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ABSTRACT: Attenuation effects can be significant in photoacoustic tomography since the generated pressure signals are broadband, and ignoring them may lead to image artifacts and blurring. La Rivière et al. [Opt. Lett. 31(6), pp. 781-783, (2006)] had previously derived a method for modeling the attenuation effect and correcting for it in the image reconstruction. This was done by relating the ideal, unattenuated pressure signals to the attenuated pressure signals via an integral operator. We derive an integral operator relating the attenuated pressure signals to the absorbed optical energy for a planar measurement geometry. The matrix operator relating the two quantities is a function of the temporal frequency, attenuation coefficient and the two-dimensional spatial frequency. We perform singular-value decomposition (SVD) of this integral operator to study the problem further. We find that the smallest singular values correspond to wavelet-like eigenvectors in which most of the energy is concentrated at times corresponding to greater depths in tissue. This allows us to characterize the ill-posedness of recovering the absorbed optical energy distribution at different depths in an attenuating medium. This integral equation can be inverted using standard SVD methods, and the initial pressure distribution can be recovered. We conduct simulations and derive an algorithm for image reconstruction using SVD for a planar measurement geometry. We also study the noise and resolution properties of this image-reconstruction method.
Journal of Biomedical Optics 06/2012; 17(6):061204. · 3.16 Impact Factor
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ABSTRACT: In recent years, the authors and others have been exploring the use of penalized-likelihood sinogram-domain smoothing and restoration approaches for emission and transmission tomography. The motivation for this strategy was initially pragmatic: to provide a more computationally feasible alternative to fully iterative penalized-likelihood image reconstruction involving expensive backprojections and reprojections, while still obtaining some of the benefits of the statistical modeling employed in penalized-likelihood approaches. In this work, the authors seek to compare the two approaches in greater detail.
The sinogram-domain strategy entails estimating the "ideal" line integrals needed for reconstruction of an activity or attenuation distribution from the set of noisy, potentially degraded tomographic measurements by maximizing a penalized-likelihood objective function. The objective function models the data statistics as well as any degradation that can be represented in the sinogram domain. The estimated line integrals can then be input to analytic reconstruction algorithms such as filtered backprojection (FBP). The authors compare this to fully iterative approaches maximizing similar objective functions.
The authors present mathematical analyses based on so-called equivalent optimization problems that establish that the approaches can be made precisely equivalent under certain restrictive conditions. More significantly, by use of resolution-variance tradeoff studies, the authors show that they can yield very similar performance under more relaxed, realistic conditions.
The sinogram- and image-domain approaches are equivalent under certain restrictive conditions and can perform very similarly under more relaxed conditions. The match is particularly good for fully sampled, high-resolution CT geometries. One limitation of the sinogram-domain approach relative to the image-domain approach is the difficulty of imposing additional constraints, such as image non-negativity.
Medical Physics 08/2011; 38(8):4811-23. · 2.83 Impact Factor
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ABSTRACT: Photoacoustic tomography (PAT), also known as optoacoustic or thermoacoustic tomography, is a hybrid imaging technique that possesses great potential for a wide range of biomedical imaging applications. Image reconstruction in PAT is tantamount to solving an inverse source problem, where the source represents the optical energy absorption distribution in the object that is induced by an interrogating pulsed optical waveform. In this work, we re-examine the PAT image reconstruction problem from a Fourier domain perspective by use of established time-harmonic inverse source concepts. A mathematical relationship between the photoacoustic pressure wavefield data on an aperture that encloses the object and the three-dimensional Fourier transform of the optical absorption distribution evaluated on a collection of concentric spheres is investigated. In addition to providing a framework for deriving both exact and approximate analytic reconstruction formulae, we demonstrate that this mapping provides an intuitive means of understanding certain spatial resolution characteristics of PAT.
Inverse Problems 11/2007; 23(6):S21. · 1.88 Impact Factor
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ABSTRACT: In this paper, we derive a monotonic penalized-likelihood algorithm for image reconstruction in X-ray fluorescence computed tomography (XFCT) when the attenuation maps at the energies of the fluorescence X-rays are unknown. In XFCT, a sample is irradiated with pencil beams of monochromatic synchrotron radiation that stimulate the emission of fluorescence X-rays from atoms of elements whose K- or L-edges lie below the energy of the stimulating beam. Scanning and rotating the object through the beam allows for acquisition of a tomographic dataset that can be used to reconstruct images of the distribution of the elements in question. XFCT is a stimulated emission tomography modality, and it is thus necessary to correct for attenuation of the incident and fluorescence photons. The attenuation map is, however, generally known only at the stimulating beam energy and not at the energies of the various fluorescence X-rays of interest. We have developed a penalized-likelihood image reconstruction strategy for this problem. The approach alternates between updating the distribution of a given element and updating the attenuation map for that element's fluorescence X-rays. The approach is guaranteed to increase the penalized likelihood at each iteration. Because the joint objective function is not necessarily concave, the approach may drive the solution to a local maximum. To encourage the algorithm to seek out a reasonable local maximum, we include in the objective function a prior that encourages a relationship, based on physical considerations, between the fluorescence attenuation map and the distribution of the element being reconstructed.
IEEE Transactions on Medical Imaging 10/2006; 25(9):1117-29. · 3.64 Impact Factor
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ABSTRACT: We formulate computed tomography (CT) sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. CT measurement data are degraded by a number of factors-including beam hardening and off-focal radiation-that produce artifacts in reconstructed images unless properly corrected. Currently, such effects are addressed by a sequence of sinogram-preprocessing steps, including deconvolution corrections for off-focal radiation, that have the potential to amplify noise. Noise itself is generally mitigated through apodization of the reconstruction kernel, which effectively ignores the measurement statistics, although in high-noise situations adaptive filtering methods that loosely model data statistics are sometimes applied. As an alternative, we present a general imaging model relating the degraded measurements to the sinogram of ideal line integrals and propose to estimate these line integrals by iteratively optimizing a statistically based objective function. We consider three different strategies for estimating the set of ideal line integrals, one based on direct estimation of ideal "monochromatic" line integrals that have been corrected for single-material beam hardening, one based on estimation of ideal "polychromatic" line integrals that can be readily mapped to monochromatic line integrals, and one based on estimation of ideal transmitted intensities, from which ideal, monochromatic line integrals can be readily estimated. The first two approaches involve maximization of a penalized Poisson-likelihood objective function while the third involves minimization of a quadratic penalized weighted least squares (PWLS) objective applied in the transmitted intensity domain. We find that at low exposure levels typical of those being considered for screening CT, the Poisson-likelihood based approaches outperform the PWLS objective as well as a standard approach based on adaptive filtering followed by deconvolution. At higher exposure levels, the approaches all perform similarly.
IEEE Transactions on Medical Imaging 09/2006; 25(8):1022-36. · 3.64 Impact Factor
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ABSTRACT: Conventional image reconstruction methods for optoacoustic tomography (OAT) assume an idealized, non-dispersive acoustic medium. However, the linear attenuation coefficient and the phase velocity of acoustic waves propagating in soft tissue depend on temporal frequency and satisfy a known dispersion law. These frequency-dependent effects are incorporated into an optoacoustic wave equation, and a corresponding reconstruction method for OAT is developed. The improvement in image fidelity that can be achieved over conventional reconstruction methods is demonstrated by use of computer-simulation studies.
Optics Letters 04/2006; 31(6):781-3. · 3.40 Impact Factor
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ABSTRACT: We have compared the performance of two different penalty choices for a penalized-likelihood sinogram-restoration strategy we have been developing. One is a quadratic penalty we have employed previously and the other is a new median-based penalty. We compared the approaches to a noniterative adaptive filter that loosely but not explicitly models data statistics. We found that the two approaches produced similar resolution-variance tradeoffs to each other and that they outperformed the adaptive filter in the low-dose regime, which suggests that the particular choice of penalty in our approach may be less important than the fact that we are explicitly modeling data statistics at all. Since the quadratic penalty allows for derivation of an algorithm that is guaranteed to monotonically increase the penalized-likelihood objective function, we find it to be preferable to the median-based penalty.
International Journal of Biomedical Imaging 01/2006; 2006:41380.
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IEEE Trans. Med. Imaging. 01/2006; 25:1022-1036.
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Int. J. Biomedical Imaging. 01/2006; 2006.
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Patrick J La Rivière
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ABSTRACT: We have developed a sinogram smoothing approach for low-dose computed tomography (CT) that seeks to estimate the line integrals needed for reconstruction from the noisy measurements by maximizing a penalized-likelihood objective function. The maximization is performed by an algorithm derived by use of the separable paraboloidal surrogates framework. The approach overcomes some of the computational limitations of a previously proposed spline-based penalized-likelihood sinogram smoothing approach, and it is found to yield better resolution-variance tradeoffs than this spline-based approach as well an existing adaptive filtering approach. Such sinogram smoothing approaches could be valuable when applied to the low-dose data acquired in CT screening exams, such as those being considered for lung-nodule detection.
Medical Physics 07/2005; 32(6):1676-83. · 2.83 Impact Factor
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ABSTRACT: We present a statistically principled sinogram smoothing approach for X-ray computed tomography (CT) with the intent of reducing noise-induced streak artifacts. These artifacts arise in CT when some subset of the transmission measurements capture relatively few photons because of high attenuation along the measurement lines. Attempts to reduce these artifacts have focused on the use of adaptive filters that strive to tailor the degree of smoothing to the local noise levels in the measurements. While these approaches involve loose consideration of the measurement statistics to determine smoothing levels, they do not explicitly model the statistical distributions of the measurement data. In this paper, we present an explicitly statistical approach to sinogram smoothing in the presence of photon-starved measurements. It is an extension of a nonparametric sinogram smoothing approach using penalized Poisson-likelihood functions that we have previously developed for emission tomography. Because the approach explicitly models the data statistics, it is naturally adaptive--it will smooth more variable measurements more heavily than it does less variable measurements. We find that it significantly reduces streak artifacts and noise levels without comprising image resolution.
IEEE Transactions on Medical Imaging 02/2005; 24(1):105-11. · 3.64 Impact Factor
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ABSTRACT: In this paper, the sampling and aliasing consequences of employing a quarter-detector-offset (QDO) in helical computed tomography (CT) are analyzed. QDO is often used in conventional CT to reduce in-plane aliasing by eliminating data redundancies to improve radial sampling. In helical CT, these same redundancies are exploited to improve longitudinal sampling and so it might seem ill-advised to employ QDO. The relative merit of the two geometries for helical CT is studied by conducting a multidimensional sampling analysis of projection-space sampling as well as a Fourier crosstalk analysis of crosstalk among the object's Fourier basis components. Both a standard fanbeam helical CT geometry and a hypothetical parallel-beam CT geometry, which helps illuminate the more complicated fanbeam results, are analyzed. Using the sampling analysis, it was found that the use of QDO leads to very different spectral tiling than arise when not using QDO. However, due to the shape of the essential support of the projection data spectra that arises in practice, both configurations lead to very similar or identical amounts of spectral overlap. This perspective also predicts the spatially variant longitudinal aliasing that has been observed in helical CT. The crosstalk results were consistent with those of the multidimensional sampling analysis. Thus, from the standpoint of aliasing and crosstalk, no compelling difference is found between the two geometries.
IEEE Transactions on Medical Imaging 07/2004; 23(6):738-49. · 3.64 Impact Factor
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Patrick J La Rivière
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ABSTRACT: X-ray fluorescence computed tomography (XFCT) is an emerging imaging modality that allows for the reconstruction of the distribution of nonradioactive elements within a sample from measurements of fluorescence x-rays produced by irradiation of the sample with monochromatic synchrotron radiation. XFCT is not a transmission tomography modality, but rather a stimulated emission tomography modality and thus correction for attenuation of the incident and fluorescence photons is essential if accurate images are to be obtained. In this work, we develop and characterize an approximate analytic approach to image reconstruction with attenuation correction in XFCT that is applicable when the incident beam attenuation is uniform and when a factor involving fluorescence attenuation and solid angle effects satisfies a certain approximation. When these conditions hold, we demonstrate that the XFCT imaging equation reduces to the exponential Radon transform, which can be readily inverted. The necessary approximation worsens as the total fluorescence attenuation in the sample grows, but the approach is found to be relatively robust as the approximation breaks down. In a long-axis, small solid angle geometry the proposed approach performs comparably to a previously proposed, more computationally expensive approximate method across a range of attenuation levels. In a short-axis, large solid angle geometry, the proposed approach is found to outperform this previous method.
Physics in Medicine and Biology 07/2004; 49(11):2391-405. · 2.83 Impact Factor
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ABSTRACT: We have investigated the effect of computed tomography (CT) image reconstruction algorithm on the performance of our automated lung nodule detection method. Commercial CT scanners offer a choice of several algorithms for the reconstruction of projection data into transaxial images. Different algorithms produce images with substantially different properties that are apparent not only quantitatively, but also through visual assessment. During some clinical thoracic CT examinations, patient scans are reconstructed with multiple reconstruction algorithms. Thirty-eight such cases were collected to form two databases: one with patient projection data reconstructed with the "standard" reconstruction algorithm and the other with the same patient projection data reconstructed with the "lung" reconstruction algorithm. The automated nodule detection method was applied to both databases. This method is based on gray-level-thresholding techniques to segment the lung regions from each CT section to create a segmented lung volume. Further gray-level-thresholding techniques are applied within the segmented lung volume to identify a set of lung nodule candidates. Rule-based and linear discriminant classifiers are used to differentiate between lung nodule candidates that correspond to actual nodules and those that correspond to non-nodules. The automated method that was applied to both databases was exactly the same, except that the classifiers were calibrated separately for each database. For comparison, the classifier then was trained on one database and tested independently on the other database. When applied to the databases in this manner, the automated method demonstrated overall a similar level of performance, indicating an encouraging degree of robustness.
Medical Physics 04/2003; 30(3):461-72. · 2.83 Impact Factor
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ABSTRACT: In this study, we examine longitudinal aliasing properties in multislice helical computed tomography (CT) volumes reconstructed under the multiple parallel fanbeam approximation by use of a 180LI-type algorithm. We focus on the differences between the multislice case and the single-slice case, which has been studied previously. Specifically, we examine longitudinal aliasing properties in four-slice scanners for helical pitches 3 and 6, which are sometimes called "preferred" in four-slice helical CT, because it is believed that the effective longitudinal sampling intervals at these pitches are equivalent to those in single-slice helical CT operating at pitches 1 and 2, respectively. While these equivalences have been supported by comparative studies of slice-sensitivity profiles in single- and multislice helical CT, artifacts have been observed in pitch-3 and pitch-6 multislice images that were not evident in their purported single-slice counterparts. We attribute these differences to aliasing arising in the multislice reconstructions that is not present in the single-slice counterparts. We find that the aliasing has two principal origins: sampling effects similar to those in the single-slice case and cone-beam effects. The difference between the multislice, pitch-3 and single-slice, pitch-1 results is attributed to the small cone angle in multislice helical CT, which introduces inconsistencies among the measurements of different detector rows. The difference between multislice, pitch-6 and single-slice, pitch-2 results is attributed to a combination of the cone angle and genuine differences in sampling patterns. It is argued, however, that the lack of strict equivalence with single-slice counterparts does not necessarily undermine the claim that pitches 3 and 6 are "preferred" relative to other pitches in multislice helical CT.
IEEE Transactions on Medical Imaging 12/2002; 21(11):1366-73. · 3.64 Impact Factor
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ABSTRACT: In this work, we investigate longitudinal sampling and aliasing effects in multi-slice helical CT. We demonstrate that longitudinal aliasing can be a significant, complicated, and potentially detrimental effect in multi-slice helical CT reconstructions. Multi-slice helical CT scans are generally undersampled longitudinally for all pitches of clinical interest, and the resulting aliasing effects are spatially variant. As in the single-slice case, aliasing is shown to be negligible at the isocentre for circularly symmetric objects due to a fortuitous aliasing cancellation phenomenon. However, away from the isocentre, aliasing effects can be significant, spatially variant, and highly pitch dependent. This implies that measures more sophisticated than isocentre slice sensitivity profiles are needed to characterize longitudinal properties of multi-slice helical CT systems. Such measures are particularly important in assessing the question of whether there are preferred pitches in helical CT. Previous analyses have generally focused only on isocentre sampling patterns, and our more global analysis leads to somewhat different conclusions than have been reached before, suggesting that pitches 3, 4, 5, and 6 are favourable, and that half-integer pitches are somewhat suboptimal.
Physics in Medicine and Biology 09/2002; 47(15):2797-810. · 2.83 Impact Factor
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ABSTRACT: Spatially variant longitudinal aliasing plagues most volumes reconstructed from single-slice helical computed tomography data, and its presence can degrade resolution and distort image structures. We have recently developed a Fourier-based approach to longitudinal interpolation in helical computed tomography that can, for scans performed at pitch 1 or lower, essentially eliminate this longitudinal aliasing by exploiting a generalization of the Whittaker-Shannon sampling theorem whose conditions are satisfied by the interlaced pairs of direct and complementary longitudinal samples. However, the algorithm is computationally intensive and cannot be pipelined. In this paper, we address this shortcoming by deriving two spatial-domain, projection-data weighting functions that approximate the application of the Fourier-based approach, and preserve its aliasing suppression properties to some degree, while allowing for a pipelined implementation. The first approach, which we call simply 180AA, for anti-aliasing, is a direct spatial-domain approximation of the 180FT approach. The second approach, which we call 180BSP, is based on an approximate generalized interpolation approach making use of B-splines. Studies of aliasing and resolution properties in reconstructions from simulated data indicate that while the 180AA and 180BSP approaches do not perfectly replicate the favorable aliasing suppression and resolution properties of the 180FT approach, they do represent an improvement over the clinically standard 180LI approach on these fronts.
IEEE Transactions on Medical Imaging 09/2002; 21(8):978-90. · 3.64 Impact Factor
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ABSTRACT: Volumes reconstructed by standard methods from single-slice helical computed tomography (CT) data have been shown to have noise levels that are highly nonuniform relative to those in conventional CT. These noise nonuniformities can affect low-contrast object detectability and have also been identified as the cause of the zebra artifacts that plague maximum intensity projection (MIP) images of such volumes. While these spatially variant noise levels have their root in the peculiarities of the helical scan geometry, there is also a strong dependence on the interpolation and reconstruction algorithms employed. In this paper, we seek to develop image reconstruction strategies that eliminate or reduce, at its source, the nonuniformity of noise levels in helical CT relative to that in conventional CT. We pursue two approaches, independently and in concert. We argue, and verify, that Fourier-based longitudinal interpolation approaches lead to more uniform noise ratios than do the standard 360LI and 180LI approaches. We also demonstrate that a Fourier-based fan-to-parallel rebinning algorithm, used as an alternative to fanbeam filtered backprojection for slice reconstruction, also leads to more uniform noise ratios, even when making use of the 180LI and 360LI interpolation approaches.
Medical Physics 07/2002; 29(6):943-51. · 2.83 Impact Factor
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IEEE Trans. Med. Imaging. 01/2002; 21:1366-1373.
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IEEE Trans. Med. Imaging. 01/2000; 19:773-786.
