Limited Data Problems for the Generalized Radon Transform in ${{\mathbb R}^n}$
نویسندگان
چکیده
منابع مشابه
Limited Data Problems for the Generalized Radon Transform in ℝn
We consider the generalized Radon transform (defined in terms of smooth weight functions) on hyperplanes in Rn. We analyze general filtered backprojection type reconstruction methods for limited data with filters given by general pseudodifferential operators. We provide microlocal characterizations of visible and added singularities in Rn and define modified versions of reconstruction operators...
متن کاملEndpoint Bounds for a Generalized Radon Transform
We prove that convolution with arclength measure on the curve parametrized by h(t) := (t, t, . . . , t) is a bounded operator from L(R) to L(R) for the full conjectured range of exponents, improving on a result due to M. Christ. We also obtain nearly sharp Lorentz space bounds.
متن کاملGeneralized multi-directional discrete Radon transform
This paper presents a discrete generalized multi-directional Radon transform (GMDRT) and its exact inversion algorithm. GMDRT is an extension of the classical Radon transform. It aims to project parameterized curves and geometric objects following several directions. For this purpose, we propose an algebraic formalism of the Radon Transform presenting the forward transform as a matrix-vector_ m...
متن کاملA Uniqueness result for a generalized Radon transform
There exist five families of Lipschitz curves on the unit square such that any continuous function is uniquely defined by the values of its integral (properly defined) along these curves. We present this uniqueness result as a consequence of the Kolmogorov’s superposition theorem.
متن کاملThe generalized Radon transform: Sampling, accuracy and memory considerations
The generalized Radon (or Hough) transform is a well-known tool for detecting parameterized shapes in an image. The Radon transform is a mapping between the image space and a parameter space. The coordinates of a point in the latter correspond to the parameters of a shape in the image. The amplitude at that point corresponds to the amount of evidence for that shape. In this paper we discuss thr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2016
ISSN: 0036-1410,1095-7154
DOI: 10.1137/15m1045405