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L. A. Shepp

Bio: L. A. Shepp is an academic researcher from Bell Labs. The author has contributed to research in topics: Fourier transform & Search algorithm. The author has an hindex of 3, co-authored 3 publications receiving 2307 citations.

Papers
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Journal ArticleDOI
L. A. Shepp1, B. F. Logan1
TL;DR: The authors compare the Fourier algorithm and a search algorithm using a simulated phantom to speed the search algorithm by using fewer interactions leaves decreased resolution in the region just inside the skull which could mask a subdural hematoma.
Abstract: The Fourier reconstruction may be viewed simply in the spatial domain as the sum of each line integral times a weighting function of the distance from the line to the point of reconstruction A modified weighting function simultaneously achieves accuracy, simplicity, low computation time, as well as low sensitivity to noise Using a simulated phantom, the authors compare the Fourier algorithm and a search algorithm The search algorithm required 12 iterations to obtain a reconstruction of accuracy and resolution comparable to that of the Fourier reconstruction, and was more sensitive to noise To speed the search algorithm by using fewer interactions leaves decreased resolution in the region just inside the skull which could mask a subdural hematoma

2,100 citations

Journal ArticleDOI
L. A. Shepp1, B. F. Logan1
TL;DR: In this article, a modified version of a previously studied algorithm was used to reconstruct the attenuation coefficients of a simulated head section from x-ray transmission measurements, which was then used to perform absolute measurements of attenuation coefficient at points interior to the skull.
Abstract: Several algorithms have been proposed for reconstructing the variable attenuation coefficients of tissues inside the skull from x-ray transmission measurements. We show that a simulated head section is accurately reconstructed by a modification, which is both fast and simple, of a previously studied algorithm. The possibility of using the algorithm to perform absolute measurements of the attenuation coefficient at points interior to the skull is high.

270 citations

Journal ArticleDOI
D. Maydan1, L. A. Shepp1, Z. H. Cho
TL;DR: In this article, a rotating cathode filament with a fixed large stationary circular anode is used to provide a planar X-ray image of the human heart, where the detectors near the focal point are moved synchronously out of the slice plane.
Abstract: Computerized tomographic imaging of the heart has great potential diagnostic value. The difficulty is that heart motion limits the data acquisition time to below 0.1 sec., but standard X-ray sources are not of sufficient intensity or mobility. A simple solution is proposed by using a rotating cathode filament with a fixed large stationary circular anode. In this design, X-ray detectors are placed on a concentric circle interior to the anode. To allow true planar X-ray projections, the detectors near the focal spot which would block the X-ray beam are moved synchronously out of the slice plane. An alternative method is also discussed where the detectors remain stationary and the nearer blocking detectors act as a filter for the X-ray beam.

10 citations


Cited by
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Journal Article
TL;DR: In this article, a convolution-backprojection formula is deduced for direct reconstruction of a three-dimensional density function from a set of two-dimensional projections, which has useful properties, including errors that are relatively small in many practical instances and a form that leads to convenient computation.
Abstract: A convolution-backprojection formula is deduced for direct reconstruction of a three-dimensional density function from a set of two-dimensional projections. The formula is approximate but has useful properties, including errors that are relatively small in many practical instances and a form that leads to convenient computation. It reduces to the standard fan-beam formula in the plane that is perpendicular to the axis of rotation and contains the point source. The algorithm is applied to a mathematical phantom as an example of its performance.

5,356 citations

Journal ArticleDOI
TL;DR: In this article, a convolution-backprojection formula is deduced for direct reconstruction of a three-dimensional density function from a set of two-dimensional projections, which has useful properties, including errors that are relatively small in many practical instances and a form that leads to convenient computation.
Abstract: A convolution-backprojection formula is deduced for direct reconstruction of a three-dimensional density function from a set of two-dimensional projections. The formula is approximate but has useful properties, including errors that are relatively small in many practical instances and a form that leads to convenient computation. It reduces to the standard fan-beam formula in the plane that is perpendicular to the axis of rotation and contains the point source. The algorithm is applied to a mathematical phantom as an example of its performance.

5,329 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a more accurate general mathematical model for ET where an unknown emission density generates, and is to be reconstructed from, the number of counts n*(d) in each of D detector units d. Within the model, they gave an algorithm for determining an estimate? of? which maximizes the probability p(n*|?) of observing the actual detector count data n* over all possible densities?.
Abstract: Previous models for emission tomography (ET) do not distinguish the physics of ET from that of transmission tomography. We give a more accurate general mathematical model for ET where an unknown emission density ? = ?(x, y, z) generates, and is to be reconstructed from, the number of counts n*(d) in each of D detector units d. Within the model, we give an algorithm for determining an estimate ? of ? which maximizes the probability p(n*|?) of observing the actual detector count data n* over all possible densities ?. Let independent Poisson variables n(b) with unknown means ?(b), b = 1, ···, B represent the number of unobserved emissions in each of B boxes (pixels) partitioning an object containing an emitter. Suppose each emission in box b is detected in detector unit d with probability p(b, d), d = 1, ···, D with p(b, d) a one-step transition matrix, assumed known. We observe the total number n* = n*(d) of emissions in each detector unit d and want to estimate the unknown ? = ?(b), b = 1, ···, B. For each ?, the observed data n* has probability or likelihood p(n*|?). The EM algorithm of mathematical statistics starts with an initial estimate ?0 and gives the following simple iterative procedure for obtaining a new estimate ?new, from an old estimate ?old, to obtain ?k, k = 1, 2, ···, ?new(b)= ?old(b) ?Dd=1 n*(d)p(b,d)/??old(b?)p(b?,d),b=1,···B.

4,288 citations

Journal ArticleDOI

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2,428 citations

Journal ArticleDOI
TL;DR: This implementation of the Algebraic Reconstruction Technique appears to have a computational advantage over the more traditional implementation of ART and potential applications include image reconstruction in conjunction with ray tracing for ultrasound and microwave tomography.

1,539 citations