Abstract: Tomographic reconstruction in two dimensions isconcerned with the reconstruction of a positive,bounded function f(x, y) and its compact domain ofsupport approximately icron from noisy and possiblysparse samples of its radon- transform projections,g(t, approximately icron@). If the pair (f,approximately icron@) is referred to as an object, afinitely parameterized object is one in which both f(x,y) and approximately icron are determined uniquely by afinite number of parameters. For instance, a binaryN-sided polygonal object in the plane is uniquelyspecified by exactly 2N parameters which may be thevertices, normals to the sides, etc. In this work westudy the optimal reconstruction of finitelyparameterized objects from noisy projections. Inspecific, we focus our study on the optimalreconstruction of binary polygonal objects from noisyprojections. We show that when the projections arecorrupted by Gaussian white noise, the optimal maximumlikelihood (ML) solution to the reconstruction problemis the solution to a nonlinear optimization problem.This optimization problem is formulated over aparameter space which is a finite dimensional Euclideanspace. We also demonstrate that in general, the momentsof an object can be estimated directly from theprojection data and that using these estimated moments,a good initial guess for the numerical solution to thenonlinear optimization problem may be constructed.Finally, we study the performance of the proposedalgorithms from both statistical and computationalviewpoints. !11
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