The mathematical principles of tomographic imaging using detected (unscattered) X- or gamma-rays are based on the two-dimensional Radon transform and many of its variants. In this paper, we show that two new generalizations, called conical Radon transforms, are related to three-dimensional imaging processes based on detected Compton scattered radiation. The first class of conical Radon transfor...

Let R, denote the Radon transform on R” that integrates a function over hyperplanes in given smooth positive measures p depending on the hyperplane. We characterize the measures ,u for which R, is rotation invariant. We prove rotation invariant transforms are all one-to-one and hence invertible on the domain of square integrable functions of compact support, Li(R”). We prove the hole theorem: i...

The radon transform arise in natural way, if X-rays traverses a body, like in a computer tomograph. Thus, to nd out the internal structur of a body in computer tomography corresponds to reconstructions a function from their radon transform. This report deals with a parallized numerical reconstruction algorithm, in particular the ltered backprojection. The ltered backprojection uses high dimensi...

In this study a time-frequency method based on Wigner-Ville Distribution (WVD) is used for detection and parameter estimation of Frequency Modulated Continuous Wave (FM-CW) Radar Signal. The proposed method uses the Pseudo-Wigner-Ville Distribution (PWVD) as a time-frequency detection technique and Radon Transform to identify the parameter of the modulation. The Wigner-Ville Radon Transform (WV...

Alignment of images of printed text is needed as a preprocessing for the purpose of OCR. The test for an image alignment is easily developed by summation of pixels horizontally. However, the angel of orientation of the text is not easily estimated. In this paper, a method for estimation of this angle is presented. The Radon transform is used. The spaces between lines are considered as thick lin...

results the mean radon concentration in the drinking water of aliabad katoul is 2.90 ± 0.57 bq/l. conclusions the radon concentration in aliabad katoul is below the limit for hazardous levels, but some precautions will make conditions even safer for the local populace. objectives the aim of this study is to evaluate the concentration of soluble radon in the drinking water of the city of aliabad...

In this paper a novel filtered back-projection algorithm for inversion of a discretized Radon transform is presented. It makes use of invariance properties possessed by both the Radon transform its dual. By switching to log-polar coordinates, both operators can be expressed in a displacement invariant manner. Explicit expressions for the corresponding transfer functions are calculated. Furtherm...