Image reconstruction from finite numbers of projections

Smith, PR; Peters, T. M.; Bates, R. H. T.

doi:10.1088/0305-4470/6/3/011

Cited by 141 publications

(32 citation statements)

References 20 publications

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“…The core of this approach is to add constraints to the unknowns so that the matrix can be solved. Various algorithms have been investigated in limited-view X-ray and CT imaging (12)(13)(14)(15)(16)(17)(18). These studies show that general constraints on characteristics including total variance, signal uniformity, and object shapes are able to reduce the ambiguity of the reconstruction.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Three‐dimensional reconstruction of limited‐view projections for contrast‐enhanced magnetic resonance angiography at high temporal and spatial resolution

Huang

Gurr²,

Wright

2005

Magnetic Resonance in Med

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The feasibility of reconstructing three-dimensional (3D) MRI data sets from limited-view projections is investigated in phantom and in vivo animal studies to improve the temporal resolution of magnetic resonance angiography without sacrificing spatial resolution. Thirty-two pairs of orthogonal biplane projections are acquired in an interleaved manner during the first pass of a contrast agent. The full data set is reconstructed as a priori 3D information. Each pair of projections is then reconstructed into an individual 3D data set based on a correlation analysis with the a priori data set. In this way, time-resolved 3D data sets at 1-to 2-s time intervals are reconstructed with submillimeter spatial resolution. Three-dimensional (3D) contrast-enhanced magnetic resonance angiography (MRA) has been widely applied as a minimally invasive vascular imaging modality (1). To avoid venous enhancement and to improve arterial signalto-noise ratio (SNR) of the 3D data set, elliptical centricordered (EC) sequences are normally used to acquire central regions of k-space at the peak arterial enhancement (2). This requires accurate timing of the contrast arrival at the region of interest and also a good estimate of the contrast distribution time through the region on a patient-by-patient basis to optimize the acquisition parameters such as the injection rate, repetition time (TR), and data matrix size (3). Recessed EC sequences (4) were developed to minimize artifacts associated with timing errors and successfully improved the robustness of contrast-enhanced MRA in clinical applications. However, in some particular situations, such as among patients with arteriovenous fistula or arteriovenous malformations, the blood flow pattern may be significantly altered by irregular pathways and the time for artery-vein contrast passage may be shortened to only a few seconds (5). In such circumstances, venous contamination cannot be avoided even with an accurate timing of the contrast arrival.Time-resolved MRA has been developed for the applications where temporal resolution is of critical importance. Techniques such as time-resolved imaging of contrast kinetics (TRICKS) and projection-reconstruction TRICKS (6 -8) are able to produce 3D data sets at a high temporal rate (2-4 s/3D set) by undersampling data and using view-sharing reconstructions. Therefore, difficulties associated with contrast timing are avoided, and pathologic information can potentially be observed. However, these techniques are not without limitations. Due to the view-sharing (or sliding window) reconstructions, temporal information is smoothed. Therefore, rapid signal changes are not expected to be captured well. Furthermore, the undersampling of high-resolution data both spatially and temporally introduces concerns about the accuracy of the dynamic signals in small vessels.Alternatively, high temporal resolution can be achieved by trading off the spatial resolution in the through-plane dimension (9). This works well clinically when the signal overlapping in the throu...

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Section: Discussionmentioning

confidence: 99%

“…It has been shown in X-ray imaging that 3D data can be reconstructed from a limited number of projections (n Ͻ 10) without significant artifacts if the data are sufficiently sparse (12,13). However, assumptions about signal uniformity and/or structure connectivity are required as constraints to resolve the ambiguity problems of the reconstruction.…”

mentioning

confidence: 99%

Three‐dimensional reconstruction of limited‐view projections for contrast‐enhanced magnetic resonance angiography at high temporal and spatial resolution

Huang

Gurr²,

Wright

2005

Magnetic Resonance in Med

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“…Using the formalism of Bracewell and Thompson (14), Lauzon and Rutt (15) have shown that the polar PSF is given by the spin integration of $(r), where $(r) is the 1 D IFT of the discrete (as opposed to continuous) ramp filter, which is the weighting function of Eq. [6]. Thus, (r) are oscillatory and asymmetrical in the radial direction, with their peak amplitude occurring near (j/Akr).…”

Section: Aliasingmentioning

confidence: 95%

“…Also, these artifacts may depend on the reconstruction algorithm used. For uniform k-space polar sampling, i.e., equally spaced radial and azimuthal samples, the images may be reconstructed by using either the gridding algorithm (1)(2)(3)(4) or the convolution backprojection algorithm (5)(6)(7).…”

Section: Introductionmentioning

confidence: 99%

Polar sampling in k‐space: Reconstruction effects

Lauzon

Rutt

1998

Magnetic Resonance in Med

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Magnetic resonance images are most commonly computed by taking the inverse Fourier transform of the k-space data. This transformation can potentially create artifacts in the image, depending on the reconstruction algorithm used. For equally spaced radial and azimuthal k-space polar sampling, both gridding and convolution backprojection are applicable. However, these algorithms potentially can yield different resolution, signal-to-noise ratio, and aliasing characteristics in the reconstructed image. Here, these effects are analyzed and their tradeoffs are discussed. It is shown that, provided the modulation transfer function and the signal-to-noise ratio are considered together, these algorithms perform similarly. In contrast, their aliasing behavior is different, since their respective point spread functions (PSF) differ. In gridding, the PSF is composed of the mainlobe and ringlobes that lead to aliasing. Conversely, there are no ringlobes in the convolution backprojection PSF, thus radial aliasing effects are minimized. Also, a hybrid gridding and convolution backprojection reconstruction is presented for radially nonequidistant k-space polar sampling.

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“…An inverse Fourier transform requires a continuous function and so radial interpolation is required to fill the gaps in Fourier space [37]; the quality of the reconstruction is greatly affected by the type of interpolation method used [45]. Although elegant, Fourier reconstruction methods have the disadvantage of being computationally intensive and difficult to implement for electron tomography.…”

Section: The Central Slice Theorem and Fourier Space Reconstructionmentioning

confidence: 99%

Tomography Using the Transmission Electron Microscope

Midgley

Handbook of Microscopy for Nanotechnology

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Image reconstruction from finite numbers of projections

Cited by 141 publications

References 20 publications

Three‐dimensional reconstruction of limited‐view projections for contrast‐enhanced magnetic resonance angiography at high temporal and spatial resolution

Three‐dimensional reconstruction of limited‐view projections for contrast‐enhanced magnetic resonance angiography at high temporal and spatial resolution

Polar sampling in k‐space: Reconstruction effects

Tomography Using the Transmission Electron Microscope

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