Bayesian approach to limited-angle reconstruction in computed tomography

Hanson, Kenneth M.; Wecksung, G.W.

doi:10.1364/josa.73.001501

Cited by 122 publications

(32 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In using these techniques, if the approximate shape of an object to be reconstructed is known beforehand, Bayesian methods of reconstruction can incorporate the known structural characteristics and produce substantially improved reconstructions from limited data. However, if the assumptions about the structural characteristics of the object differ only slightly, the prior that results from such assumptions can lead to very poor reconstructions [Hanson and Wecksung, 1983]. In addition, if the mean of the desired reconstruction varies from that of the prior, the fixed mean of the prior will prevent these structural characteristics to be reflected in the reconstruction.…”

Section: Flexible Prior Models Theorymentioning

confidence: 99%

Flexible Prior Models: Three‐dimensional ionospheric tomography

Cornely

2003

Radio Science

View full text Add to dashboard Cite

[1] A three-dimensional ionospheric reconstruction system is presented that models ionospheric dynamics and accounts for well-known limitations in the available data by using geometrically transformed prior models based on available models, such as the Parameterized Ionospheric Model (PIM) or the International Reference Ionosphere (IRI), to produce density solutions consistent with available Total Electron Content (TEC) measurement data. It is known that current state of the art prior density models, such as PIM or IRI, can only simulate a statistical mean ionosphere. As a result, sudden variations in ionospheric electron density will not be represented in these models. This paper focuses on a three-dimensional ionospheric density reconstruction system that uses a set of geometrical transformations to produce Flexible Prior Models (FPM). The Flexible Prior Model process allows means to include flexibility in a prior model in the form of geometrical variations that are not well represented in current state-of-the-art ionospheric prior density models. The updated priors are used as initial solution models for a set of (A, B) Multiplicative Algebraic Reconstruction Technique (ABMART) algorithms, that can easily incorporate additional information and provide a spatially constrained density solution, consistent with the available data and our current knowledge of ionospheric dynamics. The ultimate goal is to create a three-dimensional adaptive ionospheric electron density reconstruction system that would make it possible to generate real-time ionospheric maps supported by available TEC data. Such maps would be of significant utility in predicting and correcting the impact of electron density gradients and irregularities on radio waves.

show abstract

Section: Flexible Prior Models Theorymentioning

confidence: 99%

Flexible Prior Models: Three‐dimensional ionospheric tomography

Cornely

2003

Radio Science

View full text Add to dashboard Cite

show abstract

“…Whatever prior isused,itsstrength affects theamount thereconstruction isoffset from thetrueimage (Hanson,1990b;Myers and Hanson,1990).ltisimportant tounderstandthecharacteristics ofsolutions obtainedregardless oftheprior chosen.Itisrecognized thatthepriorprovides . the regula.rization essential to solving ill-posed problem's (Nashed, I981;Titterington, 1985), which arise because H possesses a null:space (Hanson and Wecksung, 1983;Hanson, 1987).…”

Section: Posterior Probabilitymentioning

confidence: 99%

Making Binary Decisions Based on the Posterior Probability Distribution Associated with Tomographic Reconstructions

Hanson

1992

Maximum Entropy and Bayesian Methods

Self Cite

View full text Add to dashboard Cite

This report was prepared as an account of work sponsored by an agency of the United States Government, Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or .!'i:. process disclosed, or represents that its use would not infringe privately owned rights. Refer' ,',:, ence herein to any specific commercial product, process, or service by trade name, trademark, ' _, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom-_" , ,_ mendation, or favoring by the United States Government or any agency thereof, The views /_i[_[/ [) i: ,,_,,. and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. ' /_._],_ By acceptance of this article, the p_,'bli_i_errec,_gnlzesthat the U.S. Government retains a nonexclusive, royalty.fre_ license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes.

show abstract

“…Bayesian reconstruction algorithms are also used and they are known to substantially improve the accuracy of the reconstruction obtained from limited data, if the object under study does not differ very much in size, shape or position from the assumed model. Difficulties arise when the spatial coordinate of the prior model is held fixed relative to the spatial coordinate system of the reconstruction [Hanson and Wecksung, 1983]. A technique that has been used to represent variations in an image being restored for a general class of distortion has been reported by Hanson [1992].…”

Section: Introductionmentioning

confidence: 99%

Three‐dimensional ionospheric tomography via band‐limited constrained iterative cross‐entropy minimization

Cornely

Kuklinski

2005

Radio Science

View full text Add to dashboard Cite

[1] The problem of reconstructing ionospheric electron density from ground-based receiver to satellite total electron content (TEC) measurements is formulated as an underdetermined discrete linear inverse problem. If receivers and satellite orbit are coplanar, then a single two-dimensional (2-D) imaging plane can be used as a geometrical model. In most cases, receiver locations are determined by convenience and availability of sites, and thus a 3-D imaging volume is required in order to capture the part of the electron density solution that is associated with gaps between receiver stations within a chain. It is well understood that spurious features, or ''wings,'' associated with these gaps can be produced in tomographic image reconstructions where ray path coverage from individual stations is lost or minimal. In this paper, a 3-D reconstruction system that takes advantage of a multiple-chain data acquisition geometry and provides a solution consistent with available TEC data everywhere within a receiver chain is presented. The reconstruction system exploits the fact that gaps, created by longitudinally unaligned receivers within a chain, can be captured as additional planes of constant longitudes within the 3-D imaging volume. With parameterized ionospheric model (PIM)-generated data as a nonnegative prior estimate of the electron density, the reconstruction algorithm uses constraints based on prior knowledge of the 3-D spatial Fourier transform of the prior electron density as a smoothing mechanism in the tomographic reconstruction process. Consequent to the underlined Fourier transform formulation, a unique solution is produced at locations that contributed to the measured TEC data, and a solution is interpolated within the remainder of the imaging volume. The band-limited BISMART algorithm has been evaluated using a multiple-receiver chain TEC data acquisition system, under known ionospheric conditions. The algorithm satisfactorily reconstructs density solutions, consistent with small-scale enhancements, irregularities, and troughs in the auroral ionosphere, from the available TEC data. The quality of the density reconstructions, coupled with the computational efficiency of this algorithm, indicates the potential utility of this technique for real-time three-and four-dimensional ionospheric tomography.Citation: Cornely, P.-R. J., and W. S. Kuklinski (2005), Three-dimensional ionospheric tomography via band-limited constrained iterative cross-entropy minimization, Radio Sci., 40, RS5S90,

show abstract

Bayesian approach to limited-angle reconstruction in computed tomography

Cited by 122 publications

References 26 publications

Flexible Prior Models: Three‐dimensional ionospheric tomography

Flexible Prior Models: Three‐dimensional ionospheric tomography

Making Binary Decisions Based on the Posterior Probability Distribution Associated with Tomographic Reconstructions

Three‐dimensional ionospheric tomography via band‐limited constrained iterative cross‐entropy minimization

Contact Info

Product

Resources

About