I think it is good that researchers are beginning to develop various
approaches to the problem of high speed 3D reconstruction from 2D projection
data. In particular it is nice that algorithms for asymmetric data are being
developed since they have a very broad application area.

The paper has some fundamental flaws if it is supposed to compete with work
in the field of 3D reconstruction in general; certainly the audience
interested in this kind of software development is also found in the area
of medical applications, from PET SPECT and NMR to the more similar CT
procedures. The work presented here is of the type non-iterative
3D reconstruction algorithm, which has been the most used procedure in
biological research, but which nowadays are rather far from what is achieved
with methods used in the medical application areas by iterative methods of
various kinds (including maximum likelihood techniques). Even in a virus
icosahedral reconstruction application a maximum entropy algorithm has been
developed and shown in practice to perform well. These methods are not so
well parallelized yet, but the current paper doesn't even discuss these
methods and/or if the presented algorithm with increased speed will
be a survivor in the longer perspective in spite of the lower qualitative
and quantitive performance (compared to iterative procedures).

A second flaw is the lack of discussion of prior art: it is well known that
a parallel implementation of the filtered backprojection algorithm, used for
asymmetric objects, is up and running since some years at the supercomputer
center in San Diego. At least a minimal discussion must be present were the
work is compared with the papers from collaborators around Dr. Mark
Ellismans group at NCMIR in San Diego.

A technical remark is that the discrepancies between the icosahedrally
averaged center of the non-icosahedral region in the slices shown in figs
5&6 are not discussed in detail, but nontheless very interesting (the
symmetry seen here is a generated artefact) because it means that the
two reconstruction methods really gives different results, not only a
speed-up factor for the presented algorithm. The interpolation algorithm
used to place the 2D DFT into the 3D space have not been evaluated or
more analytically commented upon.

The paper has its strength in the analysis of the number of operations
used at different steps in the algorithm, but unless the critique above is
met, the paper is more like a technical report and shouldn't be published in
a scientific journal.