Fig 1.
Sinc filter for filtered backprojection algorithm.
Fig 2.
(a-c) are reproduced with permission from http://www.endrainc.com. The green box in (d) delineates the spatial support of a representative reconstructed field of view. The dimensions of this reconstructed volume are typically set to 2 × 2 × 2 cm, and the isotropic reconstruction resolution typically to 0.2 mm. The blue dots show the locations of the 128 transducers in the bowl.
Fig 3.
(a) Overall scanner impulse response pd0(t) = p0(t)*ht(t), and (b) its frequency spectrum.
Fig 4.
(a, b) Dot and vessel phantoms printed onto transparent overhead projector film using a standard black and white laser printer. (c) Perfused and excised mouse brain. Left side: front of the brain. Right side: rear of the brain (cerebellum). (d) In vivo subcutaneous mouse tumor model. Notice the dimple at the bottom of the plastic tray (indicated by the black arrow), which contains a small amount of coupling fluid (water), and is used to help position the subcutaneous tumor. The diameter of the dimple is 15 mm.
Fig 5.
Representative slices through the perfused and excised mouse brain.
Fig 6.
Example Gaussian fit to a 1D intensity profile in order to estimate the FWHM and CNR of point-like or linear features.
Fig 7.
Frequency spectra of deconvolved pencil point signals, filter parameter optimization, and maximum intensity projections (MIP).
(a-b) Average Fourier spectrum of the deconvolved pencil point signals, and MIP, using Fourier filter. The normalized correlation coefficient (NCC) C is equal to 0.6620. (c-e) Wiener filter example spectra and normalized correlation coefficients. ‘Orig’ stands for the average frequency spectrum before deconvolution. The maximum NCC value was achieved as σ tended to infinity (uniform distribution), with C tending to 0.733. Note that convergence was already reached for values of σ ≈ 20MHz and above. (f-h) Tikhonov filter example spectra and normalized correlation coefficients. Maximum NCC achieved at β = 125 and C = 0.7914. The image intensities of the reconstructions are normalized (black: 0, white: 1), and the dimensions of the MIP images are 10 × 10 mm.
Fig 8.
Noise (measured by NSSD) versus resolution (measured by FWHM) curves for various filter choices and parameter settings.
The parameter σ is expressed in MHz; the parameter β is unitless.
Fig 9.
Reconstructions by each deconvolution method.
First row: dot phantom. Second row: vessel phantom. Third row: subcutaneous mouse tumor. Fourth row: mouse brain. First column: Fourier filter. Second column: Wiener filter. Third column: Tikhonov method. Fourth column: illustrative line profiles. The image intensities of the reconstructions are normalized (black: 0, white: 1), and the dimensions of the MIP images are 20 × 20 mm.
Fig 10.
FHWM and CNR of various linear features by the three deconvolution methods.
The ground truth FWHM is known only for the artificial phantoms.
Fig 11.
Robustness to noise of each deconvolution filter, as illustrated for the dot phantom.
σ denotes the standard deviation of the zero-mean Gaussian noise added to the pressure signals, expressed as a percentage of the maximum pressure signal value. Each filter is used at its optimal setting, as determined in the Filter parameter optimization section. The line profiles in the right hand side column have been normalized. The image intensities of the reconstructions are normalized as well (black: 0, white: 1), and the dimensions of the MIP images are 20 × 20 mm.
Fig 12.
Robustness to noise of each deconvolution filter, as illustrated for the vessel phantom.
σ denotes the standard deviation of the zero-mean Gaussian noise added to the pressure signals, expressed as a percentage of the maximum pressure signal value. Each filter is used at its optimal setting, as determined in the Filter parameter optimization section. The image intensities of the reconstructions are normalized (black: 0, white: 1), and the dimensions of the MIP images are 20 × 20 mm.
Fig 13.
Robustness to noise of each deconvolution filter, as illustrated for the vascularized subcutaneous mouse tumor.
σ denotes the standard deviation of the zero-mean Gaussian noise added to the pressure signals, expressed as a percentage of the maximum pressure signal value. Each filter is used at its optimal setting, as determined in the Filter parameter optimization section. The image intensities of the reconstructions are normalized (black: 0, white: 1), and the dimensions of the MIP images are 20 × 20 mm.
Fig 14.
Robustness to noise of each deconvolution filter, as illustrated for the perfused and excised mouse brain.
σ denotes the standard deviation of the zero-mean Gaussian noise added to the pressure signals, expressed as a percentage of the maximum pressure signal value. Each filter is used at its optimal setting, as determined in the Filter parameter optimization section. The image intensities of the reconstructions are normalized (black: 0, white: 1), and the dimensions of the MIP images are 20 × 20 mm.