arXiv subjects

Maxime Dahan

Publications and source records attributed to Maxime Dahan.

7 recordsLinked to original sources

arXiv2021

Image Restoration by Combined Order Regularization with Optimal Spatial Adaptation

Total Variation (TV) and related extensions have been popular in image restoration due to their robust performance and wide applicability. While the original formulation is still relevant after two decades of extensive research, its extensions that combine derivatives of first- and second-order are now being explored for better performance, with examples being Combined Order TV (COTV) and Total Generalized Variation (TGV). As an improvement over such multi-order convex formulations, we propose a novel non-convex regularization functional which adaptively combines Hessian-Schatten (HS) norm and first order TV (TV1) functionals with spatially varying weight. This adaptive weight itself is controlled by another regularization term; the total cost becomes the sum of this adaptively weighted HS-TV1 term, the regularization term for the adaptive weight, and the data-fitting term. The reconstruction is obtained by jointly minimizing w.r.t. the required image and the adaptive weight. We construct a block coordinate descent method for this minimization with proof of convergence, which alternates between minimization w.r.t. the required image and the adaptive weights. We derive exact computational formula for minimization w.r.t. the adaptive weight, and construct an ADMM algorithm for minimization w.r.t. to the required image. We compare the proposed method using image recovery examples including MRI reconstruction and microscopy deconvolution.

eess.IV↗

arXiv2015

InferenceMAP: Mapping of Single-Molecule Dynamics with Bayesian Inference

Single-particle tracking (SPT) grants unprecedented insight into cellular function at the molecular scale [1]. Throughout the cell, the movement of single-molecules is generally heterogeneous and complex. Hence, there is an imperative to understand the multi-scale nature of single-molecule dynamics in biological systems. We have previously shown that with high-density SPT, spatial maps of the parameters that dictate molecule motion can be generated to intricately describe cellular environments [2,3,4]. To date, however, there exist no publically available tools that reconcile trajectory data to generate the aforementioned maps. We address this void in the SPT community with InferenceMAP: an interactive software package that uses a powerful Bayesian method to map the dynamic cellular space experienced by individual biomolecules.

q-bio.QM↗

arXiv2015

Pitfalls in the quantitative analysis of random walks and the mapping of single-molecule dynamics at the cellular scale

In recent years Bayesian Inference has become an efficient tool to analyse single molecule trajectories. Recently, high density single molecule tagging, Langevin Equation modelling and Bayesian Inference [10] have been used to infer diffusion, force and potential fields at the full cell scale. In this short comment, we point out pitfalls [1, 2] to avoid in single molecule analysis in order to get unbiased results and reliable fields at various scales.

physics.bio-ph↗

arXiv2015

Mapping the energy and diffusion landscapes of membrane proteins at the cell surface using high-density single-molecule imaging and Bayesian inference: application to the multi-scale dynamics of glycine receptors in the neuronal membrane

Protein mobility is conventionally analyzed in terms of an effective diffusion. Yet, this description often fails to properly distinguish and evaluate the physical parameters (such as the membrane friction) and the biochemical interactions governing the motion. Here, we present a method combining high-density single-molecule imaging and statistical inference to separately map the diffusion and energy landscapes of membrane proteins across the cell surface at ~100 nm resolution (with acquisition of a few minutes). When applying these analytical tools to glycine neurotransmitter receptors (GlyRs) at inhibitory synapses, we find that gephyrin scaffolds act as shallow energy traps (~3 kBT) for GlyRs, with a depth modulated by the biochemical properties of the receptor-gephyrin interaction loop. In turn, the inferred maps can be used to simulate the dynamics of proteins in the membrane, from the level of individual receptors to that of the population, and thereby, to model the stochastic fluctuations of physiological parameters (such as the number of receptors at synapses). Overall, our approach provides a powerful and comprehensive framework with which to analyze biochemical interactions in living cells and to decipher the multi-scale dynamics of biomolecules in complex cellular environments.

physics.bio-ph↗

arXiv2013

Hyperspectral fluorescence microscopy based on Compressive Sampling

The mathematical theory of compressed sensing (CS) asserts that one can acquire signals from measurements whose rate is much lower than the total bandwidth. Whereas the CS theory is now well developed, challenges concerning hardware implementations of CS-based acquisition devices-especially in optics-have only started being addressed. This paper presents an implementation of compressive sensing in fluorescence microscopy and its applications to biomedical imaging. Our CS microscope combines a dynamic structured wide-field illumination and a fast and sensitive single-point fluorescence detection to enable reconstructions of images of fluorescent beads, cells, and tissues with undersampling ratios (between the number of pixels and number of measurements) up to 32. We further demonstrate a hyperspectral mode and record images with 128 spectral channels and undersampling ratios up to 64, illustrating the potential benefits of CS acquisition for higher-dimensional signals, which typically exhibits extreme redundancy. Altogether, our results emphasize the interest of CS schemes for acquisition at a significantly reduced rate and point to some remaining challenges for CS fluorescence microscopy.

cs.IT↗

arXiv2012

Compressive Fluorescence Microscopy for Biological and Hyperspectral Imaging

The mathematical theory of compressed sensing (CS) asserts that one can acquire signals from measurements whose rate is much lower than the total bandwidth. Whereas the CS theory is now well developed, challenges concerning hardware implementations of CS-based acquisition devices---especially in optics---have only started being addressed. This paper presents an implementation of compressive sensing in fluorescence microscopy and its applications to biomedical imaging. Our CS microscope combines a dynamic structured wide-field illumination and a fast and sensitive single-point fluorescence detection to enable reconstructions of images of fluorescent beads, cells and tissues with undersampling ratios (between the number of pixels and number of measurements) up to 32. We further demonstrate a hyperspectral mode and record images with 128 spectral channels and undersampling ratios up to 64, illustrating the potential benefits of CS acquisition for higher dimensional signals which typically exhibits extreme redundancy. Altogether, our results emphasize the interest of CS schemes for acquisition at a significantly reduced rate and point out to some remaining challenges for CS fluorescence microscopy.

stat.AP↗

arXiv2004

Measurement of the radiative and non-radiative decay rates of single CdSe nanocrystals through controlled modification of their spontaneous emission

We present a simple method to measure the radiative and non-radiative recombination rates of individual fluorescent emitters at room temperature. By placing a single molecule successively close and far from a dielectric interface and simultaneously measuring its photoluminescence decay and its orientation, both the radiative and non-radiative recombination rates can be determined. For CdSe nanocrystals, our results demonstrate that the fluorescence quantum efficiency, determined at the single molecule level, is 98% in average, far above the value expected from conventional ensemble experiments. The bi-dimensionnal nature of the transition dipole is also directly evidenced from a single particle measurement.

cond-mat.other↗