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Fig. 3. Fourier and MPM spectra of the simulated signal shown in Fig. 2 (rescaled).

Figure 3 Fourier and MPM spectra of the simulated signal shown in Fig. 2 (rescaled).

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Fig. 1. Examples of clinical percussion signals from (a) chest anc (b) abdomen. parts of the body [23], t hey could provide a natural basis for efficient decomposition and parameterization of percussion sig- nals. Their proper identification could also help single out per- cussion responses of ind ividual organs. The main issue with using the Fourier analysis for this purpose is broadening of the spectral peaks due to in herent damping of the vibrations in- duced by the percussion event, which causes peak overlapping and masking of the lower amplitude peaks. Being able to au- tomatically identify the damped harmonic modes in the signal would immediately address the aforementioned issue. Employ- ing an efficient algorithm decomposing the percussion signal into a sum of damped complex exponentials would constitute a considerable improvement over the laborious nonlinear fitting technique.
Fig. 1. Examples of clinical percussion signals from (a) chest anc (b) abdomen. parts of the body [23], t hey could provide a natural basis for efficient decomposition and parameterization of percussion sig- nals. Their proper identification could also help single out per- cussion responses of ind ividual organs. The main issue with using the Fourier analysis for this purpose is broadening of the spectral peaks due to in herent damping of the vibrations in- duced by the percussion event, which causes peak overlapping and masking of the lower amplitude peaks. Being able to au- tomatically identify the damped harmonic modes in the signal would immediately address the aforementioned issue. Employ- ing an efficient algorithm decomposing the percussion signal into a sum of damped complex exponentials would constitute a considerable improvement over the laborious nonlinear fitting technique.
where Y," is the Moore—Penrose pseudoinverse of Y,. The EDS frequencies and damping factors are then derived as fi = arg (A;) /(27Ts) and d; = —Re (A;) /Ts. Once M and z, are known, the residues R; can be found from the following least-squares problem [17], [18]: The amplitudes A; and initial phases y; of individual EDS are then calculated from the residues. MPM is available as a function in various software packages including “Spencer” [22], LabView, MATLAB, and others. The results shown in this paper were produced with our custom Lab View software based on the algorithm described in [18].
where Y," is the Moore—Penrose pseudoinverse of Y,. The EDS frequencies and damping factors are then derived as fi = arg (A;) /(27Ts) and d; = —Re (A;) /Ts. Once M and z, are known, the residues R; can be found from the following least-squares problem [17], [18]: The amplitudes A; and initial phases y; of individual EDS are then calculated from the residues. MPM is available as a function in various software packages including “Spencer” [22], LabView, MATLAB, and others. The results shown in this paper were produced with our custom Lab View software based on the algorithm described in [18].
‘ig. 2. Simulated signal waveform (no-noise case).
‘ig. 2. Simulated signal waveform (no-noise case).
PARAMETERS OF SIX EDS IN THE SIMULATED SIGNAL of individual EDS components detected by the MPM in this signal. Notably, the MPM finds the original, undamped EDS frequencies f;, while the locations of the spectral maxima corre- spond to damped frequencies F; = ,/ f? — (27d;)?. Although the difference between f; and F; is usually small and can be neglected, it becomes noticeable in the highly damped and low- frequency resonant percussion signals.
PARAMETERS OF SIX EDS IN THE SIMULATED SIGNAL of individual EDS components detected by the MPM in this signal. Notably, the MPM finds the original, undamped EDS frequencies f;, while the locations of the spectral maxima corre- spond to damped frequencies F; = ,/ f? — (27d;)?. Although the difference between f; and F; is usually small and can be neglected, it becomes noticeable in the highly damped and low- frequency resonant percussion signals.
Fig. 4. Number of significant EDS detected by the MPM in the six-mode signal with different amounts of noise. EDS amplitude threshold values are indicated by squares—0.01; circles—0.05; triangles—O. 1.
Fig. 4. Number of significant EDS detected by the MPM in the six-mode signal with different amounts of noise. EDS amplitude threshold values are indicated by squares—0.01; circles—0.05; triangles—O. 1.
Fig. 5. Relative MS reconstruction error from significant EDS exceeding different threshold values indicated by squares—0.01; circles—0.05; triangles— 0.1.
Fig. 5. Relative MS reconstruction error from significant EDS exceeding different threshold values indicated by squares—0.01; circles—0.05; triangles— 0.1.
Fig. 6. Amplitude spectrum of the signal from Fig. l(a) before and after subtracting the noise spectrum, which is shown as well.
Fig. 6. Amplitude spectrum of the signal from Fig. l(a) before and after subtracting the noise spectrum, which is shown as well.
FREQUENCY AND A / d VALUES FOR TEN STRONGEST EDS FOUND IN PERCUSSION SIGNALS SHOWN IN FIG. 1(A), (B)
FREQUENCY AND A / d VALUES FOR TEN STRONGEST EDS FOUND IN PERCUSSION SIGNALS SHOWN IN FIG. 1(A), (B)
Fig. 9. Spectral fitting of a chest percussion signal with Lorentzian curves. Original spectrum—black dots; the fit—continuous line; Lorentzian components—dashed lines.
Fig. 9. Spectral fitting of a chest percussion signal with Lorentzian curves. Original spectrum—black dots; the fit—continuous line; Lorentzian components—dashed lines.
Fig. 10. (a) Frequency histogram of the spectral peaks of the upper chest signals from 30 volunteers using the FFT method (the frequency bin was set to 5 Hz). (b) Frequency histogram of the main EDS for the upper chest signals from 30 volunteers decomposed by the MPM (the frequency bin was set to 5 Hz).
Fig. 10. (a) Frequency histogram of the spectral peaks of the upper chest signals from 30 volunteers using the FFT method (the frequency bin was set to 5 Hz). (b) Frequency histogram of the main EDS for the upper chest signals from 30 volunteers decomposed by the MPM (the frequency bin was set to 5 Hz).
Fig. 11. EDS frequencies of chest (white), right abdominal (black), and stom- ach (hatched) percussion signals from 30 volunteers (for some volunteers, the data were taken more than once).
Fig. 11. EDS frequencies of chest (white), right abdominal (black), and stom- ach (hatched) percussion signals from 30 volunteers (for some volunteers, the data were taken more than once).
FIVE Most SIGNIFICANT EDS PRODUCED BY THE MPM FOR THE CHEST SIGNALS ACQUIRED BEFORE AND AFTER CARBONATED DRINK CONSUMPTIO! with the frequency of the abdominal oscillation. In the no-gas experiment (see Fig. 12), the abdominal bubble was very small and located deeply in the intestines, far from the diaphragm, so it did not affect its damping. Consumption of the carbonated drink introduced a larger pocket located directly under the diaphragm, noticeably reducing its damping. Also notably, after introducing gas in the abdomen the width of the second peak was reduced (lower damping) leading to better exposure of the first peak (see Fig. 13).
FIVE Most SIGNIFICANT EDS PRODUCED BY THE MPM FOR THE CHEST SIGNALS ACQUIRED BEFORE AND AFTER CARBONATED DRINK CONSUMPTIO! with the frequency of the abdominal oscillation. In the no-gas experiment (see Fig. 12), the abdominal bubble was very small and located deeply in the intestines, far from the diaphragm, so it did not affect its damping. Consumption of the carbonated drink introduced a larger pocket located directly under the diaphragm, noticeably reducing its damping. Also notably, after introducing gas in the abdomen the width of the second peak was reduced (lower damping) leading to better exposure of the first peak (see Fig. 13).
Fig. 12. Frequency spectrum of the percussion signals for the subject with no gas in the abdominal cavity (black squares—chest, open circles—stomach, black triangles—abdomen).
Fig. 12. Frequency spectrum of the percussion signals for the subject with no gas in the abdominal cavity (black squares—chest, open circles—stomach, black triangles—abdomen).
Fig. 13. Frequency spectrum of the percussion signals from the subject with gas in the abdominal cavity (black squares—chest, open triangles—abdomen).
Fig. 13. Frequency spectrum of the percussion signals from the subject with gas in the abdominal cavity (black squares—chest, open triangles—abdomen).
Physical Society since 1998. Bee ee Ce SES eee E Cee Ee ee Oe plications of ultrasound including NDE, acoustic tomography, and transcranial imaging with phased arrays.
Physical Society since 1998. Bee ee Ce SES eee E Cee Ee ee Oe plications of ultrasound including NDE, acoustic tomography, and transcranial imaging with phased arrays.
In 2005, he was a Full Professor in Physics from the Russian Federation Government in Scientific Equipment and Methods for Experimental Physics, he is the founding Director General of the Institute for Diagnostic Imaging Research, University of Windsor, Windsor, ON, Canada, which is a multidis- ciplinary, collaborative research and innovation consortium. He is also a Full Faculty Professor in the Department of Physics, University of Windsor, Wind- sor, and in 2007 he was granted the title of Distinguished University Professor. In 2004, based on an initiative by Chryslers, a new Canadian start-up high-tech Company “Tessonics Corporation” was created with its main mission for the commercialization of the research products developed by Maev’s R&D team at the University of Windsor. He is providing an important leading technical role in this new enterprise. The extraordinarily diverse range of disciplines encom- passed by him includes theoretical fundamentals of physical acoustics, research in ultrasonic and nonlinear acoustical imaging, nanostructural properties of ad- vanced materials, and its analysis. He is an author of 4 monographs, an editor and coeditor of 9 books, has published more than 440 per-reviewed items, in- cluding 113 articles in leading international journals, 287 referred conferences proceedings, and holds 29 international patents. —— ee lee el ee ee He received combined B.Sc. and M.Sc. degrees in physics from the Chair of Acoustics at Moscow State University, Moscow, Russia. He defended his Ph.D. thesis titled “Nonlinear acoustical phenomena in lay- ered structures” in 1989. He held the position of researcher in B. I. Stepanov’s Institute of Physics, National Academy of Science of Belarus. Since 1998 he has been a Research Associate at the Department of Physics, University of Windsor, Windsor, ON, Canada. As a member of the Centre for Imaging Research and Advanced Materials Charac- terization, he participates in numerous research projects in physical acoustics and development of ultrasonic nondestructive evaluation applications. ss — His research interests include adaptive signal rep: resentations and analysis and their applications in the al engineering.
In 2005, he was a Full Professor in Physics from the Russian Federation Government in Scientific Equipment and Methods for Experimental Physics, he is the founding Director General of the Institute for Diagnostic Imaging Research, University of Windsor, Windsor, ON, Canada, which is a multidis- ciplinary, collaborative research and innovation consortium. He is also a Full Faculty Professor in the Department of Physics, University of Windsor, Wind- sor, and in 2007 he was granted the title of Distinguished University Professor. In 2004, based on an initiative by Chryslers, a new Canadian start-up high-tech Company “Tessonics Corporation” was created with its main mission for the commercialization of the research products developed by Maev’s R&D team at the University of Windsor. He is providing an important leading technical role in this new enterprise. The extraordinarily diverse range of disciplines encom- passed by him includes theoretical fundamentals of physical acoustics, research in ultrasonic and nonlinear acoustical imaging, nanostructural properties of ad- vanced materials, and its analysis. He is an author of 4 monographs, an editor and coeditor of 9 books, has published more than 440 per-reviewed items, in- cluding 113 articles in leading international journals, 287 referred conferences proceedings, and holds 29 international patents. —— ee lee el ee ee He received combined B.Sc. and M.Sc. degrees in physics from the Chair of Acoustics at Moscow State University, Moscow, Russia. He defended his Ph.D. thesis titled “Nonlinear acoustical phenomena in lay- ered structures” in 1989. He held the position of researcher in B. I. Stepanov’s Institute of Physics, National Academy of Science of Belarus. Since 1998 he has been a Research Associate at the Department of Physics, University of Windsor, Windsor, ON, Canada. As a member of the Centre for Imaging Research and Advanced Materials Charac- terization, he participates in numerous research projects in physical acoustics and development of ultrasonic nondestructive evaluation applications. ss — His research interests include adaptive signal rep: resentations and analysis and their applications in the al engineering.
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