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Concept

Déconvolution

Résumé

En mathématiques, la déconvolution est un procédé algorithmique destiné à inverser les effets de la convolution. Le concept de déconvolution est largement utilisé en traitement du signal et , notamment en microscopie et astronomie. L'objectif de la déconvolution Le problème est de déterminer la solution f d'une équation de la forme : :f * g = h , On note ici par h un signal tel qu'il est acquis et f le signal que l'on désire estimer ou restaurer, mais qui a été convolué par une réponse impulsionnelle g lors de l'acquisition. La réponse impulsionnelle est souvent (surtout en traitement d'image) aussi nommée fonction d'étalement du point (point spread function ou PSF en anglais). Lorsque l'on a affaire à un processus physique d'acquisition, la mesure h est souvent entachée d'un bruit de mesure ε : :(f * g) + \varepsilon = h , L'opération de déconvolution sera ren

Source officielle

https://fr.wikipedia.org/wiki/D%C3%A9convolution

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Unités associées (11)

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Concepts associés (12)

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Cours associés (12)

Introduction to the different contrast enhancing methods in optical microscopy. Basic hands-on experience with optical microscopes at EPFL's BioImaging and Optics Facility. How to investigate biological samples? How to obtain high quality images?

Study of advanced image processing; mathematical imaging. Development of image-processing software and prototyping in JAVA; application to real-world examples in industrial vision and biomedical imaging.

Identification of discrete-time linear models using experimental data is studied. The correlation method and spectral analysis are used to identify nonparametric models and the subspace and prediction error methods to estimate the plant and noise model parameters. Hands-on labs are included.

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Séances de cours associées (12)

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Publications associées (70)

Optimization Of Compound Regularization Parameters Based On Stein'S Unbiased Risk Estimate

Xin Liu, Jiaqi Liu, Hanjie Pan, Feng Xue

Recently, the type of compound regularizers has become a popular choice for signal reconstruction. The estimation quality is generally sensitive to the values of multiple regularization parameters. In this work, based on BDF algorithm, we develop a data-driven optimization scheme based on minimization of Stein's unbiased risk estimate (SURE) statistically equivalent to mean squared error (MSE). We propose a recursive evaluation of SURE to monitor the MSE during BDF iteration; the optimal values of the multiple parameters are then identified by the minimum SURE. Monte-Carlo simulation is applied to compute SURE for large-scale data. We exemplify the proposed method with image deconvolution. Numerical experiments show that the proposed method leads to highly accurate estimates of regularization parameters and nearly optimal restoration performance.

Ieee2017

Chargement

Fast and automated wavelet-regularized image restoration in fluorescence microscopy

Cédric René Jean Vonesch

The subject of this thesis is image restoration, that is, deconvolution and denoising. Our work is motivated by applications in the rapidly expanding field of biological imaging and in particular fluorescence microscopy. Inverse problems in this area typically involve regularly structured but high-dimensional data sets, thus requiring a specific tradeoff between restoration quality, computational complexity and user interaction. Our interest lies in novel algorithmic solutions for addressing these challenges. The common point of our developments is that they rely centrally on wavelets and multilevel concepts. The thesis is organized in three main parts. In the first part, we provide a general overview of fluorescence microscopy in the context of biological research. We then review the current state of the art in deconvolution microscopy, within a unifying variational framework. The second part is concerned with deconvolution using a non-quadratic (typically ℓ1) wavelet-domain regularization. In the context of deconvolution microscopy, this approach is novel. It amounts to imposing a sparsity constraint on the object to be recovered, a concept that has recently attracted considerable interest in signal and image processing. This type of regularization was shown to belong to the most effective restoration methods, but it involves a computationally challenging optimization problem. We propose a multilevel version of the standard "thresholded Landweber" algorithm that yields a substantial acceleration. This allows us to apply wavelet regularization to large-scale deconvolution problems encountered in deconvolution microscopy. In the third part, we present some applications of risk estimation techniques for automating the process of image restoration. We first propose a denoising method that is specifically designed for very low light intensities. The algorithm is designed from the beginning for complete self-adjustment of its parameters and for low computational complexity. It also performs competitively with most existing approaches for Poisson intensity estimation. Our second contribution is a general method for estimating the signal-to-noise ratio during the execution of iterative image-restoration procedures; it is applicable to most algorithms emanating from variational formulations, in particular those involving wavelet regularization.

EPFL2009

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, , ,

Neural activity occurs in the shape of spatially organized patterns: networks of brain regions activate in synchrony. Many of these functional networks also happen to be strongly structurally connected. We use this information to revisit the fundamental problem of functional magnetic resonance imaging (fMRI) data deconvolution. Using tools from graph signal processing (GSP), we extend total activation, a spatio-temporal deconvolution technique, to data defined on graph domains. The resulting approach simultaneously cancels out the effect of the haemodynamics, and promotes spatial patterns that are in harmony with predefined structural wirings. More precisely, we minimize a functional involving one data fidelity and two regularization terms. The first regularizer uses the concept of generalized total variation to promote sparsity in the activity transients domain. The second term controls the overall spatial variation over the graph structure. We demonstrate the relevance of this structurally-driven regularization on synthetic and experimental data.

IEEE2019

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Fast and automated wavelet-regularized image restoration in fluorescence microscopy

Cédric René Jean Vonesch

EPFL2009