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Comparison of Deconvolution Filters for Photoacoustic Tomography.

Van de Sompel D, Sasportas LS, Jokerst JV, Gambhir SS - PLoS ONE (2016)

Bottom Line: It was found that the Tikhonov filter yielded the most accurate balance of lower and higher frequency content (as measured by comparing the spectra of deconvolved impulse response signals to the ideal flat frequency spectrum), achieved a competitive image resolution and contrast-to-noise ratio, and yielded the greatest robustness to noise.In addition, its robustness to noise was poorer than that of the Tikhonov filter.Overall, the Tikhonov filter was deemed to produce the most desirable image reconstructions.

View Article: PubMed Central - PubMed

Affiliation: Molecular Imaging Program at Stanford (MIPS), Stanford University School of Medicine, Stanford University, Stanford, CA 94305, United States of America.

ABSTRACT
In this work, we compare the merits of three temporal data deconvolution methods for use in the filtered backprojection algorithm for photoacoustic tomography (PAT). We evaluate the standard Fourier division technique, the Wiener deconvolution filter, and a Tikhonov L-2 norm regularized matrix inversion method. Our experiments were carried out on subjects of various appearances, namely a pencil lead, two man-made phantoms, an in vivo subcutaneous mouse tumor model, and a perfused and excised mouse brain. All subjects were scanned using an imaging system with a rotatable hemispherical bowl, into which 128 ultrasound transducer elements were embedded in a spiral pattern. We characterized the frequency response of each deconvolution method, compared the final image quality achieved by each deconvolution technique, and evaluated each method's robustness to noise. The frequency response was quantified by measuring the accuracy with which each filter recovered the ideal flat frequency spectrum of an experimentally measured impulse response. Image quality under the various scenarios was quantified by computing noise versus resolution curves for a point source phantom, as well as the full width at half maximum (FWHM) and contrast-to-noise ratio (CNR) of selected image features such as dots and linear structures in additional imaging subjects. It was found that the Tikhonov filter yielded the most accurate balance of lower and higher frequency content (as measured by comparing the spectra of deconvolved impulse response signals to the ideal flat frequency spectrum), achieved a competitive image resolution and contrast-to-noise ratio, and yielded the greatest robustness to noise. While the Wiener filter achieved a similar image resolution, it tended to underrepresent the lower frequency content of the deconvolved signals, and hence of the reconstructed images after backprojection. In addition, its robustness to noise was poorer than that of the Tikhonov filter. The performance of the Fourier filter was found to be the poorest of all three methods, based on the reconstructed images' lowest resolution (blurriest appearance), generally lowest contrast-to-noise ratio, and lowest robustness to noise. Overall, the Tikhonov filter was deemed to produce the most desirable image reconstructions.

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FHWM and CNR of various linear features by the three deconvolution methods.The ground truth FWHM is known only for the artificial phantoms.
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pone.0152597.g010: FHWM and CNR of various linear features by the three deconvolution methods.The ground truth FWHM is known only for the artificial phantoms.

Mentions: Qualitatively, the image reconstructions by the Fourier method appear slightly blurrier than those by the Wiener and Tikhonov methods. This can be appreciated in the images as well as the intensity profiles, and is confirmed by the FWHM estimates in Fig 10(a). The blurrier appearance of the Fourier reconstructions is due to the underrepresentation of low frequencies in the scanner impulse response pd0(t) (due to the band-pass nature of the transducer and hence underrepresentation of low frequencies in the transducer impulse response ht(t)—see Fig 3). As a result, the Fourier division technique disproportionately boosts lower frequencies in the data space, and consequently in the image space after backprojection. Stated differently, any small and poorly measured magnitudes in the low frequencies of the transducer response end up magnifying the equally poorly measured low frequencies in the recorded signal. As a result, the amplified lower frequencies lead to blurrier image appearances. Note that the higher frequencies in the deconvolved signals tend to be overly amplified as well, due to a similar underrepresentation of higher frequencies in the scanner impulse response pd0(t). However, this effect is mitigated by the standard practice of applying a high-frequency suppressing filter (see Methods section) after the Fourier division. While a similar regularization could be applied at lower frequencies, such measures would lead us further away from applying a standard Fourier division deconvolution. Our purpose is to compare the performance of the standard Fourier division deconvolution to alternative methods, namely the Wiener and Tikhonov deconvolution methods. Next, we observe that the difference between the three deconvolution methods is most pronounced for the mouse brain. This is likely due to the fact that the spherical projections of the brain possess more lower frequency content than those of the other imaging subjects. This enables a more obvious demonstration of the difference in the frequency balancing by the various methods. Note in particular that the Tikhonov filter appears to achieve a superior balance between high and low spatial frequencies compared to the Fourier and (admittedly similar) Wiener filters. This observation agrees with the prediction made in the “Tikhonov: optimization of the parameter β” section.


Comparison of Deconvolution Filters for Photoacoustic Tomography.

Van de Sompel D, Sasportas LS, Jokerst JV, Gambhir SS - PLoS ONE (2016)

FHWM and CNR of various linear features by the three deconvolution methods.The ground truth FWHM is known only for the artificial phantoms.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4816281&req=5

pone.0152597.g010: FHWM and CNR of various linear features by the three deconvolution methods.The ground truth FWHM is known only for the artificial phantoms.
Mentions: Qualitatively, the image reconstructions by the Fourier method appear slightly blurrier than those by the Wiener and Tikhonov methods. This can be appreciated in the images as well as the intensity profiles, and is confirmed by the FWHM estimates in Fig 10(a). The blurrier appearance of the Fourier reconstructions is due to the underrepresentation of low frequencies in the scanner impulse response pd0(t) (due to the band-pass nature of the transducer and hence underrepresentation of low frequencies in the transducer impulse response ht(t)—see Fig 3). As a result, the Fourier division technique disproportionately boosts lower frequencies in the data space, and consequently in the image space after backprojection. Stated differently, any small and poorly measured magnitudes in the low frequencies of the transducer response end up magnifying the equally poorly measured low frequencies in the recorded signal. As a result, the amplified lower frequencies lead to blurrier image appearances. Note that the higher frequencies in the deconvolved signals tend to be overly amplified as well, due to a similar underrepresentation of higher frequencies in the scanner impulse response pd0(t). However, this effect is mitigated by the standard practice of applying a high-frequency suppressing filter (see Methods section) after the Fourier division. While a similar regularization could be applied at lower frequencies, such measures would lead us further away from applying a standard Fourier division deconvolution. Our purpose is to compare the performance of the standard Fourier division deconvolution to alternative methods, namely the Wiener and Tikhonov deconvolution methods. Next, we observe that the difference between the three deconvolution methods is most pronounced for the mouse brain. This is likely due to the fact that the spherical projections of the brain possess more lower frequency content than those of the other imaging subjects. This enables a more obvious demonstration of the difference in the frequency balancing by the various methods. Note in particular that the Tikhonov filter appears to achieve a superior balance between high and low spatial frequencies compared to the Fourier and (admittedly similar) Wiener filters. This observation agrees with the prediction made in the “Tikhonov: optimization of the parameter β” section.

Bottom Line: It was found that the Tikhonov filter yielded the most accurate balance of lower and higher frequency content (as measured by comparing the spectra of deconvolved impulse response signals to the ideal flat frequency spectrum), achieved a competitive image resolution and contrast-to-noise ratio, and yielded the greatest robustness to noise.In addition, its robustness to noise was poorer than that of the Tikhonov filter.Overall, the Tikhonov filter was deemed to produce the most desirable image reconstructions.

View Article: PubMed Central - PubMed

Affiliation: Molecular Imaging Program at Stanford (MIPS), Stanford University School of Medicine, Stanford University, Stanford, CA 94305, United States of America.

ABSTRACT
In this work, we compare the merits of three temporal data deconvolution methods for use in the filtered backprojection algorithm for photoacoustic tomography (PAT). We evaluate the standard Fourier division technique, the Wiener deconvolution filter, and a Tikhonov L-2 norm regularized matrix inversion method. Our experiments were carried out on subjects of various appearances, namely a pencil lead, two man-made phantoms, an in vivo subcutaneous mouse tumor model, and a perfused and excised mouse brain. All subjects were scanned using an imaging system with a rotatable hemispherical bowl, into which 128 ultrasound transducer elements were embedded in a spiral pattern. We characterized the frequency response of each deconvolution method, compared the final image quality achieved by each deconvolution technique, and evaluated each method's robustness to noise. The frequency response was quantified by measuring the accuracy with which each filter recovered the ideal flat frequency spectrum of an experimentally measured impulse response. Image quality under the various scenarios was quantified by computing noise versus resolution curves for a point source phantom, as well as the full width at half maximum (FWHM) and contrast-to-noise ratio (CNR) of selected image features such as dots and linear structures in additional imaging subjects. It was found that the Tikhonov filter yielded the most accurate balance of lower and higher frequency content (as measured by comparing the spectra of deconvolved impulse response signals to the ideal flat frequency spectrum), achieved a competitive image resolution and contrast-to-noise ratio, and yielded the greatest robustness to noise. While the Wiener filter achieved a similar image resolution, it tended to underrepresent the lower frequency content of the deconvolved signals, and hence of the reconstructed images after backprojection. In addition, its robustness to noise was poorer than that of the Tikhonov filter. The performance of the Fourier filter was found to be the poorest of all three methods, based on the reconstructed images' lowest resolution (blurriest appearance), generally lowest contrast-to-noise ratio, and lowest robustness to noise. Overall, the Tikhonov filter was deemed to produce the most desirable image reconstructions.

Show MeSH
Related in: MedlinePlus