New fast algorithms of multidimensional Fourier and Radon discrete transforms
نویسندگان
چکیده
This paper describes a fast new n{D Discrete Radon Transform (DRT) and a fast exact inversion algorithm for it, without interpolating from polar to Cartesian coordinates or using the backprojection operator. New approach is based on the fast Nussbaumer's Polynomial Transform (NPT).
منابع مشابه
Fast algorithms of multidimensional discrete nonseparable -wave transforms
Fast algorithms for a wide class of non–separable n–dimensional (nD) discrete unitary K– transforms (DKT) are introduced. They need less 1D DKTs than in the case of the classical radix–2 FFT–type approach. The method utilizes a decomposition of the nDK–transform into the product of a new nD discrete Radon transform and of a set of parallel/independ 1D K–transforms. If the nD K–transform has a s...
متن کاملA Method for Validating Multidimensional Fast Fourier Transform (FFT) Algorithms,
A method is described for validating fast Fourier transforms (FFTs) based on the use of simple input fiinctions whose discrete Fourier transforms can be evaluated in closed form. Explicit analytical results are developed for one-dimensional and two-dimensional discrete Fourier transforms. The analytical results are easily generalized to higher dimensions. The results offer a means for validatin...
متن کاملFast Inversion of the Exponential Radon Transform by Using Fast Laplace Transforms
Abstract. The Fourier slice theorem used for the standard Radon transform generalizes to a Laplace counterpart when considering the exponential Radon transform. We show how to use this fact in combination with using algorithms for unequally spaced fast Laplace transforms to construct fast and accurate methods for computing, both the forward exponential Radon transform and the corresponding back...
متن کاملDiscrete radon transform
This paper describes the discrete Radon transform (DRT) and the exact inversion algorithm for it. Similar to the discrete Fourier transform (DFT), the DRT is defined for periodic vector-sequences and studied as a transform in its own right. Casting the forward transform as a matrix-vector multiplication, the key observation is that the matrix-although very large-has a block-circulant structure....
متن کاملImplementation of the Radon Transform Using Non-equispaced Discrete Fourier Transforms
This report discusses the implementation of the Radon transform in the Analysts’ Detection Support System (ADSS) environment using non-equispaced Discrete Fourier Transforms (DFTs). It provides an analysis and experimental results for discretisation error and the use of matched filtering to enhance peaks in the transform. APPROVED FOR PUBLIC RELEASE
متن کاملذخیره 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 1999