Novikov’s inversion formula for the attenuated Radon transform—A new approach
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چکیده
منابع مشابه
Novikov ’ s Inversion Formula for the Attenuated Radon Transform — A New Approach
We study the inversion of weighted Radon transforms in two dimensions,Rρf (L) = ∫ L f (·) ρ(L, ·) ds, where the weight function ρ(L, x), L a line and x ∈ L, has a special form. It was an important breakthrough when R.G. Novikov recently gave an explicit formula for the inverse of Rρ when ρ has the form (1.2); in this case Rρ is called the attenuated Radon transform. Here we prove similar result...
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A convolution backprojection algorithm was derived by Tretiak and Metz to reconstruct two-dimensional (2-D) transaxial slices from uniformly attenuated parallel-beam projections. Using transformation of coordinates, this algorithm can be modified to obtain a formulation useful to reconstruct uniformly attenuated fan-beam projections. Unlike that for parallel-beam projections, this formulation d...
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هدف اصلی از این تحقیق به دست آوردن و مقایسه حق بیمه باورمندی در مدل های شمارشی گزارش نشده برای داده های طولی می باشد. در این تحقیق حق بیمه های پبش گویی بر اساس توابع ضرر مربع خطا و نمایی محاسبه شده و با هم مقایسه می شود. تمایل به گرفتن پاداش و جایزه یکی از دلایل مهم برای گزارش ندادن تصادفات می باشد و افراد برای استفاده از تخفیف اغلب از گزارش تصادفات با هزینه پائین خودداری می کنند، در این تحقیق ...
15 صفحه اولLocal Inversion of the Radon
We use the theory of the continuous wavelet transform to derive inversion formulas for the Radon transform on L 1 \L 2 (R d). These inversion formulas turn out to be local in even dimensions in the following sense. In order to recover a function f from its Radon transform in a ball of radius R > 0 about a point x to within error , we can nd () > 0 such that this can be accomplished by knowing t...
متن کاملAn Analytical Inversion of the Nonuniformly Attenuated Radon Transform With Variable Focal-Length Fan-Beam Collimators
Single photon emission computed tomography (SPECT) is based on the measurement of radiation emitted by a radiotracer injected into the patient. Because of photoelectric absorption and Compton scatter, the gamma photons are attenuated inside the body before arriving at the detector. A quantitative reconstruction must consider the attenuation, which is usually nonuniform. Novikov has derived an e...
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ژورنال
عنوان ژورنال: Journal of Geometric Analysis
سال: 2004
ISSN: 1050-6926,1559-002X
DOI: 10.1007/bf02922067