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Highly penetrating cosmic ray muons constantly shower the earth at a rate of about 1 muon per cm2 per minute. We have developed a technique which exploits the multiple Coulomb scattering of these particles to perform nondestructive inspection without the use of artificial radiation. In prior work [1]-[3], we have described heuristic methods for processing muon data to create reconstructed images. In this paper, we present a maximum likelihood/expectation maximization tomographic reconstruction algorithm designed for the technique. This algorithm borrows much from techniques used in medical imaging, particularly emission tomography, but the statistics of muon scattering dictates differences. We describe the statistical model for multiple scattering, derive the reconstruction algorithm, and present simulated examples. We also propose methods to improve the robustness of the algorithm to experimental errors and events departing from the statistical model.

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A delay-vector phase space reconstruction in which the delay time satisfies a minimum redundan~ criterion is compared with a reconstruction obtained using a singular system approach, Minimum redundancy produces the better reconstruction. The reconstructions are compared using a distortion functional .~ which measures how well the location of a point in the original phase space can be determ~i~ed on the basis of its image under the reconstruction process. The superiority of the redundancy analysis over the singular system analysis ~s found to arise from the former's foundation on the notion of general independence as opposed to the latter's foundation on the notion of linear independence.