  In many applications of tomography, the acquired projections are either
limited in number or contain a significant amount of noise. In these cases,
standard reconstruction methods tend to produce artifacts that can make further
analysis difficult. Advanced regularized iterative methods, such as total
variation minimization, are often able to achieve a higher reconstruction
quality by exploiting prior knowledge about the scanned object. In practice,
however, these methods often have prohibitively long computation times or large
memory requirements. Furthermore, since they are based on minimizing a global
objective function, regularized iterative methods need to reconstruct the
entire scanned object, even when one is only interested in a (small) region of
the reconstructed image.
  In this paper, we present a method to approximate regularized iterative
reconstruction methods inside a (small) region of the scanned object. The
method only performs computations inside the region of interest, ensuring low
computational requirements. Reconstruction results for different phantom images
and types of regularization are given, showing that reconstructions of the
proposed local method are almost identical to those of the global regularized
iterative methods that are approximated, even for relatively small regions of
interest. Furthermore, we show that larger regions can be reconstructed
efficiently by reconstructing several small regions in parallel and combining
them into a single reconstruction afterwards.
