To give a physical interpretation of such a quantized Minkowski space we construct the Hilbert space representation and find that the relevant time and space operators have a discrete spectrum. It serves as a good example of quantizing Minkowski space. In this lecture I discuss the algebraic structure of a q-deformed four-vector space. Experimental results indicate that the high-resolution datasets reconstructed using the proposed method exhibit greater quality, both quantitatively and qualitatively, than those obtained using conventional methods, such as interpolation using spherical radial basis functions (SRBFs). We then encode these relationships in a graph and use it to regularize an inverse problem associated with recovering a high q - space resolution dataset from its low-resolution counterpart.
Qspace quality testing Patch#
More specifically, we establish the relationships between signal measurements in x - q space using a patch matching mechanism that caters to unstructured data. In this paper, we show how non-local self-similar information in the x - q space of diffusion MRI data can be harnessed for q - space upsampling. Particularly in clinical settings, scan time is limited and only a sparse coverage of the vast q - space is possible. Q-Space Upsampling Using x- q Space Regularization.Ĭhen, Geng Dong, Bin Zhang, Yong Shen, Dinggang Yap, Pew-ThianĪcquisition time in diffusion MRI increases with the number of diffusion-weighted images that need to be acquired. â–º Power laws provide a comprehensive and quantitative description of scattering â–º Similar power laws appear in scattering from aggregates and irregular particles. â–º The power laws uncover patterns involving length scales and functionalities. Highlights: â–º Angular scattering functions for spheres show power laws versus the wave vector q. The benefits of Q-space analysis are that it provides a simple and comprehensive description of scattering in terms of power laws with quantifiable exponents it can be used to differentiate scattering by particles of different shapes, and it yields a physical understanding of scattering based on diffraction. It applies to scattering from dielectric spheres of arbitrary size and refractive index (Mie scattering), fractal aggregates and irregularly shaped particles such as dusts. It also systematically describes the magnitude of the scattering and the interference ripple structure that often underlies the power laws. The analysis uncovers power law descriptions of the scattering with length scale dependent crossovers between the power laws. This analysis involves plotting the scattered intensity versus the scattering wave vector q=(4Ï€/λ)sin(θ/2) on a double log plot. This review describes and demonstrates the Q-space analysis of light scattering by particles. International Nuclear Information System (INIS) Q-space analysis of scattering by particles: A review The overall features found for the ice crystals are similar to features in scattering from same sized spheres. The effects of significant absorption on the scattering profile are also studied. The analysis uncovers features common to all the shapes: a forward scattering regime with intensity quantitatively related to the Rayleigh scattering by the particle and the internal coupling parameter, followed by a Guinier regime dependent upon the particle size, a complex power law regime with incipient two dimensional diffraction effects, and, in some cases, an enhanced backscattering regime. Q-space analysis is applied to extensive simulations of the single-scattering properties of ice crystals with various habits/shapes over a range of sizes. Ding, Jiachen Chakrabarti, Amitabha Yang, Ping Sorensen, Christopher M. Q-space analysis of light scattering by ice crystals
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