Quantification in optical sectioning microscopy: a comparison of some deconvolution algorithms in view of 3D image segmentation

Abstract

Optical microscopy allows us to study living fluorescent biological samples. Optical sectioning is a technique to obtain three-dimensional (3D) information about the observed object by acquiring a stack of two-dimensional (2D) images at different depths through the sample. However, the specific shape of the 3D optical transfer function of the optical microscope leads to images presenting defects, such as, for example, an apparent elongation along the vertical axis. It is therefore necessary to preprocess the images before any quantitative measurement is performed. This image restoration can be obtained by deconvolution of the acquired 3D image. We have tested several deconvolution algorithms on synthetic images, obtained by convolution of a solid sphere with a measured point spread function. We have compared the restored image with the original one (shape and volume). The linear least-squares method is fast, but artefacts are still present in the restored images. The Carrington method is well adapted to thin objects. The maximum likelihood-expectation maximization method leads to a good reconstruction of the object, but is very time consuming.Résumé. La microscopie optique permet l'étude de spécimens biologiques vivants et fluorescents. La technique par coupes sériées donne des informations tridimensionnelles (3D) sur l'objetétudié par l'acquisition d'une pile d'images bidimensionnellesà différentes profondeurs de focalisationà travers l'échantillon. Les spécificités de la fonction de transfert optique 3D du microscope conduisentà des images présentant des défauts, comme par exemple uneélongation apparente selon l'axe vertical. Il est donc nécessaire de traiter les images avant toute mesure quantitative. On procèdeà une déconvolution de l'image 3D obtenue. Nous avons testé différents algorithmes de déconvolution sur des images de synthèse obtenues par convolution d'une bille pleine avec une fonction de transfert optique mesurée. Nous avons comparé, en forme et en volume, les images restaurées avec l'image d'origine. La méthode 'linear least square' est rapide, mais l'image restaurée présente des artefacts. La méthode de Carrington est bien adaptéeà la restauration d'objets fins. La méthode 'maximum likelihood-expectation maximization' permet une bonne reconstruction des images, mais demande de grands temps de calcul.

Diffraction microtomography with sample rotation: primary result on the influence of a missing apple core in the recorded frequency space

“…Note however that in tomography with specimen rotation, this axis of lower image quality corresponds to the physical rotation axis of the specimen, while in conventional microscopy, the optical axis is the direction of worst imaging conditions. Note also that the observed elongation along the rotation axis in diffractive tomography with sample rotation is less pronounced than that observed in standard transmission microscopy or in fluorescence microscopy along the optical axis [13,14]. This can be easily understood if one considers the so-called missing-cone in transmission or fluorescence microscopy [15]: while high frequencies are captured along lateral axes, no frequencies are measured along the optical axis, and even the maximum thickness of the captured frequency support along this direction is several times smaller than its lateral extension.…”

“…The effect of the missing apple core is indeed very similar to the effect of the missing-cone in transmission microscopy or fluorescence microscopy, which influence becomes more and more visible for smaller object, and which precludes an efficient specimen reconstruction, even after deconvolution [13]. Note however that in tomography with specimen rotation, this axis of lower image quality corresponds to the physical rotation axis of the specimen, while in conventional microscopy, the optical axis is the direction of worst imaging conditions.…”

<title>PSF identification applied to 3D fluorescence microscopy quantification</title>

“…In order to gain in stability, deconvolution is associated with a Wiener pre-filtering. In this paper we use the MAP deconvolution method, for its advantage of speed [13]. This algorithm is based on a Baesian statistical image formation process, in which the regularization consists of modifying slightly the lowest eigenvalues taking into account the image spectrum.…”

Three-dimensional optical imaging in layered media

“…Using the optical sectioning technique a three dimensional image can be obtained and the resolution can be improved with a deconvolution technique but this is time consuming. [1] In the last decades, intensive developments of methods have been carried out to image biological samples using electromagnetic probes [2,3]. The resolution is in some cases below the Rayleigh criterion, i.e., better than a half of the wavelength of the exciting field.…”