Fibronectin Extra Domains tune cellular responses and confer topographically distinct features to fibril networks.

Cellular fibronectin (FN; also known as FN1) variants harboring one or two alternatively spliced so-called extra domains (EDB and EDA) play a central bioregulatory role during development, repair processes and fibrosis. Yet, how the extra domains impact fibrillar assembly and function of the molecule remains unclear. Leveraging a unique biological toolset and image analysis pipeline for direct comparison of the variants, we demonstrate that the presence of one or both extra domains impacts FN assembly, function and physical properties of the matrix. When presented to FN-null fibroblasts, extra domain-containing variants differentially regulate pH homeostasis, survival and TGF-ß signaling by tuning the magnitude of cellular responses, rather than triggering independent molecular switches. Numerical analyses of fiber topologies highlight significant differences in variant-specific structural features and provide a first step for the development of a generative model of FN networks to unravel assembly mechanisms and investigate the physical and functional versatility of extracellular matrix landscapes.This article has an associated First Person interview with the first author of the paper.

A spatial statistical framework for the parametric study of fiber networks: Application to fibronectin deposition by normal and activated fibroblasts.

Due to the complex architectural diversity of biological networks, there is an increasing need to complement statistical analyses with a qualitative and local description of their spatial properties. One such network is the extracellular matrix (ECM), a biological scaffold for which changes in its spatial organization significantly impact tissue functions in health and disease. Quantifying variations in the fibrillar architecture of major ECM proteins should considerably advance our understanding of the link between tissue structure and function. Inspired by the analysis of functional magnetic resonance imaging (fMRI) images, we propose a novel statistical analysis approach embedded into a machine learning paradigm, to measure and detect local variations of meaningful ECM parameters. We show that parametric maps representing fiber length and pore directionality can be analyzed within the proposed framework to differentiate among various tissue states. The parametric maps are derived from graph-based representations that reflect the network architecture of fibronectin (FN) fibers in a normal, or disease-mimicking in vitro setting. Such tools can potentially lead to a better characterization of dynamic matrix networks within fibrotic tumor microenvironments and contribute to the development of better imaging modalities for monitoring their remodeling and normalization following therapeutic intervention.

COL0RME: Super-resolution microscopy based on sparse blinking/fluctuating fluorophore localization and intensity estimation.

To overcome the physical barriers caused by light diffraction, super-resolution techniques are often applied in fluorescence microscopy. State-of-the-art approaches require specific and often demanding acquisition conditions to achieve adequate levels of both spatial and temporal resolution. Analyzing the stochastic fluctuations of the fluorescent molecules provides a solution to the aforementioned limitations, as sufficiently high spatio-temporal resolution for live-cell imaging can be achieved using common microscopes and conventional fluorescent dyes. Based on this idea, we present COL0RME, a method for covariance-based super-resolution microscopy with intensity estimation, which achieves good spatio-temporal resolution by solving a sparse optimization problem in the covariance domain and discuss automatic parameter selection strategies. The method is composed of two steps: the former where both the emitters' independence and the sparse distribution of the fluorescent molecules are exploited to provide an accurate localization; the latter where real intensity values are estimated given the computed support. The paper is furnished with several numerical results both on synthetic and real fluorescence microscopy images and several comparisons with state-of-the art approaches are provided. Our results show that COL0RME outperforms competing methods exploiting analogously temporal fluctuations; in particular, it achieves better localization, reduces background artifacts, and avoids fine parameter tuning.

Off-The-Grid Variational Sparse Spike Recovery: Methods and Algorithms.

Gridless sparse spike reconstruction is a rather new research field with significant results for the super-resolution problem, where we want to retrieve fine-scale details from a noisy and filtered acquisition. To tackle this problem, we are interested in optimisation under some prior, typically the sparsity i.e., the source is composed of spikes. Following the seminal work on the generalised LASSO for measures called the Beurling-Lasso (BLASSO), we will give a review on the chief theoretical and numerical breakthrough of the off-the-grid inverse problem, as we illustrate its usefulness to the super-resolution problem in Single Molecule Localisation Microscopy (SMLM) through new reconstruction metrics and tests on synthetic and real SMLM data we performed for this review.

New ℓ2 - ℓ0 algorithm for single-molecule localization microscopy.

Among the many super-resolution techniques for microscopy, single-molecule localization microscopy methods are widely used. This technique raises the difficult question of precisely localizing fluorophores from a blurred, under-resolved, and noisy acquisition. In this work, we focus on the grid-based approach in the context of a high density of fluorophores formalized by a ℓ2 least-square term and sparsity term modeled with ℓ0 pseudo-norm. We consider both the constrained formulation and the penalized formulation. Based on recent results, we formulate the ℓ0 pseudo-norm as a convex minimization problem. This is done by introducing an auxiliary variable. An exact biconvex reformulation of the ℓ2 - ℓ0 constrained and penalized problems is proposed with a minimization algorithm. The algorithms, named CoBic (Constrained Biconvex) and PeBic (Penalized Biconvex) are applied to the problem of single-molecule localization microscopy and we compare the results with other recently proposed methods.

Blind deconvolution for thin-layered confocal imaging.

We propose an alternate minimization algorithm for estimating the point-spread function (PSF) of a confocal laser scanning microscope and the specimen fluorescence distribution. A three-dimensional separable Gaussian model is used to restrict the PSF solution space and a constraint on the specimen is used so as to favor the stabilization and convergence of the algorithm. The results obtained from the simulation show that the PSF can be estimated to a high degree of accuracy, and those on real data show better deconvolution as compared to a full theoretical PSF model.

Nanometric axial resolution of fibronectin assembly units achieved with an efficient reconstruction approach for multi-angle-TIRF microscopy.

High resolution imaging of molecules at the cell-substrate interface is required for understanding key biological processes. Here we propose a complete pipeline for multi-angle total internal reflection fluorescence microscopy (MA-TIRF) going from instrument design and calibration procedures to numerical reconstruction. Our custom setup is endowed with a homogeneous field illumination and precise excitation beam angle. Given a set of MA-TIRF acquisitions, we deploy an efficient joint deconvolution/reconstruction algorithm based on a variational formulation of the inverse problem. This algorithm offers the possibility of using various regularizations and can run on graphics processing unit (GPU) for rapid reconstruction. Moreover, it can be easily used with other MA-TIRF devices and we provide it as an open-source software. This ensemble has enabled us to visualize and measure with unprecedented nanometric resolution, the depth of molecular components of the fibronectin assembly machinery at the basal surface of endothelial cells.

Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution.

Confocal laser scanning microscopy is a powerful and popular technique for 3D imaging of biological specimens. Although confocal microscopy images are much sharper than standard epifluorescence ones, they are still degraded by residual out-of-focus light and by Poisson noise due to photon-limited detection. Several deconvolution methods have been proposed to reduce these degradations, including the Richardson-Lucy iterative algorithm, which computes maximum likelihood estimation adapted to Poisson statistics. As this algorithm tends to amplify noise, regularization constraints based on some prior knowledge on the data have to be applied to stabilize the solution. Here, we propose to combine the Richardson-Lucy algorithm with a regularization constraint based on Total Variation, which suppresses unstable oscillations while preserving object edges. We show on simulated and real images that this constraint improves the deconvolution results as compared with the unregularized Richardson-Lucy algorithm, both visually and quantitatively.

Wavelet-based level set evolution for classification of textured images.

We present a supervised classification model based on a variational approach. This model is specifically devoted to textured images. We want to get a partition of an image, composed of texture regions separated by regular interfaces. Each kind of texture defines a class. We use a wavelet packet transform to analyze the textures, characterized by their energy distribution in each sub-band. In order to have an image segmentation according to the classes, we model the regions and their interfaces by level set functions. We define a functional on these level sets whose minimizers define the optimal classification according to texture. A system of coupled PDEs is deduced from the functional. By solving this system, each region evolves according to its wavelet coefficients and interacts with the neighbor regions in order to obtain a partition with regular contours. Experiments are shown on synthetic and real images.

An adaptive Gaussian model for satellite image deblurring.

The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem, which can be regularized within a Bayesian context by using an a priori model of the reconstructed solution. Since real satellite data show spatially variant characteristics, we propose here to use an inhomogeneous model. We use the maximum likelihood estimator (MLE) to estimate its parameters and we show that the MLE computed on the corrupted image is not suitable for image deconvolution because it is not robust to noise. We then show that the estimation is correct only if it is made from the original image. Since this image is unknown, we need to compute an approximation of sufficiently good quality to provide useful estimation results. Such an approximation is provided by a wavelet-based deconvolution algorithm. Thus, a hybrid method is first used to estimate the space-variant parameters from this image and then to compute the regularized solution. The obtained results on high resolution satellite images simultaneously exhibit sharp edges, correctly restored textures, and a high SNR in homogeneous areas, since the proposed technique adapts to the local characteristics of the data.

Sparse Poisson noisy image deblurring.

Deblurring noisy Poisson images has recently been a subject of an increasing amount of works in many areas such as astronomy and biological imaging. In this paper, we focus on confocal microscopy, which is a very popular technique for 3-D imaging of biological living specimens that gives images with a very good resolution (several hundreds of nanometers), although degraded by both blur and Poisson noise. Deconvolution methods have been proposed to reduce these degradations, and in this paper, we focus on techniques that promote the introduction of an explicit prior on the solution. One difficulty of these techniques is to set the value of the parameter, which weights the tradeoff between the data term and the regularizing term. Only few works have been devoted to the research of an automatic selection of this regularizing parameter when considering Poisson noise; therefore, it is often set manually such that it gives the best visual results. We present here two recent methods to estimate this regularizing parameter, and we first propose an improvement of these estimators, which takes advantage of confocal images. Following these estimators, we secondly propose to express the problem of the deconvolution of Poisson noisy images as the minimization of a new constrained problem. The proposed constrained formulation is well suited to this application domain since it is directly expressed using the antilog likelihood of the Poisson distribution and therefore does not require any approximation. We show how to solve the unconstrained and constrained problems using the recent alternating-direction technique, and we present results on synthetic and real data using well-known priors, such as total variation and wavelet transforms. Among these wavelet transforms, we specially focus on the dual-tree complex wavelet transform and on the dictionary composed of curvelets and an undecimated wavelet transform.

Parametric blind deconvolution for confocal laser scanning microscopy.

In this paper, we propose a method for the iterative restoration of fluorescence Confocal Laser Scanning Microscopic (CLSM) images and parametric estimation of the acquisition system's Point Spread Function (PSF). The CLSM is an optical fluorescence microscope that scans a specimen in 3D and uses a pinhole to reject most of the out-of-focus light. However, the quality of the images suffers from two basic physical limitations. The diffraction-limited nature of the optical system, and the reduced amount of light detected by the photomultiplier cause blur and photon counting noise respectively. These images can hence benefit from post-processing restoration methods based on deconvolution. An efficient method for parametric blind image deconvolution involves the simultaneous estimation of the specimen 3D distribution of fluorescent sources and the microscope PSF. By using a model for the microscope image acquisition physical process, we reduce the number of free parameters describing the PSF and introduce constraints. The parameters of the PSF may vary during the course of experimentation, and so they have to be estimated directly from the observed data. A priori model of the specimen is further applied to stabilize the alternate minimization algorithm and to converge to the solutions.