Abstract
Linear programming is used in discrete tomography to solve the relaxed problem of reconstructing a function f with values in the interval [0,1]. The linear program minimizes the uniform norm Ax - 6∞ or the 1-norm ∞∞Ax - b∞∞1 of the error on the projections. We can add to this objective function a linear penalty function p(x) for trying to obtain smooth solutions. The same approach can be used in computerized tomography. The question is if it can provide better images than the classical methods of computerized tomography. The aim of this chapter is to provide a tentative answer. We present a preliminary study on real acquisitions from a phantom and provide reconstructions from a few projections, with qualities similar to the traditional methods.
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Gerard, Y., Feschet, F. (2007). Application of a Discrete Tomography Approach to Computerized Tomography. In: Herman, G.T., Kuba, A. (eds) Advances in Discrete Tomography and Its Applications. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4543-4_16
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DOI: https://doi.org/10.1007/978-0-8176-4543-4_16
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