Add to ORKGIn this paper we study a class of broken ray transforms (BRT), which can be implemented with flat and/or curved detectors. In the case of two detectors we obtain an inversion formula, which involves a second-order derivative of the data and integration along characteristics. In the case of three detectors, we obtain an inversion formula, which is purely local and involves only the first-order derivatives of the data. Hence the formula solves the interior problem. Neither the object nor the source and detectors require to be rotated in order to obtain a complete data set. We also prove a theorem, which describes the range of the BRT in the case of three detectors. Finally, the results of numerical experiments are presented
We reduce the broken ray transform on some Riemannian manifolds (with corners) to the geodesic ray t...
Abstract. We reduce the broken ray transform on some Rie-mannian manifolds (with corners) to the geo...
Let X and X∗ denote a restricted ray transform along curves and a corresponding backprojection opera...
In this paper we study a class of broken ray transforms (BRT), which can be implemented with flat an...
Broken Ray transform (BRT) arises when one considers a narrow x-ray beam propagating through medium ...
The broken ray transform (BRT) is an integral of a function along a union of two rays with a common ...
Graduation date: 2016Single-scattering tomography describes a model of photon transfer through a obj...
Abstract. We study the broken ray transform on n-dimensional Eu-clidean domains where the reflecting...
The classical problem of X-ray tomography asks whether one can reconstruct a function from its integ...
Abstract. We study a particular broken ray transform on the Euclidean unit square and establish inje...
We define the star transform as a generalization of the broken ray transform introduced by us in pre...
Abstract. We reduce boundary determination of an unknown function and its normal derivatives from th...
The windowed ray transform is the generalization of the "Analytic-Signal Transform" which ...
We define the star transform as a generalization of the broken ray transform for image reconstructio...
The sensitivity of ray and beam theoretical seismograms to changes in velocity models and curved int...
We reduce the broken ray transform on some Riemannian manifolds (with corners) to the geodesic ray t...
Abstract. We reduce the broken ray transform on some Rie-mannian manifolds (with corners) to the geo...
Let X and X∗ denote a restricted ray transform along curves and a corresponding backprojection opera...
In this paper we study a class of broken ray transforms (BRT), which can be implemented with flat an...
Broken Ray transform (BRT) arises when one considers a narrow x-ray beam propagating through medium ...
The broken ray transform (BRT) is an integral of a function along a union of two rays with a common ...
Graduation date: 2016Single-scattering tomography describes a model of photon transfer through a obj...
Abstract. We study the broken ray transform on n-dimensional Eu-clidean domains where the reflecting...
The classical problem of X-ray tomography asks whether one can reconstruct a function from its integ...
Abstract. We study a particular broken ray transform on the Euclidean unit square and establish inje...
We define the star transform as a generalization of the broken ray transform introduced by us in pre...
Abstract. We reduce boundary determination of an unknown function and its normal derivatives from th...
The windowed ray transform is the generalization of the "Analytic-Signal Transform" which ...
We define the star transform as a generalization of the broken ray transform for image reconstructio...
The sensitivity of ray and beam theoretical seismograms to changes in velocity models and curved int...
We reduce the broken ray transform on some Riemannian manifolds (with corners) to the geodesic ray t...
Abstract. We reduce the broken ray transform on some Rie-mannian manifolds (with corners) to the geo...
Let X and X∗ denote a restricted ray transform along curves and a corresponding backprojection opera...