X. Pan

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.

Noise properties of periodic interpolation methods with implications for few-view tomography

A number of methods exist specifically for the interpolation of periodic functions from a finite number of samples. When the samples are known exactly, exact interpolation is possible under certain conditions, such as when the function is bandlimited to the Nyquist frequency of the samples. However, when the samples are corrupted by noise, it is just as important to consider the noise properties of the resulting interpolated curve as it is to consider its accuracy. In this work, the authors derive analytic expressions for the covariance and variance of curves interpolated by three periodic interpolation methods-circular sampling theorem, zero-padding, and periodic spline interpolation-when the samples are corrupted by additive, zero-mean noise. The authors perform empirical studies for the special cases of white and Poisson noise and find the results to be in agreement with the analytic derivations. The implications of these findings for few-view tomography are also discussed.

Image reconstruction with a half-detector in single-photon emission computed tomography with nonuniform attenuation

In parallel beam computed tomography, measured projections at conjugate views are mathematically identical. This symmetry can be exploited for either reducing the scanning angle or the size of the detector arrays. In single-photon emission computed tomography (SPECT), because the gamma rays in the conjugate views suffer different photon attenuation, measured projections at conjugate views are generally different. Therefore, it had been widely considered that projections covering 360 deg and the whole detector face are required for exact reconstruction of the distributions of gamma-ray emitters. In this work, we show that projections covering 360 deg, but acquired with a half-detector viewing half of the image space, provide the necessary information to reconstruct a unique image in SPECT with nonuniform attenuation.

Asymmetric fan-beam configurations with spatially varying focal lengths and shift-variant filtering reconstruction

We present an algorithm for image reconstruction from data acquired by use of an asymmetric fan-beam configuration with a spatially varying focal length. This algorithm is a natural generalization of our previous algorithm for fan-beam computed tomography (CT) that involves shift-variant filtering, and it possesses desirable noise and numerical properties similar to those in the previous algorithm. We performed computer simulation studies to validate and evaluate the proposed algorithm, and quantitative results demonstrate that the proposed algorithm possesses desirable noise and numerical properties. The filtered backprojection algorithm can reconstruct images from data acquired in a configuration with a constant focal length. In this situation, the proposed algorithm yields images with lower and more uniform noise properties than the filtered backprojection algorithm.

Preliminary investigation on algorithm-enabled PET-configuration design

The reduction of detectors in PET systems, without significantly compromising the PET utility, is an important cost consideration in a PET-system design. Recent advances in algorithm development can be used for enabling the design and assessment of innovative PET systems. In this work, we investigate PET configurations with reduced number of detectors by using the ASD-POCS algorithm that was developed originally for image reconstruction in CT. We carry out simulation studies that demonstrate the potential of the algorithm in enabling the design of advanced PET imaging configurations with reduced number of detectors.

Preliminary study of optimization-based image reconstruction from dental cone-beam CT data

Cone-beam CT (CBCT) has gained considerable popularity in dentistry over the past decade. The increasing use of dental CBCT also raised concern about potential radiation risk. It is thus desirable to lower the radiation dose in CBCT data acquisition. However, image quality may be degraded when current analytic-based algorithms are used for reconstructing images from low-dose CBCT data. Recently, optimization-based algorithms have been investigated for image reconstruction from data containing high levels of noise. In this work, we apply an optimization-based algorithm to reconstructing images from standard- and low-dose dental CBCT data sets. The result shows that optimization-based reconstructions from standard-dose data are comparable to images clinically used, and that optimization-based reconstructions from low-dose data show improved quality over clinical ones.

A preliminary investigation of image reconstruction with variable resolutions in diagnostic CT

For certain applications in tomographic imaging, precise knowledge of the image within a regions of interest (ROI) is often desired, while rough knowledge outside the ROI is sufficient. Conventional iterative algorithms can only yield image values on uniform grids. It is of practical merit to develop iterative algorithms for image reconstruction with variable resolutions - a high-resolution ROI image and a coarse image outside the ROI. In this work, we investigate optimization-based algorithms for image reconstruction with variable spatial resolutions. We apply the modified algorithms to real cadaver data acquired with a Toshiba diagnostic CT scanner. The results of our study show that optimization-based algorithms can be developed for yielding image reconstruction on grids with variable resolutions. This work may also have implications for lowering computation load.

Few-view tomography using interpolating and smoothing splines with implications for cardiac SPECT

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 (EBP) 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 nature 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.

Direct spline-based inversion of the three-dimensional Radon transform with application to cardiac phantom data

While the exact inverse three-dimensional Radon transform is a continuous integral equation, the discrete nature of the data output by tomographic imaging systems demands that images be reconstructed using a discrete approximation to the transform. However, by fitting an analytic function to the planar-integral data prior to reconstruction, one can avoid such approximations and preserve and exploit the continuous nature of the inverse transform. The authors present methods for the evaluation of the inverse 3D Radon transform in which cubic spline functions are fit to the planar-integral data, allowing exact computation of the second derivative that appears in the inversion formula and also eliminating the need for interpolation upon backprojection. This approach is theoretically intriguing and has the advantage of directness when one wishes to smooth noisy data prior to reconstruction. In this case, a smoothing spline can be fit to the data and reconstruction can proceed directly from the spline coefficients. The authors find that the 3D direct-spline algorithm has superior resolution to 3D filtered backprojection, albeit with higher noise, and that it has a slightly lower ideal-observer signal-to-noise ratio for the detection of a 1-cm, spherical lesion with a 6:1 lesion-background concentration ratio.