Image reconstruction algorithm for single-photon-emission computed tomography with uniform attenuation

Inouye, T.; Kose, Katsumi; Hasegawa, Akira

doi:10.1088/0031-9155/34/3/003

Cited by 80 publications

(51 citation statements)

References 7 publications

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“…Various reconstruction methods were developed under this assumption, see for example [5][6][7][8][9][10][11][12][13][14][15][16][17]. A nice theory unifying most of these methods in a common framework was presented in [18,19].…”

Section: Geometrically (E µ O P)(φ S) Just Like (A a P)(φ S)mentioning

confidence: 99%

Image reconstruction from truncated data in single-photon emission computed tomography with uniform attenuation

et al. 2007

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We present a mathematical analysis of the problem of image reconstruction from truncated data in two-dimensional (2D) single-photon emission computed tomography (SPECT). Recent results in classical tomography have shown that accurate reconstruction of some parts of the object is possible in the presence of truncation. We have investigated how these results extend to 2D parallel-beam SPECT, assuming that the attenuation map is known and constant in a convex region that includes all activity sources. Our main result is a proof that, just like in classical tomography accurate SPECT reconstruction at a given location x ∈ , does not require the data on all lines passing through ; some amount of truncation can be tolerated. Experimental reconstruction results based on computer-simulated data are given in support of the theory.

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Section: Geometrically (E µ O P)(φ S) Just Like (A a P)(φ S)mentioning

confidence: 99%

Image reconstruction from truncated data in single-photon emission computed tomography with uniform attenuation

et al. 2007

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“…This approach leads to a relationship between the circular harmonic decomposition of the Fourier transform of f and the circular harmonic decomposition of the Fourier transform of T µ f . An alternative method of inversion based on the circular harmonic decomposition of the Fourier transform of f and T µ f was derived by Tretiak et al [3] and Inouye et al [8] using two different approaches. In [5], Metz et.…”

Section: Introductionmentioning

confidence: 99%

“…suggested a weighted linear summation of positive and negative frequencies of the circular harmonic decomposition of the Fourier transform of projections for reconstruction. It was shown that different choices of weight functions provide reconstruction formulas proposed in [7,3,8].…”

Section: Introductionmentioning

confidence: 99%

A new exact inversion method for exponential Radon transform using the harmonic analysis of the Euclidean motion group

Yarman¹,

Yazıcı²

2007

Inverse Problems &Amp; Imaging

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Abstract. This paper presents a new method for the exponential Radon transform inversion based on the harmonic analysis of the Euclidean motion group of the plane. The proposed inversion method is based on the observation that the exponential Radon transform can be modified to obtain a new transform, defined as the modified exponential Radon transform, that can be expressed as a convolution on the Euclidean motion group. The convolution representation of the modified exponential Radon transform is block diagonalized in the Euclidean motion group Fourier domain. Further analysis of the block diagonal representation provides a class of relationships between the spherical harmonic decompositions of the Fourier transforms of the function and its exponential Radon transform. These relationships and the block diagonalization lead to three new reconstruction algorithms. The proposed algorithms are implemented using the fast implementation of the Euclidean motion group Fourier transform and their performances are demonstrated in numerical simulations. Our study shows that convolution representation and harmonic analysis over groups motivates novel solutions for the inversion of the exponential Radon transform.

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“…The simple collimator routinely used in SPECT scans is the parallel-hole collimator. The image reconstruction algorithms with uniform attenuation correction for this parallel-beam geometry are well known (Bellini et al 1979, Tretiak and Metz 1980, Gullberg and Budinger 1981, Clough and Barrett 1983, Inouye et al 1989, Metz and Pan 1995 and an analytical image reconstruction algorithm with non-uniform attenuation correction for parallel-beam geometry was presented in Novikov (2002).…”

Section: Introductionmentioning

confidence: 99%

An analytical algorithm for skew-slit collimator SPECT with uniform attenuation correction

2006

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To replace the conventional pinhole (normal cone-beam) collimator, a novel skew-slit collimator was previously proposed and a Novikov-type algorithm developed to reconstruct images using the skew-slit geometry. The goal of this paper is to develop a reconstruction algorithm that has better noise control than the Novikov-type algorithm. The new algorithm is able to compensate for uniform attenuation, and computer simulation results show that reconstructed images are less noisy.

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Image reconstruction algorithm for single-photon-emission computed tomography with uniform attenuation

Cited by 80 publications

References 7 publications

Image reconstruction from truncated data in single-photon emission computed tomography with uniform attenuation

Image reconstruction from truncated data in single-photon emission computed tomography with uniform attenuation

A new exact inversion method for exponential Radon transform using the harmonic analysis of the Euclidean motion group

An analytical algorithm for skew-slit collimator SPECT with uniform attenuation correction

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