Chris Kamphuis

Accelerated iterative transmission CT reconstruction using an ordered subsets convex algorithm

Iterative maximum likelihood (ML) transmission computed tomography algorithms have distinct advantages over Fourier-based reconstruction, but unfortunately require increased computation time. The convex algorithm is a relatively fast iterative ML algorithm but it is nevertheless too slow for many applications. Therefore, an acceleration of this algorithm by using ordered subsets of projections is proposed [ordered subsets convex algorithm (OSC)]. OSC applies the convex algorithm sequentially to subsets of projections, OSC was compared with the convex algorithm using simulated and physical thorax phantom data. Reconstructions were performed for OSC using eight and 16 subsets (eight and four projections/subset, respectively). Global errors, image noise, contrast recovery, and likelihood increase were calculated. Results show that OSC is faster than the convex algorithm, the amount of acceleration being approximately proportional to the number of subsets in OSC, and it causes only a slight increase of noise and global errors in the reconstructions. Images and image profiles of the reconstructions were in good agreement, In conclusion, OSC and the convex algorithm result in similar image quality but OSC is more than an order of magnitude faster.

Ordered subset reconstruction for x-ray CT

Statistical methods for image reconstruction such as the maximum likelihood expectation maximization are more robust and flexible than analytical inversion methods and allow for accurate modelling of the counting statistics and photon transport during acquisition of projection data. Statistical reconstruction is prohibitively slow when applied to clinical x-ray CT due to the large data sets and the high number of iterations required for reconstructing high-resolution images. Recently, however, powerful methods for accelerating statistical reconstruction have been proposed which, instead of accessing all projections simultaneously for updating an image estimate, are based on accessing a subset of projections at the time during iterative reconstruction. In this paper we study images generated by the convex algorithm accelerated by the use of ordered subsets (the OS convex algorithm (OSC)) for data sets with sizes, noise levels and spatial resolution representative of x-ray CT imaging. It is only in the case of extremely high acceleration factors (higher than 50, corresponding to fewer than 20 projections per subset), that areas with incorrect grey values appear in the reconstructed images, and that image noise increases compared with the standard convex algorithm. These image degradations can be adequately corrected for by running the final iteration of OSC with a reduced number of subsets. Even by applying such a relatively slow final iteration, OSC produces almost an equal resolution and lesion contrast as the standard convex algorithm, but more than two orders of magnitude faster.

Improved SPECT quantitation using fully three-dimensional iterative spatially variant scatter response compensation

The quality and quantitative accuracy of iteratively reconstructed SPECT images improves when better point spread function (PSF) models of the gamma camera are used during reconstruction. Here, inclusion in the PSF model of photon crosstalk between different slices caused by limited gamma camera resolution and scatter is examined. A three-dimensional (3-D) projector back-projector (proback) has been developed which models both the distance dependent detector point spread function and the object shape-dependent scatter point spread function of single photon emission computed tomography (SPECT). A table occupying only a few megabytes of memory is sufficient to represent this scatter model. The contents of this table are obtained by evaluating an analytical expression for object shape-dependent scatter. The proposed approach avoids the huge memory requirements of storing the full transition matrix needed for 3-D reconstruction including object shape-dependent scatter. In addition, the method avoids the need for lengthy Monte Carlo simulations to generate such a matrix. In order to assess the quantitative accuracy of the method, reconstructions of a water filled cylinder containing regions of different activity levels and of simulated 3-D brain projection data have been evaluated for technetium-99m. It is shown that fully 3-D reconstruction including complete detector response and object shape-dependent scatter modeling clearly outperforms simpler methods that lack a complete detector response and/or a complete scatter response model. Fully 3-D scatter correction yields the best quantitation of volumes of interest and the best contrast-to-noise curves.

Dual matrix ordered subsets reconstruction for accelerated 3D scatter compensation in single-photon emission tomography

Abstract. Three-dimensional (3D) iterative maximum likelihood expectation maximization (ML-EM) algorithms for single-photon emission tomography (SPET) are capable of correcting image-degrading effects of non-uniform attenuation, distance-dependent camera response and patient shape-dependent scatter. However, the resulting improvements in quantitation, resolution and signal-to-noise ratio (SNR) are obtained at the cost of a huge computational burden. This paper presents a new acceleration method for ML-EM: dual matrix ordered subsets (DM-OS). DM-OS combines two acceleration methods: (a) different matrices for projection and back-projection and (b) ordered subsets of projections. DM-OS was compared with ML-EM on simulated data and on physical thorax phantom data, for both 180° and 360° orbits. Contrast, normalized standard deviation and mean squared error were calculated for the digital phantom experiment. DM-OS resulted in similar image quality to ML-EM, even for speed-up factors of 200 compared to ML-EM in the case of 120 projections. The thorax phantom data could be reconstructed 50 times faster (60 projections) using DM-OS with preservation of image quality. ML-EM and DM-OS with scatter compensation showed significant improvement of SNR compared to ML-EM without scatter compensation. Furthermore, inclusion of complex image formation models in the computer code is simplified in the case of DM-OS. It is thus shown that DM-OS is a fast and relatively simple algorithm for 3D iterative scatter compensation, with similar results to conventional ML-EM, for both 180° and 360° acquired data.

Evaluation of OS-EM vs. ML-EM for 1D, 2D and fully 3D SPECT reconstruction

For SPECT reconstruction, iterative Maximum Likelihood Expectation Maximization (ML-EM) estimation has a huge computational burden. The objective of this paper is to compare images obtained by ML-EM and an EM algorithm acting on Ordered Subsets of projections (OS-EM). Two digital phantoms, a cylinder with two cold spots and an ellipsoid with several hot spots and one cold spot were reconstructed from 120 simulated noisy projections. 1D (/spl delta/-like point source response), 2D (single slice response) and fully 3D reconstruction were investigated. Three quantities were calculated for the evaluation, viz. contrast, normalized standard deviation and mean squared error. In the case of fully 3D reconstruction, OS-EM 60 reconstructions (i.e., using 60 ordered subsets) were very close to ML-EM reconstructions. This shows that the OS-EM algorithm is an extremely fast and efficient method to accelerate iterative SPECT reconstruction with speed-up factors of close to half the number of projections.

Influence of collimator hole dimensions on parallel and cone-beam brain SPECT

This study assesses the influence of collimator hole dimensions on the accuracy of brain SPECT. To this end, four low energy, parallel hole (PH) collimators and four low energy, half cone beam (CB) collimators with different hole dimensions were simulated. The simulated projection data were representative of Ultra High Resolution (UHR), High Resolution (HR), Medium Resolution (MR), and General Purpose (GP) collimators. Reconstruction was performed with the Ordered Subsets Expectation Maximization (OS-FM) algorithm with and without correction for the camera response (CRC and NCRC, respectively). The distance-dependent blurring kernel used in CRC matched the blurring used in the simulations. Image accuracy was assessed by calculating contrast-to-noise ratios (CTN) in a phantom containing cold spheres and by calculating Mean Squared Errors (MSE) between the true 3D Hoffman brain phantom and its reconstructions. For the accuracy of PH collimators, results indicate that when NCRC is applied, the UHR collimator results in better CTN ratios and lower MSE than the collimators with lower resolution. However, when CRC is applied, the GP collimator outperforms the higher resolution collimators. For the CB collimators, the low resolution collimators (GP and MR) result in the best CTN ratios and the lowest MSE, regardless if CRC is applied.

Effects of truncation of transmission projections on cardiac SPECT images acquired by a right-angle dual-camera with half-fan-beam collimators

Right-angle dual-head SPECT systems equipped with half-fan-beam collimators have some advantages compared to right-angle dual-head systems with parallel-hole collimators. A potential drawback of the half-fan-beam system in cardiac studies is that it potentially truncates the transmission data and therefore yields attenuation maps containing inaccuracies in an area to the dorso-lateral region of the torso. The objective of this study is to investigate whether the transmission projection truncation introduces artifacts into iteratively reconstructed emission images of the heart. To this end, a combined cardiac emission transmission study was simulated, modeling 514 mm wide detectors and collimators with focal line distances of 890 mm. Emission images were reconstructed iteratively on the basis of truncated and untruncated attenuation maps. The iterative reconstruction methods include the detector response, and compensate for attenuation and scatter in media with non-uniform density. The results indicate that attenuation- and scatter-corrected cardiac studies are not significantly influenced by the truncation of dorso-lateral region of the patient in the transmission projections, even if the patient is extremely large.

Accelerated SPECT reconstruction using OS-EM with only two projections per subset

In SPECT reconstruction, iterative Maximum Likelihood Expectation Maximization (ML-EM) estimation has a huge computational burden. The objective of this paper is to investigate how large a reduction in computation time can be obtained by using an algorithm acting on Ordered Subsets of projections (OS-EM). The authors validated OS-EM for a high number of subsets (which correlates with a high acceleration factor). Two phantoms, a cylinder with two cold spots and an ellipsoid with several hot spots and one cold spot were reconstructed from 120 noisy projections with the aid of a 1D (/spl delta/-like point source response), 2D (single slice response) and fully 3D PSF model. Signal-to-noise ratios (SNRs) and mean squared errors between phantoms and reconstructions as a function of contrast were calculated for OS-FM and ML-EM. Surprisingly, OS-EM outperforms ML-EM at high iteration numbers for the cylindrical phantom: OS-FM reconstructed images generally have a higher contrast at equivalent noise levels. For the ellipsoidal phantom the results of OS-EM are not superior, but certainly adequate, particularly so for the 3D PSF model, even when 60 subsets of opposing projections are used. In conclusion, the OS-EM algorithm using a high number of subsets is an extremely fast and reliable method to accelerate iterative SPECT reconstruction.

Evaluation of 2D and 3D photon scatter detection kernels for quantitative SPECT reconstruction

The quality and quantitative accuracy of iteratively reconstructed SPECT images improves when better models of the photon detection kernel are used during reconstruction, and especially when compensation for photon crosstalk between transaxial slices is performed (fully 3D reconstruction). This photon crosstalk is caused by limited gamma camera resolution and scatter and can be compensated for by fully 3D iterative detector and scatter response compensation. A fully 3D projector back-projector (proback) has been developed that evaluates both the distance dependent detector kernel and the object shape dependent photon scatter kernel of SPECT. Different models of increasing accuracy are investigated, for homogeneous attenuating media. These include 2D and 3D reconstruction with and without scatter compensation. In order to assess the quantitative accuracy of the different algorithms, reconstructions of a water filled cylinder containing regions of different activity levels were performed. In addition, reconstructions of simulated 3D brain projection data are evaluated. Fully 3D scatter compensation results in the best quantitation of regions of interest and the highest signal-to-noise ratios.