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We propose a new method to reconstruct data acquired in a local tomographysetup. This method uses an initial reconstruction and refines it by correctingthe low frequency artifacts known as the cupping effect. A basis of Gaussianfunctions is used to correct the initial reconstruction. The coefficients ofthis basis are iteratively optimized under the constraint of a known subregion.Using a coarse basis reduces the degrees of freedom of the problem whileactually correcting the cupping effect. Simulations show that the known regionconstraint yields an unbiased reconstruction, in accordance to uniquenesstheorems stated in local tomography.

A practical local tomography reconstruction algorithm based on known subregion