Repliement de spectre

Résumé

thumb|300px|Ce graphique démontre le repliement du spectre d'un signal sinusoïdal de fréquence f = 0,9, confondu avec un signal de fréquence f = 0,1 lors d'un échantillonnage de période T = 1,0. Le repliement de spectre (aliasing en anglais) est un phénomène qui introduit, dans un signal qui module une fréquence porteuse ou dans un signal échantillonné, des fréquences qui ne devraient pas s'y trouver, lorsque la fréquence porteuse ou la fréquence d'échantillonnage sont inférieures à deux fois la fréquence maximale contenue dans le signal. Cette distorsion se produit parce qu'un signal de fréquence f a exactement le même effet sur le signal modulé que ceux de fréquence (fréquence porteuse - fréquence f). De même, dans le cas d'un signal échantillonné, tous les signaux dont l'écart de fréquence avec la fréquence d'échantillonnage est identique se représentent par les mêmes échantillons. Lorsqu'on reconstitue le signal d'origine, il est impossible de distinguer ces composantes dont la re

Source officielle

https://fr.wikipedia.org/wiki/Repliement_de_spectre

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L'échantillonnage consiste à prélever les valeurs d'un signal à intervalles définis, généralement réguliers. Il produit une suite de valeurs discrètes nommées échantillons. Généralités L

vignette|Symbole normé du convertisseur analogique numérique Un convertisseur analogique-numérique (CAN, parfois convertisseur A/N, ou en anglais ADC pour Analog to Digital Converter ou plus simpleme

Le théorème d'échantillonnage, dit aussi théorème de Shannon ou théorème de Nyquist-Shannon, établit les conditions qui permettent l'échantillonnage d'un signal de largeur spectrale et d'amplitude lim

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Aliasing in images is often considered as a nuisance. Artificial low frequency patterns and jagged edges appear when an image is sampled at a too low frequency. However, aliasing also conveys useful information about the high frequency content of the image, which is exploited in super-resolution applications. We use a set of input images of the same scene to extract such high frequency information and create a higher resolution aliasing-free image. Typically, there is a small shift or more complex motion between the different images, such that they contain slightly different information about the scene. Super-resolution image reconstruction can be formulated as a multichannel sampling problem with unknown offsets. This results in a set of equations that are linear in the unknown signal coefficients but nonlinear in the offsets. This thesis concentrates on the computation of these offsets, as they are an essential prerequisite for an accurate high resolution reconstruction. If a part of the image spectra is free of aliasing, the planar shift and rotation parameters can be computed using only this low frequency information. In such a case, the images can be registered pairwise to a reference image. Such a method is not applicable if the images are undersampled by a factor of two or larger. A higher number of images needs to be registered jointly. Two subspace methods are discussed for such highly aliased images. The first approach is based on a Fourier description of the aliased signals as a sum of overlapping parts of the spectrum. It uses a rank condition to find the correct offsets. The second one uses a more general expansion in an arbitrary Hilbert space to compute the signal offsets. The sampled signal is represented as a linear combination of sampled basis functions. The offsets are computed by projecting the signal onto varying subspaces. Under certain conditions, in particular for bandlimited signals, the nonlinear super-resolution equations can be written as a set of polynomial equations. Using Buchberger's algorithm, the solution can then be computed as a Gröbner basis for the corresponding polynomial ideal. After a description of a standard algorithm, adaptations are made for the use with noisy measurements. The techniques presented in this thesis are tested in simulations and practical experiments. The experiments are performed on sets of real images taken with a digital camera. The results show the validity of the algorithms: registration parameters are computed with subpixel precision, and aliasing is accurately removed from the resulting high resolution image. This thesis is produced according to the concepts of reproducible research. All the results and examples used in this thesis are reproducible using the code and data available online.

EPFL2006

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Asymmetric Metal-Dielectric Metacylinders and Their Potential Applications From Engineering Scattering Patterns to Spatial Optical Signal Processing

Romain Christophe Rémy Fleury, Ali Momeni, Mahdi Safari

We propose a bianisotropic hybrid metal-dielectric structure comprising dielectric and metallic cylindrical wedges wherein the composite metacylinder enables advanced control of electric, magnetic, and magnetoelectric resonances. We establish a theoretical framework in which the electromagnetic response of this meta-atom is described through the electric and magnetic multipole moments. The complete dynamic polarizability tensor, expressed in a compact form, is derived as a function of the Mie-scattering coefficients. Further, the constitutive parameters—determined analytically—illustrate the tunability of the structure’s frequency and strength of resonances in light of its high degree of geometric freedom. Flexibility in the design makes the proposed metacylinder a viable candidate for various applications in the microscopic (single meta-atom) and macroscopic (metasurface) levels. We show that the highly versatile bianisotropic meta-atom is amenable to being designed for the desired electromagnetic response, such as electric dipole-free and zero or near-zero (backward and forward) scattering at the microscopic level. In addition, we show that the azimuthal asymmetry gives rise to normal polarizability components, which are vital elements in synthesizing asymmetric optical transfer function at the macroscopic level. We conduct a precise inspection, from the microscopic to the macroscopic level, of the metasurface synthesis for emphasizing on the role of normal polarizability components for spatial optical signal processing. It is shown that this simple two-dimensional asymmetric meta-atom can perform first-order differentiation and edge detection at normal illumination. The results reported herein contribute toward improving the physical understanding of wave interaction with artificial materials composed of asymmetric elongated metal-dielectric inclusions and open the potential of its application in spatial signal and image processing.

2021

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Speed has always been a critical consideration in magnetic resonance imaging (MRI), promising dramatic gains in imaging speed, a reduction in motion and susceptibility artifacts, and ultimately increased throughput for clinical studies. This thesis presents several new approaches to increase temporal resolution of a three dimensional (3D) echo planar imaging (EPI) sequence and explores the benefits of using high temporal resolution for both event-related brain activation and resting state networks fMRI studies. In the first approach, a new k-space traversal strategy for segmented 3D EPI is introduced which we termed as 3D reduced excitation EPI (3D RE-EPI). In this approach, two partitions are encoded per radio frequency (RF) excitation, effectively reducing the number of excitations used to acquire a 3D EPI dataset by a factor of two. With this strategy, whole-brain images with a nominal voxel size of 2mmisotropic could be acquired with a temporal resolution under half a second, using traditional parallel imaging acceleration upto 4x in the partition-encoding direction and using novel data acquisition speed-up of 2x. With 8x data acquisition speed-up in the partition-encoding direction, 3D RE-EPI produced acceptable image quality without introduction of noticeable additional artifacts. Due to increased temporal signal-to-noise ratio (tSNR) and better characterization of physiological fluctuations, the new strategy allowed detection of more resting state networks compared to standardmulti-slice two dimensional (2D) EPI and segmented 3D EPI. The approach above suffered from geometry factor (g-factor related) signal-to-noise ratio (SNR) losses, while using very high parallel imaging acceleration factor. To achieve substantial increase in the temporal resolution whilemaintaining low g-factors when high parallel imaging acceleration factors are used, the combination of segmented 3D EPI using 2D controlled aliasing with generalized autocalibrating partially parallel acquisitions (GRAPPA) was implemented in the next approach termed 3D-EPI-CAIPI. FunctionalMRI data with whole-brain coverage, a voxel size of 2 mm isotropic and a temporal resolution of 371 ms was acquired with acceptable image quality. 10-fold parallel imaging accelerated 3D-EPI-CAIPI data was shown to lower g-factor losses by as much as 10% with respect to segmented 3D EPI at 7 Tesla. Additional resting state networks were detected using 3D-EPI-CAIPI compared to a comparable standard 2D EPI acquisition. This was attributed to the improved statistics due to an increased number of volumes acquired in a given duration and because of the improved characterization of physiological signal fluctuations. Functional MRI with 400 ms temporal resolution allowed the detection of time-to-peak variations in temporal, occipital and frontal cortices haemodynamic responses due to multisensory facilitation of the order of ~200 ms. To conclude, this thesis introduces several novel techniques to increase temporal resolution of fMRI. Besides building theoretical foundations for these techniques, their applications for studying human brain functional connectivity, event-related brain activation and the ability to characterize physiological signal fluctuations at ultra-high field strength (7 Tesla) are evaluated.

EPFL2014

Chargement

Asymmetric Metal-Dielectric Metacylinders and Their Potential Applications From Engineering Scattering Patterns to Spatial Optical Signal Processing

Romain Christophe Rémy Fleury, Ali Momeni, Mahdi Safari

2021

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EPFL2014