2,875 research outputs found
Fast Mojette Transform for Discrete Tomography
A new algorithm for reconstructing a two dimensional object from a set of one
dimensional projected views is presented that is both computationally exact and
experimentally practical. The algorithm has a computational complexity of O(n
log2 n) with n = N^2 for an NxN image, is robust in the presence of noise and
produces no artefacts in the reconstruction process, as is the case with
conventional tomographic methods. The reconstruction process is approximation
free because the object is assumed to be discrete and utilizes fully discrete
Radon transforms. Noise in the projection data can be suppressed further by
introducing redundancy in the reconstruction. The number of projections
required for exact reconstruction and the response to noise can be controlled
without comprising the digital nature of the algorithm. The digital projections
are those of the Mojette Transform, a form of discrete linogram. A simple
analytical mapping is developed that compacts these projections exactly into
symmetric periodic slices within the Discrete Fourier Transform. A new digital
angle set is constructed that allows the periodic slices to completely fill all
of the objects Discrete Fourier space. Techniques are proposed to acquire these
digital projections experimentally to enable fast and robust two dimensional
reconstructions.Comment: 22 pages, 13 figures, Submitted to Elsevier Signal Processin
Fast OPED algorithm for reconstruction of images from Radon data
A fast implementation of the OPED algorithm, a reconstruction algorithm for
Radon data introduced recently, is proposed and tested. The new implementation
uses FFT for discrete sine transform and an interpolation step. The convergence
of the fast implementation is proved under the condition that the function is
mildly smooth. The numerical test shows that the accuracy of the OPED algorithm
changes little when the fast implementation is used.Comment: 13 page
Fast hyperbolic Radon transform represented as convolutions in log-polar coordinates
The hyperbolic Radon transform is a commonly used tool in seismic processing,
for instance in seismic velocity analysis, data interpolation and for multiple
removal. A direct implementation by summation of traces with different moveouts
is computationally expensive for large data sets. In this paper we present a
new method for fast computation of the hyperbolic Radon transforms. It is based
on using a log-polar sampling with which the main computational parts reduce to
computing convolutions. This allows for fast implementations by means of FFT.
In addition to the FFT operations, interpolation procedures are required for
switching between coordinates in the time-offset; Radon; and log-polar domains.
Graphical Processor Units (GPUs) are suitable to use as a computational
platform for this purpose, due to the hardware supported interpolation routines
as well as optimized routines for FFT. Performance tests show large speed-ups
of the proposed algorithm. Hence, it is suitable to use in iterative methods,
and we provide examples for data interpolation and multiple removal using this
approach.Comment: 21 pages, 10 figures, 2 table
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