[3dem] More on ART and SIRT...

[Jose-Maria Carazo]

Dear Mike,

Further to your question about ART and SIRT, let me give you my five cents,
which in essence is very simple:

Read the recent literature (besides the one that existed before I started my
own PhD Thesis), and go beyond "perception" to "proofs and experimental
facts".

In essence, the situation that Marin has described corresponds to the
perception in the 3DEM field about 35 years ago. Since then, much work has
been done on both ART and SIRT, so that we can now say that both ART-type
and SIRT-type methods converge to a regularized (and hence "stable") least
squares solution, although ART tends to be faster than SIRT.

On the point of the lack of "objective tests"..... well, just read the
relevant papers and you will judge by yourself. Indeed, these methods have
been the subject of very strict statistical tests, way beyond the common
standards in the 3DEM field. I think you will find the following readings
interesting and relevant:


Marabini, R., Rietzel, E., Schroeder, R., Herman, G.T., Carazo, J.M.:
Three-dimensional reconstruction from reduced sets of very noisy images
acquired following a single-axis tilt schema: Application of a new
three-dimensional reconstruction algorithm and objective comparison with
weighted backprojection, Journal of Structural Biology 120:363-371, 1997

and

Marabini, R., Herman, G.T., Carazo, J.-M.: 3D reconstruction in electron
microscopy using ART with smooth spherically symmetric volume elements
(blobs), Ultramicroscopy 72:53-65, 1998.

Of course, you are welcome to test them in our XMIPP system (in fact, you
may have already used them -without knowing it explicitly- while running
some of our algorithms!), and we would be happy to answer your doubts.

With best wishes..JM

PS: The following is an extract of a correspondence with Prof. Gabor Herman,
the senior author of one of the old papers Marin quoted and somebody we all
know well in the 3D reconstruction field.

- Show quoted text -

While it is true that ART and SIRT originate from the papers cited by van
Heel, there has been an enormous increase in the knowledge in the 40 years
since that time. Results published in the recent literature contradict van
Heel's message in many respect.

In particular, the words ART and SIRT are now commonly used to describe
large families of reconstruction algorithms,which may be referred to as
ART-type and SIRT-type methods. All these methods have the following in
common: they assume that the object to be reconstructed can be expressed as
a finite linear combination of some known basis functions, they translate
the process of projection taking into a system of linear equalities in the
unknown coefficients of the linear combination, and they iteratively
estimate the unknown coefficients based on the linear equalities. The
difference between ART-type and SIRT-type methods is in the nature of
thesingle iterative steps: ART-type methods use only one equality in one
iterative step, while SIRT-type methods use all the equalities in each step.

What can be achieved by these families from the point of view of the output
reconstruction is not much different; for example, there are both ART-type
and SIRT-type methods that converge to a regularized
(and hence "stable") least squares solution of the system of inequalities
(see, for example, Chapters 11 and 12 of Gabor T. Herman, Fundamentals
of Computerized Tomography: Image Reconstruction from Projections, 2nd
Edition, Springer, 2009). On the other hand, the computational performance
of ART-type methods tends to be better; to achieve a reconstructions of
similar quality, SIRT-type methods tend to need significantly more computer
time. This is demonstrated for Computerized Tomography in the
above-mentioned book: for an example in 3DEM see
Sorzano, C.O.S., Marabini, R., Boisset, N., Rietzel, E., Schroeder, R.,
Herman, G.T., Carazo, J.M.: The effect of overabundant projection directions
on 3D reconstruction algorithms, Journal of Structural Biology
133:108-118, 2001, which states that "the computational cost of SIRT is more
than an order of magnitude greater than that of ART."



-- 
Jose Maria Carazo, PhD

Cell +34639197980
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