MENT: A maximum entropy algorithm for reconstructing a source from projection data

Minerbo, Gerald

doi:10.1016/0146-664x(79)90034-0

Cited by 198 publications

(66 citation statements)

References 8 publications

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“…These techniques belong to transform methods except of the maximum entropy algorithm [81], applied to 1D Compton profiles [82,83]. This algorithm, which belongs to series expansion methods (see [9] and references therein) and is known as an algebraic technique, was proposed for image reconstruction starting from 1979 [84]. This is summarized in Table, where the following abbreviations are used: CM -Cormack method (with orthogonal Chebyshev polynomials) [1,12]; DFT -direct Fourier transform [58,74]; FBP -filtered back projection [3] using Eq.…”

Section: Discussionmentioning

confidence: 99%

“…This is summarized in Table, where the following abbreviations are used: CM -Cormack method (with orthogonal Chebyshev polynomials) [1,12]; DFT -direct Fourier transform [58,74]; FBP -filtered back projection [3] using Eq. (13); F-B -Fourier Bessel [52,53]; HP -Hermite polynomials [39]; JPJacobi polynomials [33]; ME -maximum entropy [81,84]; MFBP -modified FBP [50]; MM -Mijnarends' method [2]; PM -Pecora method [75].…”

Section: Discussionmentioning

confidence: 99%

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Transform Methods of Computerized Tomography in Studying Electronic Structure and Fermi Surfaces of Solids

Kontrym‐Sznajd

2008

Acta Phys. Pol. A

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We present mathematical methods of computerized tomography, based on an analytical inversion of the Radon transform either in terms of the Fourier transforms or series of orthogonal polynomials. These techniques, so-called transform methods, are discussed for reconstructing electronic densities from both line and plane projections measured either in the two-dimensional angular correlations of annihilation radiation or in onedimensional angular correlations of annihilation radiation and the Compton scattering experiments. This paper is devoted to review all of the papers where such techniques were applied for studying electronic momentum densities and the Fermi surface of solids by angular correlations of annihilation radiation and the Compton scattering experiments.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Transform Methods of Computerized Tomography in Studying Electronic Structure and Fermi Surfaces of Solids

Kontrym‐Sznajd

2008

Acta Phys. Pol. A

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“…The iterative methods are computationally slower but appear superior to the first group in treating systems with few projections (Ref. 13 and references therein). In the present paper algebraic reconstruction technique (ART) algorithms are used.1 4 These algorithms iteratively adjust an estimation of 6(x,y) by comparing projections calculated from the estimated 6(x,y) with the corresponding experimental projections until conver-…”

Section: Tomographic Reconstruction Methodsmentioning

confidence: 99%

Kerr effect tomography for nonintrusive spatially resolved measurements of asymmetric electric field distributions

Hertz

1986

Appl. Opt.

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“…Minerbo proposed the MENT algorithm [10] and subsequently various authors have proposed different improvements. For example, Dusassoy and Abdou [3] have introduced the extended-MENT that can process a priori information about the image to be reconstructed.…”

Section: Extended-ment Algorithmmentioning

confidence: 99%

Reconstruction-Diffusion: An Improved Maximum Entropy Reconstruction Algorithm Based on the Robust Anisotropic Diffusion

Bustos

Kim

2005

XVIII Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI'05)

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Maximum entropy (MENT) is a well-known image reconstruction algorithm. If only a small amount of acquisition data is available, this algorithm converges to a noisy and blurry image. We propose an improvement to this algorithm that consists on applying alternately the MENT reconstruction and the robust anisotropic diffusion (RAD). We have tested this idea for the reconstruction from full-angle parallel acquisition data, but the idea can be applied to any data acquisition scenario. The new technique has yielded surprisingly clear images with sharp edges even using extremely small amount of projection data.

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MENT: A maximum entropy algorithm for reconstructing a source from projection data

Cited by 198 publications

References 8 publications

Transform Methods of Computerized Tomography in Studying Electronic Structure and Fermi Surfaces of Solids

Transform Methods of Computerized Tomography in Studying Electronic Structure and Fermi Surfaces of Solids

Kerr effect tomography for nonintrusive spatially resolved measurements of asymmetric electric field distributions

Reconstruction-Diffusion: An Improved Maximum Entropy Reconstruction Algorithm Based on the Robust Anisotropic Diffusion

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