Inversion Formulas in Truncated Data Ray-Tomography

نویسنده

  • Matias Courdurier
چکیده

In Ray-Tomography the goal is to recover a function in higher dimensions from knowledge of integrals of the function along lines. For example, in the Euclidean setting we let f ∈ C∞ 0 (R), and for each straight line L in R, we define the Ray-Transform of f along L as

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Large-scale Inversion of Magnetic Data Using Golub-Kahan Bidiagonalization with Truncated Generalized Cross Validation for Regularization Parameter Estimation

In this paper a fast method for large-scale sparse inversion of magnetic data is considered. The L1-norm stabilizer is used to generate models with sharp and distinct interfaces. To deal with the non-linearity introduced by the L1-norm, a model-space iteratively reweighted least squares algorithm is used. The original model matrix is factorized using the Golub-Kahan bidiagonalization that proje...

متن کامل

Velocity Inversion with an Iterative Normal Incidence Point (NIP) Wave Tomography with Model-Based Common Diffraction Surface (CDS) Stack

Normal Incidence Point (NIP) wave tomography inversion has been recently developed to generate a velocity model using Common Reflection Surface (CRS) attributes, which is called the kinematic wavefield attribute. In this paper, we propose to use the model based Common Diffraction Surface (CDS) stack method attributes instead of data driven Common Reflection Surface attributes as an input data p...

متن کامل

Statistical inversion for medical x-ray tomography with few radiographs: I. General theory.

In x-ray tomography, the structure of a three-dimensional body is reconstructed from a collection of projection images of the body. Medical CT imaging does this using an extensive set of projections from all around the body. However, in many practical imaging situations only a small number of truncated projections are available from a limited angle of view. Three-dimensional imaging using such ...

متن کامل

Tomographic resolution without singular value decomposition

An explicit procedure is presented for computing both model and data resolution matrices within a Paige-Saunders LSQR algorithm for iterative inversion in seismic tomography. These methods are designed to avoid the need for an additional singular value decomposition of the ray-path matrix. The techniques discussed are completely general since they are based on the multiplicity of equivalent exa...

متن کامل

Gel'fand-Graev's reconstruction formula in the 3D real space.

PURPOSE Gel'fand and Graev performed classical work on the inversion of integral transforms in different spaces [Gel'fand and Graev, Funct. Anal. Appl. 25(1) 1-5 (1991)]. This paper discusses their key results for further research and development. METHODS The Gel'fand-Graev inversion formula reveals a fundamental relationship between projection data and the Hilbert transform of an image to be...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010