Ⅱ-9. Instrumentation

RIKEN Accel. Prog. Rep. 47 (2014)

Image reconstruction algorithm for gamma-ray inspection of rotating objects
H. Takeichi,＊1 T. Kambara,＊1 and A. Yoshida＊1
We develop a new method to determine the spatial
distribution of positron-emitting radioisotopes (RIs) on
rotating objects and construct a prototype system. The
details of the principle and the prototype system based on
this method are described elsewhere1). This method is basedon the same principle as the medical positron emission
tomography (PET) systems in which projection data fromall angles are collected. In the PET system, gamma-raydetectors are placed in a circular manner around a stationaryobject, or the gamma-ray detectors rotate around the object
in order to collect projection data. In this method, a pair ofgamma-ray detectors are placed in a stationary position andthe object being imaged is rotated.
Here, we present the image reconstruction algorithm of
the prototype system. The most conventional image
reconstruction algorithm in PET is filtered back-projection(FBP) 2). Projections from all angles are back-projected
onto and overlaid in the image plane using the inverse
Radon transform to reconstruct the image. Then, anappropriate image filter is applied to deblur the image.
An alternative to the FBP is the maximum likelihood –expectation maximization (ML–EM) algorithm3, 4). We
assume a two-dimensional distribution (x,y) of RI (image),and the projection data p(r,) at an angle  from the y-axis
and at a distance r from the center. ML–EM is an iterative
method. The iteration starts with an arbitrary image that isupdated gradually asjn = (jn-1 / Σ cij)(Σ (cij pi / Σ cikkn-1)),
iikThus, Equation 1 reads as follows. First, the projection of
the current estimate image is calculated (k cikkn-1).
Second, the ratio of the actual projection to the estimatedprojection is calculated (pi / k cikkn-1). Third, the ratio isback-projected to the image coordinate (1 / i cij )(i (cij pi /k cikkn-1)). Finally, the back-projected ratio is multipliedby the current estimate image (jn-1 / i cij)(i (cij pi / kcikkn-1)). In the prototype system, the iteration requires 99
steps from the initial uniform image to obtain the current
estimate image.
ML–EM is advantageous over FBP for wear diagnosis ofmechanical parts in that the image values are all nonnegative, the signal to noise ratio is higher, and there areless linear artifacts (see arrows in Fig. 2) around strong RI
sources in the image. These advantages are important for
the easy detection of weak sources near strong sources.
Further, ML–EM is more suitable for quantitativeevaluation because the sum of the image values is preserved
during the iteration and the gamma-ray attenuation in themachine and collimators can be implemented in cij.
Figure 2 shows a comparison of the FBP and ML–EMimages. The FBP image was obtained using MATLAB
iradon. The ML-EM image is based on an in-houseprogram.

(1)

where jn is the j-th pixel value in the image  of the n-thiteration, pi is the value at the i-th position in the projectionp, and cij is the probability that a gamma-ray emitted fromthe j-th pixel position is counted at the i-th position in theprojection (see Fig. 1).

Fig. 2. Comparison of the FBP (left) and ML–EM (right)images (top) and their projections (bottom). The color maps
are scaled and optimized for individual images.
Fig. 1. Schematic illustration of ML–EM
At each iteration, the projection of the current estimate
image is calculated and compared with the actual projection.
Then, the difference between the estimated and actual
projections is back-projected and used to update the current
estimate image.
＊1

RIKEN Nishina Center

References
1) T. Kambara et al.: In this report.
2) J.L. Semmlow: Biosignal and biomedical image processing(Marcel Dekker, New York, 2004).
3) L.A. Shepp and Y. Vardi: IEEE Trans. Med. Imag. 1, 113(1982).
4) K. Lange and R. Carson: J. Comput. Assist. Tomogr. 8, 306(1984).

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