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Effective technique for solving the reconstruction problems in tomography using the 2D Hartley transform

机译:使用2D Hartley变换解决层析成像重建问题的有效技术

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Abstract: One of major aspects of a problem of restoration (reconstruction) of the internal structure of various objects and other information about their properties considers the reception of the information on distribution of some physical characteristic from their experimentally obtained spectrum of integral projective data received by various methods (emissive, transmissive - by a physical principle; acoustical, optical, laser, radiological - by the type of used radiation, etc.). The given branch of investigation is known as a reconstructive tomography. The majority of methods for restoration of the images from their integral projections in reconstructive tomography are based on a fundamental generalized projective theorem with use of Fourier transform. The main difficulty in practical processing of the complex Fourier-like transforms (Laplace, Mellin transforms, etc.) despite of their convenience in analytical calculations and algebra becomes the insufficient speed of data processing for reception of the dynamic distribution image of an investigated physical characteristic. In the present work we examined the possibilities of application in various areas of a reconstructive tomography of the real-domain integral transform offered by Ralph Vinton Lyon Hartley in 1942 for study of a spectra of electrosignals, lastly named in his honor by Hartley transform. Some examples of an effective applications and basic properties of Hartley transform are presented in works of Ronald N. Bracewell. From middle of the 1960-the years there were offered various fast algorithms of calculation of discrete Fourier transform (FFT) which characterized by some advantage in speed of data processing in comparison with discrete FT, but however owing to its complexity and asymmetry FFT concedes in speed of processing to fast algorithms based on Hartley transform. !15
机译:摘要:各种物体的内部结构恢复(重构)问题的主要方面之一,以及有关其特性的其他信息,是考虑从由实验获得的,由他们接收的积分投影数据频谱中获得的一些物理特征分布信息的接收。各种方法(发射,透射-根据物理原理;声学,光学,激光,放射-通过使用的辐射类型等)。研究的给定分支称为重建层析成像。在重建层析成像中,从其整体投影恢复图像的大多数方法都是基于基本的广义投影定理,并使用傅立叶变换。尽管复杂的傅里叶式变换(拉普拉斯变换,梅林变换等)在分析计算和代数上很方便,但在实际处理中的主要困难在于数据处理速度不足,无法接收所研究的物理特征的动态分布图像。在当前的工作中,我们研究了由拉尔夫·文顿·里昂·哈特利(Ralph Vinton Lyon Hartley)在1942年提供的实域积分变换的重建层析成像在各个领域中应用的可能性,以研究电子信号频谱,最后以哈特利变换的名字命名。 Ronald N. Bracewell的作品介绍了Hartley变换的有效应用和基本属性的一些示例。从1960年代中期开始,提供了各种快速的离散傅里叶变换(FFT)计算算法,其特征在于与离散FT相比,其数据处理速度具有一定优势,但是由于其复杂性和不对称性,FFT承认了这一点。处理速度提高到基于Hartley变换的快速算法。 !15

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