A Prospective Study on Algorithms Adapted to the Spatial Frequency in Tomography

Israël-Jost, Vincent; Choquet, Philippe; Constantinesco, A.

doi:10.1155/ijbi/2006/34043

Cited by 2 publications

(2 citation statements)

References 9 publications

(11 reference statements)

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“…After we recall the construction and formulation of the FA-SART algorithm in Section 2, the aim of this paper is to give an account of how the frequency adapted (FA) SART algorithm proposed in [1] solves this problem, by using a backprojection matrix that is not directly A T , the transpose of the projection matrix A, but a matrix A ρ T , where A ρ only keeps the coefficients in the columns of A (i.e. the PSFs) that are greater than ρ times the maximum of the column.…”

Section: Introductionmentioning

confidence: 99%

Accelerating the Tomographic Reconstruction With a Frequency Adapted Algorithm

Israel-Just

Choquet

Constantinesco

2007

2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro

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In several imaging modalities involving tomographic reconstruction, the model of projection should incorporate a response of the detector that takes the limitation in spatial resolution into account. Unlike analytic methods, iterative methods easily deal with changes in the model and thus perform some kind of deconvolution together with tomographic reconstruction. However, since these methods imply a slow reconstruction of the details, it is usually worth computing many iterations to reach important high frequencies.In this paper, we analyse how the frequency adapted (FA) SART algorithm proposed in [1] solves this problem, by use of an incomplete backprojection matrix with narrower cones of backprojection. This algorithm demonstrates a significant acceleration for the reconstruction of high frequencies and also seems to give better results than those obtained with a large number of SART iterations for highly detailed structures.

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Section: Introductionmentioning

confidence: 99%

Accelerating the Tomographic Reconstruction With a Frequency Adapted Algorithm

Israel-Just

Choquet

Constantinesco

2007

2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro

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“…Here they compare the use of quadraticand median-based roughness penalties [11], and they find that the two approaches produce similar resolution-variance tradeoffs to each other, which suggests that the particular choice of penalty may be less important than the decision to use a penalty at all. Israel-Jost et al propose build frequencyadapted (FA) algorithms based on a condition of incomplete backprojection [12], leading to an FA-simultaneous algebraic reconstruction technique (FA-SART) algorithm. The results obtained with the FA-SART algorithm on a highly detailed phantom demonstrate a very fast convergence compared to the original SART algorithm.…”

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confidence: 99%

Development of Computed Tomography Algorithms

Yu¹,

Rivière²,

Tang³

2006

International Journal of Biomedical Imaging

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Over the past several years, computed tomography (CT) methods have advanced significantly, yielding novel analytic and iterative solutions applicable to medical CT and micro-CT. The resulting algorithms promise to improve spatial, contrast, or temporal resolution as well as to suppress artifacts and reduce radiation dose. Significant attention has been devoted to optimizing computational performance and to balancing conflicting requirements. Both theoretically oriented and application-specific issues are also being addressed. As a snapshot of the dynamically changing field of CT, this special issue includes 10 high-quality original papers.Because spiral cone-beam CT can be used for rapid volumetric imaging with high longitudinal resolution, the development of exact and efficient algorithms for image reconstruction from spiral cone-beam projection data has been a subject of active research in recent years. Katsevich's filtered backprojection (FBP) formula represents a significant breakthrough in this field [1]. In this special issue, Yang et al. propose a parallel implementation of Katsevich's FBP formula [2] by the one-beam cover method, in which the backprojection procedure is independently driven by cone-beam projections. Based on Katsevich's work, generalized backprojection filtration (BPF) and FBP algorithms are developed to reconstruct images from data collected along more flexible scanning trajectories [3]. Using these recently developed algorithms, Yu et al. propose a local region reconstruction scheme [4]. The principal idea is to deliver a normal radiation dose to a local region of interest (ROI) that may contain a lesion while applying a very low radiation dose to the structures outside the ROI. Both the FBP and BPF algorithms can produce excellent results with a minimal increment to the dose needed for purely local CT.Despite important advancements in the development of exact cone-beam reconstruction, approximate algorithms remain practically and theoretically valuable. Feldkamp et al.heuristically adapted the fan-beam FBP algorithm for approximate cone-beam reconstruction in the case of a circular scanning locus [5]. This formulation, called the FDK algorithm, is more desirable in many cases than exact conebeam reconstruction approaches in terms of several aspects of image quality and computational implementation. Since then, many efforts have been made to extend the FDK algorithm to other scanning configurations, leading to a series of FDK-like algorithms. In this special issue, Yan et al. propose an approximate FDK-like reconstruction algorithm for tilted-gantry CT imaging [6]. The method improves the image reconstruction by filtering the projection data along a direction that is determined by CT parameters and the tiltedgantry angle. Based on the idea that there is less redundancy for the projection data away from the central scanning plane, Yang and Ning develop a heuristic cone-beam geometric dependent weighting scheme [7], which leads to a new FDKlike half-scan algorithm. For correcting cone-be...

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A Prospective Study on Algorithms Adapted to the Spatial Frequency in Tomography

Cited by 2 publications

References 9 publications

Accelerating the Tomographic Reconstruction With a Frequency Adapted Algorithm

Accelerating the Tomographic Reconstruction With a Frequency Adapted Algorithm

Development of Computed Tomography Algorithms

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