A three-dimensional (3D) reconstruction of the cytoskeleton and a clathrin-coated pit in mammalian cells has been achieved from a focal-series of images recorded in an aberration-corrected scanning transmission electron microscope (STEM). The specimen was a metallic replica of the biological structure comprising Pt nanoparticles 2–3 nm in diameter, with a high stability under electron beam radiation. The 3D dataset was processed by an automated deconvolution procedure. The lateral resolution was 1.1 nm, set by pixel size. Particles differing by only 10 nm in vertical position were identified as separate objects with greater than 20% dip in contrast between them. We refer to this value as the axial resolution of the deconvolution or reconstruction, the ability to recognize two objects, which were unresolved in the original dataset. The resolution of the reconstruction is comparable to that achieved by tilt-series transmission electron microscopy. However, the focal-series method does not require mechanical tilting and is therefore much faster. 3D STEM images were also recorded of the Golgi ribbon in conventional thin sections containing 3T3 cells with a comparable axial resolution in the deconvolved dataset.

Neural networks can be of benefit in many image compression schemes. However, any system is constrained by the performance of the paradigm on which it is based. For example, although neural networks have been shown to improve differential pulse code modulation (DPCM) image compression, the overall performance of the system is still limited by the performance of DPCM. In this work a multiresolution neural network (MRNN) filter bank has been created for use within a state-of-the-art subband-coding framework. A polyphase implementation and training algorithm is presented. A filter bank that can synthesize the signal accurately from only the reference coefficients will be well suited for low-bitrate coding where the detail coefficients are coarsely quantized. Thus, the low-pass channel of the MRNN filter bank is trained to recreate the signal accurately. The high-pass channel is trained for perfect reconstruction so that the MRNN filter bank will also be effective at high bitrates. This paper presents an analysis of the MRNN filter bank and its potential as a transform for coding. The MRNN filter bank has been used in place of a linear filter bank in the set partitioning in hierarchical trees (SPIHT) coder. The new filter bank shows advantages over the linear filter bank for coding at low bitrates, although its performance suffers at high bitrates. However, the results are encouraging and suggest that further work in this area warranted.Les réseaux de neurones peuventêtre bénéfiques en plusieurs configurations de compression d'image. Cependant, chaque système est contraint par les performances des paradigmes sur lesquels il est basé. Par exemple, même s'il aété montré que les réseaux de neurones améliorent la compression d'imageà modulation différentielle d'impulsion codée (DPCM), la performance globale du système est encore limitée par la performance du DPCM. Dans ce travail un banc de filtresà réseau de neurones multi-résolution (MRNN) aété créé pourêtre utilisé dans le cadre d'un codage sous-bande. Une implémentation multi-phase et un algorithme d'entraînement sont présentés. Un banc de filtres qui peut synthétiser le signal de manière exacte seulement a partir des coefficients de référence est très approprié pour un codageà faible taux pour lequel les coefficients de détail sont quantifiés de façon grossière. Ainsi, le canal passe-bas du banc de filtres MRNN est entraîné pour retrouver le signal de manière exacte. Le canal passe-haut est entraîné pour une reconstruction parfaite pour que le banc de filtres MRNN puisseêtre efficaceà des taux de bitsélevés. Cet article présente une analyse du banc de filtres et son potentiel comme transformation pour le codage. Le banc de filtres MRNN aété utiliséà la place d'un banc de filtres linéairesà codeur par partition des arbres hiérarchiques (SPIHT). Ce nouveau banc de filtres montre les avantages par rapport aux bancs de filtres linéaires pour les codagesà faibles taux de bits, bien que ses performances souffrentà des taux de bitsélevés. Cependant, les résultats sont prom...

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Advances in spherical aberration correction of the scanning transmission electron microscope (STEM) have led to a reduced depth of field of the STEM probe [1]. This has made it possible to form a 3D dataset by the stacking of 2D images collected at a sequence of depth intervals through the sample thickness. Each 2D image contains the signal from objects at its corresponding depth within the sample and also the out-of-focus signals from the adjacent images (above and below). A similar effect occurs in widefield fluorescence light microscopy, where the effect is corrected for by applying a deconvolution algorithm, of which several variants exist. We discuss modification of the Expectation-Maximization deconvolution procedure originally developed for light microscopy [2], and its subsequent application to 3D STEM.In widefield light microscopy the emission and detection of photons can be modeled using Poisson statistics. The Expectation-Maximization algorithm maximizes the likelihood function of the restored image from the acquired image, given a known point spread function (PSF), and assuming Poisson emission and detection statistics. The algorithm can also be modified to estimate the PSF along with the restored image (blind deconvolution) [2]. Several constraints are used to ensure the algorithm converges to a realistic solution: the restored image is forced to be non-negative; an hourglass spatial constraint based on system optics is applied to the PSF in the spatial domain; the frequency response of a diffraction-limited system is zero outside of radial and axial bandlimits and within a biconic missing cone region [3]. Thus, a bandlimit and missing cone constraint are applied to the PSF in the frequency domain. Since 3D STEM is similar to 3D widefield light microscopy [4] a similar set of constraints can be used.For 3D STEM, there are several additional factors that need to be taken into account. For the typical magnifications used to image a biological sample, the sample is under-sampled in the lateral direction since the resolution of an aberration corrected STEM is <0.1 nm, i.e., the pixel size is larger than the probe size [4]. This means that each pixel in a vertical line receives the same number of electrons until the beam becomes larger than a pixel and the effective axial resolution is reduced by the quotient of the pixel size and the probe size. The beam opening angles commonly used are only several tens of milliradians, so the missing cone region in the frequency domain and the axial extent of the PSF are both large. Furthermore, chromatic aberration and beam energy-spread will also reduce the axial resolution [5]. Finally, scan distortions will occur when changing the focus position away from the eucentric height. We examined application of the existing deconvolution algorithm taking each of these factors into account.

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