Alexey A. Kalmykov, Vadim A. Dobryak, Andrey A. Kalmykov, Anton S. Kurilenko, Elena N. Akimova, Aliya F. Skurydina, Vladimir E. Misilov

1. 3D radio holographic images synthesis and filtration on multiprocessor
computing systems
Al. A Kalmykov, V. A. Dobryak, An. A. Kalmykov, A. S. Kurilenko,
E. N. Akimova, A. F. Skurydina, V. E. Misilov
Ural Federal University, Yekaterinburg, Russia
Krasovskii Institute of Mathematics and Mechanics, Ural Branch of RAS, Yekaterinburg,
Russia
kaa@iidt.ru, dobryak1958@gmail.com, andrey-kalmykov@yandex.ru
aen15@yandex.ru, {afinapal, out.mrscreg}@gmail.com
March 9, 2017
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2. Subsurface sounding problems
A number of problems, which are solved using the subsurface sounding is growing
today. Application of the parallel or quasi-parallel systems allows one to perform the
sounding and image synthesis in a fraction of a second.
Examples:
high-performance passenger screening systems
searching for the hidden objects in buildings
computer vision systems, archeology, etc.
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3. 3D radio holographic subsurface locator
The product developed by authors from REIT Institute UrFU. Further modification of
the image synthesis algorithm considering refraction was developed.
Fig. 1. The photo (in the center) and 3D radio images with hidden objects (right) and
without hidden objects (left)
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4. The objective of the work
to estimate performance of one parallel algorithm for 3D image synthesis using
the CPU and GPU resources,
to estimate the resolution obtained,
to propose the way to its increasing.
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5. Image synthesis algorithm
1. There is a set of beat-frequency waveforms {sk(t)}, k = 1, K, for different
positions {(xk, yk, zk)} of antenna.
2. Compute the complex spectrums of these waveforms using the Fourier transform
Sk(f) = F{sk(t)}.
The delay is τ = f · Tm/∆f, so, we get a set {Sk(τ)}. Here, Tm is the modulation
period and ∆f is the frequency deviation.
The algorithmic complexity of this step is O(N · log(N) · K), where N is the number
of quantization steps for one signal.
3. Perform phasing for the whole set
Sk(τ) = Sk(τ) · e−jφ0(τ)
,
where φ0(τ) = 2π(f0 − ∆f/2) · τ. Complexity of this step is O(N · K).
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6. 4. For all coordinates of the required volume (x, y, z), calculate the total intensity
I(x, y, z) =
K
Sk(τ) ,
where τk is the total delay of the echo from the (x, y, z) point considering possible
refractions at the media interfaces. The complexity of this step is O(M · K), where
M = X · Y · Z is the total number of voxels in the synthesized image, X, Y, Z are the
voxel resolutions for each coordinate.
The total algorithmic complexity of the algorithm is O(K(N · log(N) + M)).
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7. Numerical experiments results
The synthesized image has the following parameters:
the resolution in voxels is 100 × 100 × 300,
the beat-frequency waveforms set K has the length of 2048,
the number of quantization steps is 216.
A comparison was made for program times for multicore processor (OpenMP) and
graphic processor (CUDA). For Fast Fourier Transformation we used FFTW library for
OpenMP program and CuFFT for CUDA program.
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8. Fig. 2. Program execution time depending
on number of threads
Fig. 3. Program execution time on NVIDIA
GTX 780 Ti
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9. Linear filtartion
The problem of the low-sized subsurface object visualization motivates creating
devices with characteristics extremely close to their theoretical physical limits.
For example, consider a problem of probing different building structures. The purpose
of linear filtering consists of highlighting the low-sized objects on a background of
high-intensity reflections from reinforcements and wall surfaces.
Fig. 4. Images (left) and their spectra (right)
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10. Figure shows summary images and their spectra before (top) and after (bottom)
filtering. The object’s intensity is slightly reduces and the cross-like beams appeared,
but these are admissible distortions.
Fig. 5. Images before and after filtering (left) and their spectra (right).
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11. Figureshows images before and after
filtering. The probed object is the
ferroconcrete wall with double-layered
reinforcements of 0.3 m width. Specific
attenuation is 35 dB/m, permittivity
equals 7. The distance between the wall
and the scanner’s aperture is 1.2 m. The
objects that we want to be highlighted are
metal plates with size of 3 cm located in
the reinforcement ribs junction on one of
the ribs and between ribs on equal distance
from them and at the depth from 10 to 20
cm.
Fig. 5. Images before (top) and after
(bottom) filtering
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12. Conclusions
Analysis of algorithmic complexity of the algorithm suggested for synthesis of 3D radio
holographic images was carried out. Application of the serial and parallel processing
was considered. The experiments were carried out for performance increasing by
application of the parallel computing and vector instructions set. It was shown that by
using the GPUs, it is possible to achieve performance sufficient for the real-time
synthesis of the images. We have shown possibility of using the secondary linear
filtering for the radio-frequency 3D images to reduce the masking effect of wall
surfaces and reinforcement lattice as well as highlight the low-sized masked objects.
The developed system can locate inhomogeneity (size of which can be a few
centimeters) in double-layered reinforced concrete at the depth of a few tens of
centimeters.
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13. Thank you for your attention!
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