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74
The Weighted Distance Scheme: A Globally Optimizing Projection Ordering Method for ART
, 1997
"... The order in which the projections are applied in the Algebraic Reconstruction Technique (ART) has a great effect on speed of convergence, accuracy and the amount of noiselike artifacts in the reconstructed image. In this paper, a new projection ordering scheme for ART is presented: the Weighted ..."
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The order in which the projections are applied in the Algebraic Reconstruction Technique (ART) has a great effect on speed of convergence, accuracy and the amount of noiselike artifacts in the reconstructed image. In this paper, a new projection ordering scheme for ART is presented: the Weighted Distance Scheme (WDS). It heuristically optimizes the angular distance of a newly selected projection with respect to an extended sequence of previously applied projections. This sequence of influential projections may incorporate the complete set of all previously applied projections or any limited time interval subset thereof. The selection algorithm results in uniform sampling of the projection access space, minimizing correlation in the projection sequence. This produces more accurate images with less noiselike artifacts than previously suggested projection ordering schemes.
Transfer function restoration in 3D electron microscopy via . . .
, 2004
"... Threedimensional electron microscopy (3DEM) is a powerful tool for visualizing complex biological systems. As with any other imaging device, the electron microscope introduces a transfer function (called in this field the contrast transfer function, CTF) into the image acquisition process that mod ..."
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Cited by 7 (3 self)
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Threedimensional electron microscopy (3DEM) is a powerful tool for visualizing complex biological systems. As with any other imaging device, the electron microscope introduces a transfer function (called in this field the contrast transfer function, CTF) into the image acquisition process that modulates the various frequencies of the signal. Thus, the 3D reconstructions performed with these CTFaffected projections are also affected by an implicit 3D transfer function. For highresolution electron microscopy, the effect of the CTF is quite dramatic and limits severely the achievable resolution. In this work we make use of the iterative data refinement (IDR) technique to ameliorate the effect of the CTF. It is demonstrated that the approach can be successfully applied to noisy data.
Iterative methods for image reconstruction
 in ISBI Tutorial. 2006, http://www.eecs.umich.edu/ fessler/papers/files/talk/08/isbinotes.pdf
"... ..."
Data inversion for overresolved spectral imaging in astronomy
 Selec. Topics in Signal Proc
, 2008
"... Abstract—We present an original method for reconstructing a 3D object having two spatial dimensions and one spectral dimension from data provided by the infrared slit spectrograph on board the Spitzer Space Telescope. During acquisition, the light flux is deformed by a complex process comprising ..."
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Abstract—We present an original method for reconstructing a 3D object having two spatial dimensions and one spectral dimension from data provided by the infrared slit spectrograph on board the Spitzer Space Telescope. During acquisition, the light flux is deformed by a complex process comprising four main elements (the telescope aperture, the slit, the diffraction grating, and optical distortion) before it reaches the 2D sensor. The originality of this work lies in the physical modeling, in integral form, of this process of data formation in continuous variables. The inversion is also approached with continuous variables in a semiparametric format decomposing the object into a family of Gaussian functions. The estimate is built in a deterministic regularization framework as the minimizer of a quadratic criterion. These specificities give our method the power to overresolve. Its performance is illustrated using real and simulated data. We also present a study of the resolution showing a 1.5fold improvement relative to conventional methods. Index Terms—Bayesian estimation, interpolation, inverse problems, irregular sampling, IRS Spitzer, overresolved imaging, spectral imaging. I.
Image Reconstruction Techniques for PET
"... this report lies on the reconstruction of PET images. Therefore we start, in x2, with a statistical description of the PET measurement process. The algorithms used to reconstruct these images depend on the medical scanner and on the noise in the data. They are subdivided into three major groups. Ana ..."
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Cited by 4 (2 self)
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this report lies on the reconstruction of PET images. Therefore we start, in x2, with a statistical description of the PET measurement process. The algorithms used to reconstruct these images depend on the medical scanner and on the noise in the data. They are subdivided into three major groups. Analytical algorithms [2] are based on a continuous description of the image and the data. They formulate a continuous solution which is discretized before being implemented as a computer program. These algorithms assume that the measurement space has been uniformly sampled by the scanner and that the noise in the data can be neglected. Sometimes the available data do not satisfy these constraints, or sometimes the measurement space has been sampled too sparsely to obtain an adequate discretisation of the continuous solution. In these cases one needs to use iterative algorithms [3]. Iterative algorithms start from a discretized description of the image as a linear combination of a limited set of basis functions. They try to find the most appropriate weights according to the available data. Iterative algorithms are further subdivided into two groups, depending on whether or not the reconstruction is based on a statistical description of the measurement process. In x3 we are interested in the discretisation of images for the use of iterative reconstruction algorithms. We define constraints on the basis functions in the spatial and in the frequency domain. We find that for PET and CT spatially limited and for MRI frequency limited basis functions result in the most efficient implementations. For PET and CT we also find that the basis functions should decay as fast as possible in the frequency domain, and that for MRI the basis functions should decay as fast as possible in the spati...
Volumetric Constraints in 3D Tomography Applied to Electron Microscopy
, 2002
"... D Electron Microscopy aims at the reconstruction of density volumes corresponding to the mass distribution of macromolecules imaged with an electron microscope. There are many factors limiting the resolution achievable when this technique is applied to biomolecules: microscope transfer function, mol ..."
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D Electron Microscopy aims at the reconstruction of density volumes corresponding to the mass distribution of macromolecules imaged with an electron microscope. There are many factors limiting the resolution achievable when this technique is applied to biomolecules: microscope transfer function, molecule flexibility, lack of projections from certain directions, unknown angular distribution, image noise, etc. In this communication we propose the use of aprioriinformation such as particle symmetry, occupied volume, known surface, density nonnegativity and similarity to a known volume in order to improve the quality of the reconstruction. When a series expansion of the reconstructed volume is done, all these constraints are expressed as a set of equations which the expansion coefficients must satisfy. In this work, this equation set is specified and the effect of each one on the reconstruction of a realistic phantom is explored.
3D Reconstruction of 2D Crystals in Real Space
"... Abstract—A new algorithm for threedimensional reconstruction of twodimensional crystals from projections is presented, and its applicability to biological macromolecules imaged using transmission electron microscopy (TEM) is investigated. Its main departures from the traditional approach is that i ..."
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Abstract—A new algorithm for threedimensional reconstruction of twodimensional crystals from projections is presented, and its applicability to biological macromolecules imaged using transmission electron microscopy (TEM) is investigated. Its main departures from the traditional approach is that it works in real space, rather than in Fourier space, and it is iterative. This has the advantage of making it convenient to introduce additional constraints (such as the support of the function to be reconstructed, which may be known from alternative measurements) and has the potential of more accurately modeling the TEM image formation process. Phantom experiments indicate the superiority of the new approach even without the introduction of constraints in addition to the projection data. Index Terms—3D reconstruction, crystals, electron microscopy, image reconstruction, projections. I.
Approximation with the radial basis functions of Lewitt
 SHEFFIELD UNIV (UNITED KINGDOM) DEPT OF APPLIED MATHEMATICS, 2001. tel00680100, version 1  17 Mar 2012
"... R. M. Lewitt has introduced a family of compactly supported radial basis functions which are particularly useful in discretising for inversion illposed problems involving line integrals. We consider some practical considerations in their use and implementation, compare square and triangular grids o ..."
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R. M. Lewitt has introduced a family of compactly supported radial basis functions which are particularly useful in discretising for inversion illposed problems involving line integrals. We consider some practical considerations in their use and implementation, compare square and triangular grids of the functions in two dimensions, and describe some particularly favourable choices of the dening parameters. 1
A new representation and projection model for tomography, based on separable Bsplines
, 2012
"... Abstract—Data modelization in tomography is a key point for iterative reconstruction. The design of the projector, i.e. the numerical model of projection, is mostly influenced by the representation of the object of interest, decomposed on a discrete basis of functions. Standard projector models are ..."
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Abstract—Data modelization in tomography is a key point for iterative reconstruction. The design of the projector, i.e. the numerical model of projection, is mostly influenced by the representation of the object of interest, decomposed on a discrete basis of functions. Standard projector models are voxel or ray driven; more advanced models such as distance driven, use simple staircase voxels, giving rise to modelization errors due to their anisotropic behaviour. Moreover approximations made at the projection step amplify these errors. Though a more accurate projection could reduce approximation errors, characteristic functions of staircase voxels constitute a too coarse basis for representing a continuous function. As a result, pure modelization errors still hold. Spherically symmetric volume elements (blobs) have already been studied to eradicate such errors, but at the cost of increased