  Inversions for local helioseismology are an important and necessary step for
obtaining three-dimensional maps of various physical quantities in the solar
interior. Frequently, the full inverse problems that one would like to solve
prove intractable because of computational constraints. Due to the enormous
seismic data sets that already exist and those forthcoming, this is a problem
that needs to be addressed. To this end, we present a very efficient linear
inversion algorithm for local helioseismology. It is based on a subtractive
optimally localized averaging (SOLA) scheme in the Fourier domain, utilizing
the horizontal-translation invariance of the sensitivity kernels. In Fourier
space the problem decouples into many small problems, one for each horizontal
wave vector. This multi-channel SOLA method is demonstrated for an example
problem in time-distance helioseismology that is small enough to be solved both
in real and Fourier space. We find that both approaches are successful in
solving the inverse problem. However, the multi-channel SOLA algorithm is much
faster and can easily be parallelized.
