The availability of accurately aligned, whole-body anatomical (CT) and functional (PET) images could have a significant impact on diagnosing and staging malignant disease and on identifying and localizing metastases. Computer algorithms to align CT and PET images acquired on different scanners are generally successful for the brain, whereas image alignment in other regions of the body is more problematic. Methods: A combined PET/CT tomograph with the unique capability of acquiring accurately aligned functional and anatomical images for any part of the human body has been designed and built. The PET/CT scanner was developed as a combination of a Siemens Somatom AR.SP spiral CT and a partial-ring, rotating ECAT ART PET scanner. All components are mounted on a common rotational support within a single gantry. The PET and CT components can be operated either separately, or in combined mode. In combined mode, the CT images are used to correct the PET data for scatter and attenuation. Fully quantitative whole-body images are obtained for an axial extent of 100 cm in an imaging time of less than 1 h. When operated in PET mode alone, transmission scans are acquired with dual 137Cs sources. Results: The scanner is fully operational and the combined device has been operated successfully in a clinical environment. Over 110 patients have been imaged, covering a range of different cancers, including lung, esophageal, head and neck, melanoma, lymphoma, pancreas, and renal cell. The aligned PET and CT images are used both for diagnosing and staging disease and for evaluating response to therapy. We report the first performance measurements from the scanner and present some illustrative clinical studies acquired in cancer patients. Conclusion: A combined PET and CT scanner is a practical and effective approach to acquiring co-registered anatomical and functional images in a single scanning session.

https://jnm.snmjournals.org/content/jnumed/41/8/1369.full.pdf

A combined PET/CT scanner for clinical oncology.

Let T be a (possibly nonlinear) continuous operator on Hilbert space . If, for some starting vector x, the orbit sequence {Tkx,k = 0,1,...} converges, then the limit z is a fixed point of T; that is, Tz = z. An operator N on a Hilbert space is nonexpansive?(ne) if, for each x and y in , Even when N has fixed points the orbit sequence {Nkx} need not converge; consider the example N = ?I, where I denotes the identity operator. However, for any the iterative procedure defined by converges (weakly) to a fixed point of N whenever such points exist. This is the Krasnoselskii?Mann (KM) approach to finding fixed points of ne operators. A wide variety of iterative procedures used in signal processing and image reconstruction and elsewhere are special cases of the KM iterative procedure, for particular choices of the ne operator N. These include the Gerchberg?Papoulis method for bandlimited extrapolation, the SART algorithm of Anderson and Kak, the Landweber and projected Landweber algorithms, simultaneous and sequential methods for solving the convex feasibility problem, the ART and Cimmino methods for solving linear systems of equations, the CQ algorithm for solving the split feasibility problem and Dolidze's procedure for the variational inequality problem for monotone operators.

http://iopscience.iop.org/article/10.1088/0266-5611/20/1/006/pdf

A unified treatment of some iterative algorithms in signal processing and image reconstruction

Positron emission tomography (PET) provides metabolic information that has been documented to be useful in patient care. The properties of positron decay permit accurate imaging of the distribution of positron-emitting radiopharmaceuticals. The wide array of positron-emitting radiopharmaceuticals has been used to characterize multiple physiologic and pathologic states. PET is used for characterizing brain disorders such as Alzheimer disease and epilepsy and cardiac disorders such as coronary artery disease and myocardial viability. The neurologic and cardiac applications of PET are not covered in this review. The major utilization of PET clinically is in oncology and consists of imaging the distribution of fluorine 18 fluorodeoxyglucose (FDG). FDG, an analogue of glucose, accumulates in most tumors in a greater amount than it does in normal tissue. FDG PET is being used in diagnosis and follow-up of several malignancies, and the list of articles supporting its use continues to grow. In this review, the ph...

Clinical Applications of PET in Oncology

Celebrating the 20th anniversary of the presentation of the paper by Dempster, Laird and Rubin which popularized the EM algorithm, we investigate, after a brief historical account, strategies that aim to make the EM algorithm converge faster while maintaining its simplicity and stability (e.g. automatic monotone convergence in likelihood). First we introduce the idea of a ‘working parameter’ to facilitate the search for efficient data augmentation schemes and thus fast EM implementations. Second, summarizing various recent extensions of the EM algorithm, we formulate a general alternating expectation–conditional maximization algorithm AECM that couples flexible data augmentation schemes with model reduction schemes to achieve efficient computations. We illustrate these methods using multivariate t-models with known or unknown degrees of freedom and Poisson models for image reconstruction. We show, through both empirical and theoretical evidence, the potential for a dramatic reduction in computational time with little increase in human effort. We also discuss the intrinsic connection between EM-type algorithms and the Gibbs sampler, and the possibility of using the techniques presented here to speed up the latter. The main conclusion of the paper is that, with the help of statistical considerations, it is possible to construct algorithms that are simple, stable and fast.

The EM Algorithm—an Old Folk‐song Sung to a Fast New Tune

This paper presents two new rebinning algorithms for the reconstruction of three-dimensional (3-D) positron emission tomography (PET) data. A rebinning algorithm is one that first sorts the 3-D data into an ordinary two-dimensional (2-D) data set containing one sinogram for each transaxial slice to be reconstructed; the 3-D image is then recovered by applying to each slice a 2-D reconstruction method such as filtered-backprojection. This approach allows a significant speedup of 3-D reconstruction, which is particularly useful for applications involving dynamic acquisitions or whole-body imaging. The first new algorithm is obtained by discretizing an exact analytical inversion formula. The second algorithm, called the Fourier rebinning algorithm (FORE), is approximate but allows an efficient implementation based on taking 2-D Fourier transforms of the data. This second algorithm was implemented and applied to data acquired with the new generation of PET systems and also to simulated data for a scanner with an 18/spl deg/ axial aperture. The reconstructed images were compared to those obtained with the 3-D reprojection algorithm (3DRP) which is the standard "exact" 3-D filtered-backprojection method. Results demonstrate that FORE provides a reliable alternative to 3DRP, while at the same time achieving an order of magnitude reduction in processing time.

Exact and approximate rebinning algorithms for 3-D PET data

The authors define ordered subset processing for standard algorithms (such as expectation maximization, EM) for image restoration from projections. Ordered subsets methods group projection data into an ordered sequence of subsets (or blocks). An iteration of ordered subsets EM is defined as a single pass through all the subsets, in each subset using the current estimate to initialize application of EM with that data subset. This approach is similar in concept to block-Kaczmarz methods introduced by Eggermont et al. (1981) for iterative reconstruction. Simultaneous iterative reconstruction (SIRT) and multiplicative algebraic reconstruction (MART) techniques are well known special cases. Ordered subsets EM (OS-EM) provides a restoration imposing a natural positivity condition and with close links to the EM algorithm. OS-EM is applicable in both single photon (SPECT) and positron emission tomography (PET). In simulation studies in SPECT, the OS-EM algorithm provides an order-of-magnitude acceleration over EM, with restoration quality maintained. >

H.M. Hudson

Papers

Accelerated image reconstruction using ordered subsets of projection data