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- W2019498616 abstract "This paper deals with the reconstruction and the redundancy of the two-dimensional attenuated Radon transform (AtRT). When full measurements are available, we characterize the information on a spatially and angularly dependent function that can be retrieved from its AtRT. In particular we consider the reconstruction of isotropic scalar and vector-valued source terms. Next we consider the reconstruction of a spatially dependent function from its AtRT with half angular measurements. We show that the inversion is feasible provided that the spatial variations of the absorption coefficient are not too large. The reconstruction is based on the decomposition of the reconstruction operator in the Novikov formula into three components bounded in the L2 sense. The first component involves the measured partial data. The second component is a skew-symmetric operator. The third component is a symmetric and compact contribution whose spectral radius, which depends on the attenuation, needs to be smaller than unity in our reconstruction. In a paper (Bal and Moireau, Preprint) on the numerical implementation of the reconstruction, we show that the reconstruction algorithm can be successfully applied in situations of practical interest." @default.
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- W2019498616 date "2004-01-16" @default.
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- W2019498616 title "On the attenuated Radon transform with full and partial measurements" @default.
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- W2019498616 doi "https://doi.org/10.1088/0266-5611/20/2/006" @default.
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