, paving the way to 3D and real-time 2D reconstruction.

In this communication, a fast reconstruction algorithm is proposed for fluorescence \textit{blind} structured illumination microscopy (SIM) under the sample positivity constraint. This new algorithm is by far simpler and faster than existing solutions, paving the way to 3D and/or real-time 2D reconstruction.

A marginal likelihood estimator is proposed to super-resolution image reconstruction problem in blind structured illumination microscopy. To reduce the computational complexity, we propose an approximation of the likelihood function based on patch models.

Speckle based imagers provide super-resolved reconstructions techniques from a series of low-resolution acquisitions obtained under speckle illuminations. We demonstrate that, under physically realistic conditions, the correlation of the dataset have a super-resolution power corresponding to the squaring of the imager point spread function.

Speckle based imaging consists in forming a super-resolved reconstruction of an unknown object from low-resolution images obtained under random inhomogeneous illuminations (speckles). However, the origin of this super-resolution is unclear. In this work, we demonstrate that, under physically realistic conditions, the correlation of the data have a...

In 3-D microwave imaging, gradient-based optimization algorithms usually make use of the so-called stabilized version of the biconjugate gradient iterative method (BiCGStab) in order to solve multiple linear systems. We propose to use a block version of BiCGStab to jointly solve the mutiple right-hand side linear systems. Illuminations are partitio...

Selection of fish with appropriate fat content and anatomic distribution is searched in fish industry. This necessitates fast and accurate measurements of mass fat fraction maps on a large number of fish. The objective of this work is to assess the relevance of MRI water-fat separation for this purpose. For the separation of the water and fat image...

To analyze the next generation sequencing data, the so-called read depth signal is often segmented with standard segmentation tools. However, these tools usually assume the signal to be a piecewise constant signal and contaminated with zero mean Gaussian noise, and therefore modeling error occurs. This paper models the read depth signal with piecew...

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 $\el...

Ultrasonic non destructive testing (NDT) is an efficient method to detect flaws in industrial parts. The detection of flat bottom holes (FBH) is a typical problem, which serves as a reference in the NDT community. It is nevertheless a hard task if the FBH is short because its echo overlaps with the backwall echo. In this paper, we propose to use a...

Atomic force microscopy (AFM) is a technology that enables us to characterize the physicochemical properties of objects and, in particular, biological samples at the nano-scale. This chapter presents the type of data that can be acquired in force-volume imaging and the physical parameters that are sought to be extracted from these data. Data analys...