A formulation in concordance with sampling theorem for band-limited images reconstruction from projections
type: Item
instance of: scholarly article
title: A formulation in concordance with sampling theorem for band-limited images reconstruction from projections
zbMATH Open document ID: 0858.94004
DOI: 10.1007/BF02106105
author: Patrick Lise
author: Eric Zerbib
author: Manel Foguet
author: Joël Le Roux
published in: Multidimensional Systems and Signal Processing
publication date: 1996-06-06T00:00:00Z
review text: Image reconstruction from sampled projections has been extensively used in the field of medical imaging. Imaging means visualization, not to make visible and reconstruct what is already visible. Influenced by the classical backprojection technique of computerized tomography (CT) and coherent optical image processing, magnetic resonance tomography (MRI), for instance, has applied this method before the symplectic Fourier transform method in the super-encoding projective space became available for routine clinical examinations [\textit{W. Schempp}, Magnetic resonance imaging: Mathematical foundations and applications. J. Wiley \& Sons, New York (to appear)]. The paper under review contributes to the method of semantic filtering by presenting a filter formulation of the imaging reconstruction problem. The optimal reconstruction from a finite number of samples is performed in two steps: (i) one-dimensional convolution/backprojection, and (ii) solution of a convolution equation involving a large positive definite Toeplitz-block-Toeplitz matrix \(A\) via a conjugate gradient method. Due to the circulant block structure of \(A\), the implementation is efficiently performed by parallel processors for the multidimensional fast Fourier transform (FFT).
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 68U10
Mathematics Subject Classification ID: 93C57
Mathematics Subject Classification ID: 93C62
Mathematics Subject Classification ID: 92C55
zbMATH DE Number: 871413
zbMATH Keywords: backprojection
zbMATH Keywords: semantic filtering
zbMATH Keywords: imaging reconstruction
zbMATH Keywords: convolution equation
zbMATH Keywords: multidimensional fast Fourier transform
reviewed by: Walter Schempp
MaRDI profile type: Publication
cites work: Toeplitz Equations by Conjugate Gradients with Circulant Preconditioner
cites work: Q3786383
cites work: Q4194375
cites work: Q3325518
cites work: A computer implementation of a bayesian analysis of image reconstruction
cites work: Q3999407
cites work: Q3996223
cites work: Q5567096
cites work: A local update strategy for iterative reconstruction from projections
full work available at URL: https://doi.org/10.1007/bf02106105
OpenAlex ID: W2076899912
description: scientific article; zbMATH DE number 871413