Maximum Likelihood Reconstruction for Emission Tomography
A more accurate general mathematical model 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 is given.
OPTIMAL PATHS FOR A CAR THAT GOES BOTH FORWARDS AND BACKWARDS
The path taken by a car with a given minimum turning radius has a lower bound on its radius of curvature at each point, but the path has cusps if the car shifts into or out of reverse gear. What is…
The Fourier reconstruction of a head section
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.
On Skew Brownian Motion
- J. Harrison, L. Shepp
- Mathematics
- 1 April 1981
We consider the stochastic equation X(t) = W(t) + βlX0(t), where W is a standard Wiener process and lX0(⋅) is the local time at zero of the unknown process X. There is a unique solution X (and it is…
A Statistical Model for Positron Emission Tomography
- Y. Vardi, L. Shepp, L. Kaufman
- Mathematics
- 1 March 1985
Abstract Positron emission tomography (PET)—still in its research stages—is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body…
The Russian Option: Reduced Regret
- L. Shepp, A. Shiryaev
- Economics
- 1 August 1993
We propose a new put option where the option buyer receives the maximum price (discounted) that the option has ever traded at during the time period (which may be indefinitely long) between the…
A Mathematical Theory of Network Interference and Its Applications
- M. Win, P.C. Pinto, L. Shepp
- Computer ScienceProceedings of the IEEE
- 1 March 2009
A mathematical framework for the characterization of network interference in wireless systems in which the interferers are scattered according to a spatial Poisson process and are operating asynchronously in a wireless environment subject to path loss, shadowing, and multipath fading is introduced.
Ordered cycle lengths in a random permutation
- L. Shepp, S. P. Lloyd
- Mathematics
- 1 February 1966
1. Introduction. Problems involving a random permutation are often concerned with the cycle structure of the permutation. Let tY.n be the n! permutation operators on n numbered places, and let a(X) =…
Radon-Nikodym Derivatives of Gaussian Measures
- L. Shepp
- Mathematics
- 1 April 1966
We give simple necessary and sufficient conditions on the mean and covariance for a Gaussian measure to be equivalent to Wiener measure. This was formerly an unsolved problem [26]. An unsolved…
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