Electron Energy Loss Spectroscopy and Biology

Although most of the recent work concerning EELS in electron microscopy is related to instrumental developments, there are a number of papers relating to biological applications. The aim of this paper is to attempt to present in a pedagogical manner the subject of EELS and biology. The biologist will be taught about EELS and the physicist about the possible biological applications of this technique. The paper thus consists of: 1) a presentation of a minimum background on EELS required for biologists to realize what its potential is; 2) a description of why EELS is a useful tool in biology; 3) a description of which kind of biological problems may be resolved through EELS; 4) finally a survey relating to the problems encountered in applying EELS to biology, i.e., specimen preparation, beam damage and artefacts

Characterization of maximum likelihood solutions to image reconstruction in photon emission tomography

Characterization of maximum likelihood solutions to image reconstruction in photon emission tomography  

Cramér-Rao bounds and condition number in SPECT: Comparison between conventional thin holes collimator and emission tomography project with large and long holes collimators

Objectives: The project of emission tomography with large and long holes collimators (CACAO-TROLL), was proposed some time ago. The use of collimators with larger holes is intended to increase the number of photons detected and therefore the information available to reconstruct the images. This project is however exploratory and most research works in SPECT stick today to the conventional thin hole collimator (CTHC). It may be objected that if the number of photons increases, the information conveyed by each photon is lower. This thought is however inconsistent with our previously published demonstration using information theory. We develop here another approach. Methods: We first derived a formula to express the response function of the CACAO-TROLL acquisition, taking a complete account of the depth dependence and the attenuation of the gamma ray in the collimator. The conventional SPECT response function was modelled by using the formula of Youngho Seo (JNM 2005 vol 46 n 5 pp 868) standing for a VPC-45 LEHR collimator. For both projects, various parameters were tested in a 2D reduction of the problem in the transverse plane. Results: The results show a slight shift between the behaviour of the condition numbers and the Cramér-Rao bounds. For small image size (less than 30x30) the CACAO-TROLL project exhibits a lower condition number than CTHC, and higher Cramér-Rao bounds. For larger sizes, both factors increase steeply for CTHC. Finally, for a proper choice of the holes geometry, the Cramér-Rao bound is more than an order of magnitude better for the CACAO-TROLL project than for CTHC. Conclusions: This calculation confirms, at least in theory, that increasing the number of collected photons and the accuracy of the collimation can lead to better estimates in emission tomography. A good algorithm to fully benefit from this improved acquisition may remain a challenging point. It is to be expected that this calculation may stimulate such research in a near future

Method and an Apparatus for Deconvoluting a Noisy Measured Signal Obtained from a Sensor Device

The present invention relates to a method and apparatus for deconvolving a noisy measured signal obtained from a sensor device (100), said noisy measured signal (y(t)) being the sum of the convolution product ( x(t) ⊗ N(t) ) of an input signal (x(t)) of the sensor device, representative of a feature of physical quantity, by a convolution kernel (N(t)) defined by the response function of the sensor device (100) and a noise which interfere with the measure. The method is characterised in that said method comprises an estimate computation step (400) in the course of which a minimal estimate (xmin(t) ⊗ N(t) ) of the convolution product of the input signal by the convolution kernel of the sensor device is computed in order that said minimal estimate stays below the noisy measured signal (y(t)) and has at least one point in common with the noisy measured signal (y(t))., La présente invention porte sur un procédé et un appareil de déconvolution d\u27un signal mesuré bruité obtenu à partir d\u27un dispositif détecteur (100), ledit signal mesuré bruité (y(t)) étant la somme du produit de convolution ( x(t) ⊗ N(t) ) d\u27un signal d\u27entrée (x(t)) du dispositif détecteur, représentatif d\u27une caractéristique de quantité physique par un noyau de convolution (N(t)) défini par la fonction de réponse du dispositif détecteur (100), et d\u27un bruit qui perturbe la mesure. Le procédé est caractérisé en ce que ledit procédé comprend une étape de calcul d\u27estimation (400) au cours de laquelle une estimation minimale (xmin(t) ⊗ N(t) ) du produit de convolution du signal d\u27entrée par le noyau de convolution du dispositif détecteur est calculée afin que ladite estimation minimale reste inférieure au signal mesuré bruité (y(t)) et ait au moins un point en commun avec le signal mesuré bruité (y(t))