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The Attenuated X-ray Transform(衰减X-射线变换)李中凯教授,首都师范大学

报告时间:2014年11月26日(星期三), 下午15:00—16:00报告地点:北航数学与系统科学ag平台app下载主321学术交流厅报告摘要: The attenuated x-ray transform arises from the image reconstruction process in single photon emission computed tomography (SPECT). As a special case (after some simplification with constant attenuation), the theory of the exponential x-ray transform is far more complete than that of the attenuated x-ray transform with spatially varying attenuation. Few exact inversion formulas in the later case were found in bibliographies, and a remarkable form is due to Novikov published in 2002. But Novikov's formula, and other known ones, make use in some way of complex-variable method, and need some stronger assumptions on smoothness and decay speed at infinity of both the attenuation function and the density function. In this talk we shall present several inversion formulas for general attenuated x-ray transform by means of continuous wavelet transforms. The highlight is to introduce some admissible conditions connecting the attenuation function and the wavelet function; the inversion formulas does hold for density functions in $L^p$ both in norm and almost everywhere; and moreover we only need an assumption on integrability of the attenuation function and need not those on smoothness and decay speed. This is a joint work with Dr. Yufeng Yu. 欢迎大家参加!

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