M. V. OLIVA, H. H. MUHAMMED

between the original model and the reconstructed one,

but the difference in terms of a calculated PSNR value of

21 dB is quite considerable. But this doesn’t mean that

the method doesn’t work properly. It reflects that new

details appear in the reconstructed volume which could

be closer to the real 3D model without missing data .

5. Discussion and Conclusions

The purpose of our work was to apply a new method to

solve LPAs (e.g. with a missing cone or a missing wedge

of the acquired image-data volume) in TEM data. The

method was applied to different d atasets and the resu lting

reconstructed image volumes were evaluated. Good 3D

reconstruction results were obtained. The PSNR values

were calculated for all resulting reconstructed images.

These PSNR values were better than those obtained us-

ing existing commonly used techniques, such as POCS.

The approa ch proposed in our work can be cons idered as

a great breakthrough, because for data acquisitions li-

mited to [45˚, −45˚], POCS results in an error-rate ar ound

40%, while our approach achieves an error-rate lower

than 1% for the Hansandrey and the viral DNA gatekee-

per cases when 50% of the acquired data is missing.

However, different acquisition technique and proce-

dures will produce data with different sparsity characte-

ristics in frequency domain, which in its turn will affect

the performance of our method. For example, if a large

portion of the high frequency zones of the acquired data

is missing or corrupted, then it gets much more difficult

to reconstruct the missing part of the 3D model because

the algorithm doesn’t have e n ough prior information.

Therefore, we have to take under consideration that a

test measure is needed to determine which datasets, with

the presence of missing data, are valid or not to apply the

proposed method and get good 3D reconstruction resu lts.

If such a test is performed, it will be possible to know if

the obtained 3D reconstruction result is supposed to be

similar to the real original model (i.e. without missing

data) or not. Then it will be possible to know if the 3D

reconstruction of Philip’s crystallography dataset (pre-

sented in Figure 6) is correct or not.

One of the most exciting research projects that could

emerge from our work is the possibility to develop a new

optimized acquisition technique or procedure for TEM.

In addition, achieving a considerable reduction of radia-

tion dose applied to the specimen. Another possibility is

to adapt the proposed method and apply it to other kinds

of modalities like Computed Tomography (CT), Mag-

netic Resonance Imaging (MRI), astronomy, geophysical

exploration or other type of electron microscope tech-

niques. Since a complete reconstruction of the Hansand-

rey model took 32 hours in a common laptop (4-core 2.0

GHz and 4 Gb RAM), it would be necessary to speed up

the algorithm by implementing it using GPU techniques

(e.g. CUDA, OpenCL).

6. Acknowledgements

This paper would not have been possible without the

support and help of Dr. Philip Koeck (from the Royal

Institute of Technolog y KTH, Sweden) who supplied th e

Hansandrey dataset and Philip’s crystallography dataset.

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