2018
DOI: 10.1002/mma.5426
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On inversion and Sobolev estimate results about the weighted Radon transform

Abstract: In this paper, we derive an inversion of the weighted Radon transform by Fourier transform, Riesz potential, and integral transform. We extend results of Rigaud and Lakhal to the n‐dimensional Euclidean space. Furthermore, we obtain some properties of the weighted Radon transform. Finally, we develop some estimate results of the weighted Radon transform under Sobolev space.

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Cited by 2 publications
(1 citation statement)
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“…where, the long window length M = 5N and the short window length N = k/ i (t), k is the weight, and i (t) is the instantaneous dominant frequency of the i-th moment after the generalized S transform of the three-axis vibration signal [10], which refers to the frequency point with the highest energy among the wide spectrum corresponding to each moment after the generalized S transform. With the optimal matching impedance, in the near field of the blasting point, the moment the first break arrives the instantaneous dominant frequencies of the three axes are consistent [11].…”
Section: ) Extract the Arrival Time Information Of The First Breakmentioning
confidence: 99%
“…where, the long window length M = 5N and the short window length N = k/ i (t), k is the weight, and i (t) is the instantaneous dominant frequency of the i-th moment after the generalized S transform of the three-axis vibration signal [10], which refers to the frequency point with the highest energy among the wide spectrum corresponding to each moment after the generalized S transform. With the optimal matching impedance, in the near field of the blasting point, the moment the first break arrives the instantaneous dominant frequencies of the three axes are consistent [11].…”
Section: ) Extract the Arrival Time Information Of The First Breakmentioning
confidence: 99%