P.J. La Riviere

Reduction of noise-induced streak artifacts in X-ray computed tomography through spline-based penalized-likelihood sinogram smoothing

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. 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.

Nonparametric regression sinogram smoothing using a roughness-penalized Poisson likelihood objective function

The authors develop and investigate an approach to tomographic image reconstruction in which nonparametric regression using a roughness-penalized Poisson likelihood objective function is used to smooth each projection independently prior to reconstruction by unapodized filtered backprojection (FBP). As an added generalization, the roughness penalty is expressed in terms of a monotonic transform, known as the link function, of the projections. The approach is compared to shift-invariant projection filtering through the use of a Hanning window as well as to a related nonparametric regression approach that makes use of an objective function based on weighted least squares (WLS) rather than the Poisson likelihood. The approach is found to lead to improvements in resolution-noise tradeoffs over the Hanning filter as well as over the WLS approach. The authors also investigate the resolution and noise effects of three different link functions: the identity, square root, and logarithm links. The choice of link function is found to influence the resolution uniformity and isotropy properties of the reconstructed images. In particular, in the case of an idealized imaging system with intrinsically uniform and isotropic resolution, the choice of a square root link function yields the desirable outcome of essentially uniform and isotropic resolution in reconstructed images, with noise performance still superior to that of the Hanning filter as well as that of the WLS approach.

Monotonic penalized-likelihood image reconstruction for X-ray fluorescence computed tomography

In this work, we derive a monotonic penalized-likelihood algorithm for image reconstruction in X-ray fluorescence CT (XFCT) when the attenuation maps at the energies of the fluorescence X-rays are unknown. XFCT is not a transmission tomography modality but rather a stimulated emission tomography modality, and it is thus necessary to correct for attenuation of the incident and fluorescence photons if accurate images are to be obtained. This is challenging because the attenuation map is, in general, known only at the stimulating beam energy and not at the various fluorescence energies. 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 elements fluorescence X-rays. As derived, the approach is guaranteed to increase the penalized likelihood at each iteration.

Effects of Different Imaging Models on Least-Squares Image Reconstruction Accuracy in Photoacoustic Tomography

In the classic formulation of photoacoustic tomography (PAT), two distinct descriptions of the imaging model have been employed for developing reconstruction algorithms. We demonstrate that the numerical and statistical properties of unweighted least-squares reconstruction algorithms associated with each imaging model are generally very different. Specifically, some PAT reconstruction algorithms, including many of the iterative algorithms previously explored, do not work directly with the raw measured pressure wavefields, but rather with an integrated data function that is obtained by temporally integrating the photoacoustic wavefield. The integration modifies the statistical distribution of the data, introducing statistical correlations among samples. This change is highly significant for iterative algorithms, many of which explicitly or implicitly seek to minimize a statistical cost function. In this work, we demonstrate that iterative reconstruction by least-squares minimization yields better resolution-noise tradeoffs when working with the raw pressure data than with the integrated data commonly employed. In addition, we demonstrate that the raw-data based approach is less sensitive to certain deterministic errors, such as dc offset errors.

Correction for Resolution Nonuniformities Caused by Anode Angulation in Computed Tomography

Most X-ray tubes comprise a rotating anode that is bombarded with electrons to produce X-rays. A substantial amount of heat is generated, and to increase the area of the anode exposed to the electrons, without increasing the apparent size of the focal spot, the focal track of the anode is generally beveled with a very shallow angle (typically 5deg-7deg in a computed tomography (CT) tube). Due to the line focus principle, this allows a fairly large area of the focal track to be exposed to electrons while retaining a fairly small effective projected focal spot. One side effect of anode angulation is that the focal spot appears different from different positions in the detector array; the effective focal spot size at a constant distance from the tube will be larger for a peripheral detector channel than for a central one. These differences in the effective size of the focal spot across the fleld-of-view lead to worse resolution in the periphery than in the center of reconstructed images. In this work we describe a method for achieving more uniform resolution in fanbeam CT images by correcting for these focal spot angulation effects. We do so by modeling the effects as a series of local blurrings in the space of transmitted CT intensities and determining the effective coefficients of the corresponding discrete convolutions. The effect of these blurrings can then be compensated for in the sinogram domain through the use of a penalized-likelihood sinogram restoration model we have recently developed.

Reduced-Scan Schemes for X-Ray Fluorescence Computed Tomography

X-ray fluorescence computed tomography (XFCT) is a synchrotron-based imaging modality employed for mapping the distribution of elements within slices or volumes of intact specimens. A pencil beam of external radiation is used to stimulate emission of characteristic X-rays from within a sample, which is scanned and rotated through the pencil beam in a first-generation tomographic geometry. The measurements so obtained can be represented as generalizations of the attenuated Radon transform. The range of angular scanning employed is the subject of some variability in the XFCT imaging community, as some groups rotate the object through a full 360deg, while others employ only a 180deg rotation. In both cases, the entire object is scanned through the beam at each projection view. The use of a 180deg rotation is sometimes justified by implicit reference to a well-known symmetry property of the Radon transform, but that symmetry does not hold for the attenuated Radon transform. In this work, we demonstrate that a full scan of the object at each view coupled with a 360deg rotation does contain a two-fold data redundancy. While the redundancy does not give rise to a simple symmetry condition as in the case of the Radon transform, we will show that it does indeed license the use of the 180deg scheme. However, we will also demonstrate that when there is a single external fluorescence detector, the redundancy also licenses a potentially more attractive reduced-scan scheme, in which the object is rotated through a full 360deg, but in which only the half of the object closest to the fluorescence detector is scanned at each projection view. This new scheme may permit both reduced imaging times and improved image quality.

Transmission image reconstruction and redundant information in SPECT with asymmetric fanbeam collimation

Two novel approaches for the reconstruction of asymmetric fanbeam transmission computed tomography data are discussed. The first, called the hybrid approach, involves a Fourier-based rebinning of the fanbeam data into parallel-beam data, Reconstruction then proceeds by use of filtered backprojection (FBP). The second approach, called generalized fanbeam filtered backprojection (GFFBP), involves direct fanbeam FBP reconstruction of a modified fanbeam sinogram. In both cases, the data are multiplied by weight functions that seek to appropriately normalize redundant data while exploiting them for noise reduction. The GFFBP approach is found to have resolution-noise tradeoffs superior to those of the hybrid approach for low degrees of smoothing, although for the higher levels of smoothing likely to be of interest in practical situations, the difference between the approaches is negligible. However, GFFBPs distance-dependent fanbeam backprojection factor also produced a high-intensity peripheral artifact that impinged slightly upon the object of interest. Because it ultimately makes use of parallel-beam FBP for reconstruction, the hybrid approach avoids this artifact.

Sampling and aliasing consequences of quarter-detector offset use in helical CT

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 objects 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.

Few-view tomography using roughness-penalized nonparametric regression and periodic spline interpolation

The ability to reconstruct high-quality tomographic images from a smaller number of projections than is usually used could reduce imaging time for many nuclear-medicine studies. This would particularly benefit studies such as cardiac SPECT where patient motion during long acquisitions can lead to motion artifacts in the reconstructed images. To this end, the authors have investigated sinogram pre-processing techniques designed to enable filtered backprojection (FBP) to produce high-quality reconstructions from a small number of views. Each projection is first smoothed by performing roughness-penalized nonparametric regression using a generalized linear model that explicitly accounts for the Poisson statistics of the data. The resulting fit curves are natural cubic splines. After smoothing, additional angular views are generated using periodic spline interpolation, and images are reconstructed using FBP. The algorithm was tested on data from SPECT studies of a cardiac phantom placed at various radial offsets to enable examination of the algorithms dependence on the radial extent of the object being imaged.

Ideal-observer analysis of lesion detectability in planar, conventional SPECT, and dedicated SPECT scintimammography using effective multi-dimensional smoothing

Scintimammography, a nuclear-medicine imaging technique that relies on the preferential uptake of Tc-99m-sestamibi and other radionuclides in breast malignancies, has the potential to provide differentiation of mammographically suspicious lesions, as well as outright detection of malignancies in women with radiographically dense breasts. In this work we use the ideal-observer framework to quantify the detectability of a 1-cm lesion using three different imaging geometries: the planar technique that is the current clinical standard, conventional single-photon emission computed tomography (SPECT), in which the scintillation cameras rotate around the entire torso, and dedicated breast SPECT, in which the cameras rotate around the breast alone. We also introduce an adaptive smoothing technique for the processing of planar images and of sinograms that exploits Fourier transforms to achieve effective multidimensional smoothing at a reasonable computational cost. For the detection of a 1-cm lesion with a clinically typical 6:1 tumor-background ratio, we find ideal-observer signal-to-noise ratios (SNR) that suggest that the dedicated breast SPECT geometry is the most effective of the three, and that the adaptive, two-dimensional smoothing technique should enhance lesion detectability in the tomographic reconstructions.