Abstract
The paper discusses tomography reconstruction of distributed physical fields by means of fiber optical measuring systems (FOMN) [1] for parallel schemes of measuring lines stacking with a small number of scanning directions. This work considers the sampling theory for a case with sampling sets which are unions of two co-sets. The case of non-equidistant sampling requires application of new approaches, namely the generalized sampling theorems with group-theory basis. An explicit reconstruction formula for extracting additional (missing or distorted) projection data values are provided, using approximating of a projection function on a non regular grid. Furthermore, standard restoration algorithms are applied to this function. Two restoration methods are proposed, UQC 1 (union of quotient classes), and UQC 2. Comparative analysis of the operating efficiency of UQC 1 and UQC 2 methods versus standard analytical FBP method for fiber-optical tomography reconstruction is reported.
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