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

REIT’2017 1/13

Subsurface sounding problems

A number of problems, which are solved using the subsurface sounding is growingtoday. Application of the parallel or quasi-parallel systems allows one to perform thesounding 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.

REIT’2017 2/13

3D radio holographic subsurface locator

The product developed by authors from REIT Institute UrFU. Further modification ofthe image synthesis algorithm considering refraction was developed.

Fig. 1. The photo (in the center) and 3D radio images with hidden objects (right) andwithout hidden objects (left)

REIT’2017 3/13

The objective of the work

to estimate performance of one parallel algorithm for 3D image synthesis usingthe CPU and GPU resources,

to estimate the resolution obtained,

to propose the way to its increasing.

REIT’2017 4/13

Image synthesis algorithm

1. There is a set of beat-frequency waveforms {sk(t)}, k = 1,K, for differentpositions {(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 modulationperiod and ∆f is the frequency deviation.The algorithmic complexity of this step is O(N · log(N) ·K), where N is the numberof quantization steps for one signal.

3. Perform phasing for the whole set

S′k(τ) = Sk(τ) · e−jφ0(τ),

where φ0(τ) = 2π(f0 −∆f/2) · τ . Complexity of this step is O(N ·K).

REIT’2017 5/13

4. For all coordinates of the required volume (x, y, z), calculate the total intensity

I(x, y, z) = ‖∑K

S′k(τ)‖,

where τk is the total delay of the echo from the (x, y, z) point considering possiblerefractions at the media interfaces. The complexity of this step is O(M ·K), whereM = X · Y · Z is the total number of voxels in the synthesized image, X,Y, Z are thevoxel resolutions for each coordinate.

The total algorithmic complexity of the algorithm is O(K(N · log(N) +M)).

REIT’2017 6/13

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) andgraphic processor (CUDA). For Fast Fourier Transformation we used FFTW library forOpenMP program and CuFFT for CUDA program.

REIT’2017 7/13

Fig. 2. Program execution time dependingon number of threads

Fig. 3. Program execution time on NVIDIAGTX 780 Ti

REIT’2017 8/13

Linear filtartion

The problem of the low-sized subsurface object visualization motivates creatingdevices with characteristics extremely close to their theoretical physical limits.For example, consider a problem of probing different building structures. The purposeof linear filtering consists of highlighting the low-sized objects on a background ofhigh-intensity reflections from reinforcements and wall surfaces.

Fig. 4. Images (left) and their spectra (right)

REIT’2017 9/13

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).

REIT’2017 10/13

Figureshows images before and afterfiltering. The probed object is theferroconcrete wall with double-layeredreinforcements of 0.3 m width. Specificattenuation is 35 dB/m, permittivityequals 7. The distance between the walland the scanner’s aperture is 1.2 m. Theobjects that we want to be highlighted aremetal plates with size of 3 cm located inthe reinforcement ribs junction on one ofthe ribs and between ribs on equal distancefrom them and at the depth from 10 to 20cm.

Fig. 5. Images before (top) and after(bottom) filtering

REIT’2017 11/13

Conclusions

Analysis of algorithmic complexity of the algorithm suggested for synthesis of 3D radioholographic images was carried out. Application of the serial and parallel processingwas considered. The experiments were carried out for performance increasing byapplication of the parallel computing and vector instructions set. It was shown that byusing the GPUs, it is possible to achieve performance sufficient for the real-timesynthesis of the images. We have shown possibility of using the secondary linearfiltering for the radio-frequency 3D images to reduce the masking effect of wallsurfaces and reinforcement lattice as well as highlight the low-sized masked objects.

The developed system can locate inhomogeneity (size of which can be a fewcentimeters) in double-layered reinforced concrete at the depth of a few tens ofcentimeters.

REIT’2017 12/13

Thank you for your attention!

REIT’2017 13/13