Motion-compensated Reconstruction Research Articles

Fast iterative algorithm for the reconstruction of multishot non-cartesian diffusion data.

To accelerate the motion-compensated iterative reconstruction of multishot non-Cartesian diffusion data. The motion-compensated recovery of multishot non-Cartesian diffusion data is often performed using a modified iterative sensitivity-encoded algorithm. Specifically, the encoding matrix is replaced with a combination of nonuniform Fourier transforms and composite sensitivity functions, which account for the motion-induced phase errors. The main challenge with this scheme is the significantly increased computational complexity, which is directly related to the total number of composite sensitivity functions (number of shots × number of coils). The dimensionality of the composite sensitivity functions and hence the number of Fourier transforms within each iteration is reduced using a principal component analysis-based scheme. Using a Toeplitz-based conjugate gradient approach in combination with an augmented Lagrangian optimization scheme, a fast algorithm is proposed for the sparse recovery of diffusion data. The proposed simplifications considerably reduce the computation time, especially in the recovery of diffusion data from under-sampled reconstructions using sparse optimization. By choosing appropriate number of basis functions to approximate the composite sensitivities, faster reconstruction (close to 9 times) with effective motion compensation is achieved. The proposed enhancements can offer fast motion-compensated reconstruction of multishot diffusion data for arbitrary k-space trajectories.

Self-gated MRI motion modeling for respiratory motion compensation in integrated PET/MRI.

Accurate localization and uptake quantification of lesions in the chest and abdomen using PET imaging is challenged by respiratory motion occurring during the exam. This work describes how a stack-of-stars MRI acquisition on integrated PET/MRI systems can be used to derive a high-resolution motion model, how many respiratory phases need to be differentiated, how much MRI scan time is required, and how the model is employed for motion-corrected PET reconstruction. MRI self-gating is applied to perform respiratory gating of the MRI data and simultaneously acquired PET raw data. After gated PET reconstruction, the MRI motion model is used to fuse the individual gates into a single, motion-compensated volume with high signal-to-noise ratio (SNR). The proposed method is evaluated in vivo for 15 clinical patients. The gating requires 5-7 bins to capture the motion to an average accuracy of 2mm. With 5 bins, the motion-modeling scan can be shortened to 3-4 min. The motion-compensated reconstructions show significantly higher accuracy in lesion quantification in terms of standardized uptake value (SUV) and different measures of lesion contrast compared to ungated PET reconstruction. Furthermore, unlike gated reconstructions, the motion-compensated reconstruction does not lead to SNR loss.

Image artefact propagation in motion estimation and reconstruction in interventional cardiac C-arm CT

The acquisition of data for cardiac imaging using a C-arm computed tomography system requires several seconds and multiple heartbeats. Hence, incorporation of motion correction in the reconstruction step may improve the resulting image quality. Cardiac motion can be estimated by deformable three-dimensional (3D)/3D registration performed on initial 3D images of different heart phases. This motion information can be used for a motion-compensated reconstruction allowing the use of all acquired data for image reconstruction. However, the result of the registration procedure and hence the estimated deformations are influenced by the quality of the initial 3D images. In this paper, the sensitivity of the 3D/3D registration step to the image quality of the initial images is studied. Different reconstruction algorithms are evaluated for a recently proposed cardiac C-arm CT acquisition protocol. The initial 3D images are all based on retrospective electrocardiogram (ECG)-gated data. ECG-gating of data from a single C-arm rotation provides only a few projections per heart phase for image reconstruction. This view sparsity leads to prominent streak artefacts and a poor signal to noise ratio. Five different initial image reconstructions are evaluated: (1) cone beam filtered-backprojection (FDK), (2) cone beam filtered-backprojection and an additional bilateral filter (FFDK), (3) removal of the shadow of dense objects (catheter, pacing electrode, etc) before reconstruction with a cone beam filtered-backprojection (cathFDK), (4) removal of the shadow of dense objects before reconstruction with a cone beam filtered-backprojection and a bilateral filter (cathFFDK). The last method (5) is an iterative few-view reconstruction (FV), the prior image constrained compressed sensing combined with the improved total variation algorithm. All reconstructions are investigated with respect to the final motion-compensated reconstruction quality. The algorithms were tested on a mathematical phantom data set with and without a catheter and on two porcine models using qualitative and quantitative measures. The quantitative results of the phantom experiments show that if no dense object is present within the scan field of view, the quality of the FDK initial images is sufficient for motion estimation via 3D/3D registration. When a catheter or pacing electrode is present, the shadow of these objects needs to be removed before the initial image reconstruction. An additional bilateral filter shows no major improvement with respect to the final motion-compensated reconstruction quality. The results with respect to image quality of the cathFDK, cathFFDK and FV images are comparable. In conclusion, in terms of computational complexity, the algorithm of choice is the cathFDK algorithm

Motion correction of multi-contrast images applied to T1 and T2 quantification in cardiac MRI

The ability to manipulate image contrast and thus to obtain complementary information is one of the main advantages of MRI. Motion consistency within the whole data set is a key point in the context of multi contrast imaging. In cardiac and abdominal MRI, the acquisition strategy uses multiple breath-holds and often relies on acceleration methods that inherently suffer from a signal to-noise ratio loss. The aim of this work is to propose a free-breathing multi-contrast acquisition and reconstruction workflow to improve image quality and the subsequent data analysis. We extended a previously proposed motion-compensated image reconstruction method for multi-contrast imaging. Shared information throughout the imaging protocol is now exploited by the image reconstruction in the form of an additional constraint based on image gradient sparsity. This constraint helps to minimize the amount of data needed for efficient non-rigid motion correction. T₁and T₂weighted images were reconstructed from free-breathing acquisitions in 4 healthy volunteers and in a phantom. The impact of multi-contrast motion correction was evaluated in a phantom in terms of precision and accuracy of T₁and T₂quantification. In the phantom, the proposed method achieved an accuracy of 97.5 % on the quantified parameters against 88.0 % before motion correction. In volunteers, motion inconsistency in T₁and T₂quantification were noticeably reduced within 5 min of free-breathing acquisition. An efficient, free-breathing, multi-contrast imaging method has been demonstrated that does not require prior assumptions about contrast and that is applicable to a wide range of examinations.

Effects of Piecewise Spatial Smoothing in 4-D SPECT Reconstruction

In nuclear medicine, cardiac gated SPECT images are known to suffer from significantly increased noise owing to limited data counts. Consequently, spatial (and temporal) smoothing has been indispensable for suppressing the noise artifacts in SPECT reconstruction. However, recently we demonstrated that the benefit of spatial processing in motion-compensated reconstruction of gated SPECT (aka 4-D) could be outweighed by its adverse effects on the myocardium, which included degraded wall motion and perfusion defect detectability. In this work, we investigate whether we can alleviate these adverse effects by exploiting an alternative spatial smoothing prior in 4-D based on image total variation (TV). TV based prior is known to induce piecewise smoothing which can preserve edge features (such as boundaries of the heart wall) in reconstruction. However, it is not clear whether such a property would necessarily be beneficial for improving the accuracy of the myocardium in 4-D reconstruction. In particular, it is unknown whether it would adversely affect the detectability of perfusion defects that are small in size or low in contrast. In our evaluation study, we first use Monte Carlo simulated imaging with 4-D NURBS-based cardiac-torso (NCAT) phantom wherein the ground truth is known for quantitative comparison. We evaluated the accuracy of the reconstructed myocardium using a number of metrics, including regional and overall accuracy of the myocardium, accuracy of the phase activity curve (PAC) of the LV wall for wall motion, uniformity and spatial resolution of the LV wall, and detectability of perfusion defects using a channelized Hotelling observer (CHO). For lesion detection, we simulated perfusion defects with different sizes and contrast levels with the focus being on perfusion defects that are subtle. As a preliminary demonstration, we also tested on three sets of clinical acquisitions. From the quantitative results, it was demonstrated that TV smoothing could further reduce the error level in the myocardium in 4-D reconstruction along with motion-compensated temporal smoothing. In contrast to quadratic spatial smoothing, TV smoothing could reduce the noise level in the LV at a faster pace than the increase in the bias level, thereby achieving a net decrease in the error level. In particular, at the same noise level, TV smoothing could reduce the bias by about 30% compared to quadratic smoothing. Moreover, the CHO results indicate that TV could also improve the lesion detectability even when the lesion is small. The PAC results show that, at the same noise level, TV smoothing achieved lower temporal bias, which is also consistent with the improved spatial resolution of the LV in reconstruction. The improvement in blurring effects by TV was also observed in the clinical images.

Motion-compensated PET image reconstruction with respiratory-matched attenuation correction using two low-dose inhale and exhale CT images

Positron emission tomography (PET) is widely used for diagnosis and follow up assessment of radiotherapy. However, thoracic and abdominal PET suffers from false staging and incorrect quantification of the radioactive uptake of lesion(s) due to respiratory motion. Furthermore, respiratory motion-induced mismatch between a computed tomography (CT) attenuation map and PET data often leads to significant artifacts in the reconstructed PET image. To solve these problems, we propose a unified framework for respiratory-matched attenuation correction and motion compensation of respiratory-gated PET. For the attenuation correction, the proposed algorithm manipulates a 4D CT image virtually generated from two low-dose inhale and exhale CT images, rather than a real 4D CT image which significantly increases the radiation burden on a patient. It also utilizes CT-driven motion fields for motion compensation. To realize the proposed algorithm, we propose an improved region-based approach for non-rigid registration between body CT images, and we suggest a selection scheme of 3D CT images that are respiratory-matched to each respiratory-gated sinogram. In this work, the proposed algorithm was evaluated qualitatively and quantitatively by using patient datasets including lung and/or liver lesion(s). Experimental results show that the method can provide much clearer organ boundaries and more accurate lesion information than existing algorithms by utilizing two low-dose CT images.

Artifact‐resistant motion estimation with a patient‐specific artifact model for motion‐compensated cone‐beam CT

In image-guided radiation therapy (IGRT) valuable information for patient positioning, dose verification, and adaptive treatment planning is provided by an additional kV imaging unit. However, due to the limited gantry rotation speed during treatment the typical acquisition time is quite long. Tomographic images of the thorax suffer from motion blurring or, if a gated 4D reconstruction is performed, from significant streak artifacts. Our purpose is to provide a method that reliably estimates respiratory motion in presence of severe artifacts. The estimated motion vector fields are then used for motion-compensated image reconstruction to provide high quality respiratory-correlated 4D volumes for on-board cone-beam CT (CBCT) scans. The proposed motion estimation method consists of a model that explicitly addresses image artifacts because in presence of severe artifacts state-of-the-art registration methods tend to register artifacts rather than anatomy. Our artifact model, e.g., generates streak artifacts very similar to those included in the gated 4D CBCT images, but it does not include respiratory motion. In combination with a registration strategy, the model gives an error estimate that is used to compensate the corresponding errors of the motion vector fields that are estimated from the gated 4D CBCT images. The algorithm is tested in combination with a cyclic registration approach using temporal constraints and with a standard 3D-3D registration approach. A qualitative and quantitative evaluation of the motion-compensated results was performed using simulated rawdata created on basis of clinical CT data. Further evaluation includes patient data which were scanned with an on-board CBCT system. The model-based motion estimation method is nearly insensitive to image artifacts of gated 4D reconstructions as they are caused by angular undersampling. The motion is accurately estimated and our motion-compensated image reconstruction algorithm can correct for it. Motion artifacts of 3D standard reconstruction are significantly reduced, while almost no new artifacts are introduced. Using the artifact model allows to accurately estimate and compensate for patient motion, even if the initial reconstructions are of very low image quality. Using our approach together with a cyclic registration algorithm yields a combination which shows almost no sensitivity to sparse-view artifacts and thus ensures both high spatial and high temporal resolution.

Simultaneous motion estimation and image reconstruction (SMEIR) for 4D cone‐beam CT

Image reconstruction and motion model estimation in four-dimensional cone-beam CT (4D-CBCT) are conventionally handled as two sequential steps. Due to the limited number of projections at each phase, the image quality of 4D-CBCT is degraded by view aliasing artifacts, and the accuracy of subsequent motion modeling is decreased by the inferior 4D-CBCT. The objective of this work is to enhance both the image quality of 4D-CBCT and the accuracy of motion model estimation with a novel strategy enabling simultaneous motion estimation and image reconstruction (SMEIR). The proposed SMEIR algorithm consists of two alternating steps: (1) model-based iterative image reconstruction to obtain a motion-compensated primary CBCT (m-pCBCT) and (2) motion model estimation to obtain an optimal set of deformation vector fields (DVFs) between the m-pCBCT and other 4D-CBCT phases. The motion-compensated image reconstruction is based on the simultaneous algebraic reconstruction technique (SART) coupled with total variation minimization. During the forward- and backprojection of SART, measured projections from an entire set of 4D-CBCT are used for reconstruction of the m-pCBCT by utilizing the updated DVF. The DVF is estimated by matching the forward projection of the deformed m-pCBCT and measured projections of other phases of 4D-CBCT. The performance of the SMEIR algorithm is quantitatively evaluated on a 4D NCAT phantom. The quality of reconstructed 4D images and the accuracy of tumor motion trajectory are assessed by comparing with those resulting from conventional sequential 4D-CBCT reconstructions (FDK and total variation minimization) and motion estimation (demons algorithm). The performance of the SMEIR algorithm is further evaluated by reconstructing a lung cancer patient 4D-CBCT. Image quality of 4D-CBCT is greatly improved by the SMEIR algorithm in both phantom and patient studies. When all projections are used to reconstruct a 3D-CBCT by FDK, motion-blurring artifacts are present, leading to a 24.4% relative reconstruction error in the NACT phantom. View aliasing artifacts are present in 4D-CBCT reconstructed by FDK from 20 projections, with a relative error of 32.1%. When total variation minimization is used to reconstruct 4D-CBCT, the relative error is 18.9%. Image quality of 4D-CBCT is substantially improved by using the SMEIR algorithm and relative error is reduced to 7.6%. The maximum error (MaxE) of tumor motion determined from the DVF obtained by demons registration on a FDK-reconstructed 4D-CBCT is 3.0, 2.3, and 7.1 mm along left-right (L-R), anterior-posterior (A-P), and superior-inferior (S-I) directions, respectively. From the DVF obtained by demons registration on 4D-CBCT reconstructed by total variation minimization, the MaxE of tumor motion is reduced to 1.5, 0.5, and 5.5 mm along L-R, A-P, and S-I directions. From the DVF estimated by SMEIR algorithm, the MaxE of tumor motion is further reduced to 0.8, 0.4, and 1.5 mm along L-R, A-P, and S-I directions, respectively. The proposed SMEIR algorithm is able to estimate a motion model and reconstruct motion-compensated 4D-CBCT. The SMEIR algorithm improves image reconstruction accuracy of 4D-CBCT and tumor motion trajectory estimation accuracy as compared to conventional sequential 4D-CBCT reconstruction and motion estimation.

Image quality improvements in C-Arm CT (CACT) for liver oncology applications: Preliminary study in rabbits

Introduction: C-Arm CT (CACT) is a new imaging modality in liver oncology therapy that allows for the acquisition of 3D images intra-procedurally. CACT has been used to enhance intra-arterial therapies for the liver by improving lesion detection, avoiding non-target embolization, and allowing for more selective delivery of agents. However, one of the limitations of this technology is image artifacts created by respiratory motion. Purpose: To determine in this preliminary study improvements in image acquisition, motion compensation, and high resolution 3D reconstruction that can improve CACT image quality (IQ). Material and methods: Three adult male New Zealand white rabbits were used for this study. First, a control rabbit was used to select the best x-ray acquisition imaging protocol and then two rabbits were implanted with liver tumor to further develop 3D image reconstruction and motion compensation algorithms. Results: The best IQ was obtained using the low 80 kVp protocol with motion compensated reconstruction with high resolution and fast acquisition speed (60 fps, 5 s/scan, and 312 images). Conclusion: IQ improved by: (1) decreasing acquisition time, (2) applying motion-compensated reconstruction, and (3) high resolution 3D reconstruction. The findings of this study can be applied to future animal studies and eventually could be translated into the clinical environment.

The effect of regularization in motion compensated PET image reconstruction: a realistic numerical 4D simulation study

Following continuous improvement in PET spatial resolution, respiratory motion correction has become an important task. Two of the most common approaches that utilize all detected PET events to motion-correct PET data are the reconstruct-transform-average method (RTA) and motion-compensated image reconstruction (MCIR). In RTA, separate images are reconstructed for each respiratory frame, subsequently transformed to one reference frame and finally averaged to produce a motion-corrected image. In MCIR, the projection data from all frames are reconstructed by including motion information in the system matrix so that a motion-corrected image is reconstructed directly. Previous theoretical analyses have explained why MCIR is expected to outperform RTA. It has been suggested that MCIR creates less noise than RTA because the images for each separate respiratory frame will be severely affected by noise. However, recent investigations have shown that in the unregularized case RTA images can have fewer noise artefacts, while MCIR images are more quantitatively accurate but have the common salt-and-pepper noise. In this paper, we perform a realistic numerical 4D simulation study to compare the advantages gained by including regularization within reconstruction for RTA and MCIR, in particular using the median-root-prior incorporated in the ordered subsets maximum a posteriori one-step-late algorithm. In this investigation we have demonstrated that MCIR with proper regularization parameters reconstructs lesions with less bias and root mean square error and similar CNR and standard deviation to regularized RTA. This finding is reproducible for a variety of noise levels (25, 50, 100 million counts), lesion sizes (8 mm, 14 mm diameter) and iterations. Nevertheless, regularized RTA can also be a practical solution for motion compensation as a proper level of regularization reduces both bias and mean square error.

Improving best‐phase image quality in cardiac CT by motion correction with MAM optimization

Research in image reconstruction for cardiac CT aims at using motion correction algorithms to improve the image quality of the coronary arteries. The key to those algorithms is motion estimation, which is currently based on 3-D/3-D registration to align the structures of interest in images acquired in multiple heart phases. The need for an extended scan data range covering several heart phases is critical in terms of radiation dose to the patient and limits the clinical potential of the method. Furthermore, literature reports only slight quality improvements of the motion corrected images when compared to the most quiet phase (best-phase) that was actually used for motion estimation. In this paper a motion estimation algorithm is proposed which does not require an extended scan range but works with a short scan data interval, and which markedly improves the best-phase image quality. Motion estimation is based on the definition of motion artifact metrics (MAM) to quantify motion artifacts in a 3-D reconstructed image volume. The authors use two different MAMs, entropy, and positivity. By adjusting the motion field parameters, the MAM of the resulting motion-compensated reconstruction is optimized using a gradient descent procedure. In this way motion artifacts are minimized. For a fast and practical implementation, only analytical methods are used for motion estimation and compensation. Both the MAM-optimization and a 3-D/3-D registration-based motion estimation algorithm were investigated by means of a computer-simulated vessel with a cardiac motion profile. Image quality was evaluated using normalized cross-correlation (NCC) with the ground truth template and root-mean-square deviation (RMSD). Four coronary CT angiography patient cases were reconstructed to evaluate the clinical performance of the proposed method. For the MAM-approach, the best-phase image quality could be improved for all investigated heart phases, with a maximum improvement of the NCC value by 100% and of the RMSD value by 81%. The corresponding maximum improvements for the registration-based approach were 20% and 40%. In phases with very rapid motion the registration-based algorithm obtained better image quality, while the image quality of the MAM algorithm was superior in phases with less motion. The image quality improvement of the MAM optimization was visually confirmed for the different clinical cases. The proposed method allows a software-based best-phase image quality improvement in coronary CT angiography. A short scan data interval at the target heart phase is sufficient, no additional scan data in other cardiac phases are required. The algorithm is therefore directly applicable to any standard cardiac CT acquisition protocol.

Quantitative Statistical Methods for Image Quality Assessment

Quantitative measures of image quality and reliability are critical for both qualitative interpretation and quantitative analysis of medical images. While, in theory, it is possible to analyze reconstructed images by means of Monte Carlo simulations using a large number of noise realizations, the associated computational burden makes this approach impractical. Additionally, this approach is less meaningful in clinical scenarios, where multiple noise realizations are generally unavailable. The practical alternative is to compute closed-form analytical expressions for image quality measures. The objective of this paper is to review statistical analysis techniques that enable us to compute two key metrics: resolution (determined from the local impulse response) and covariance. The underlying methods include fixed-point approaches, which compute these metrics at a fixed point (the unique and stable solution) independent of the iterative algorithm employed, and iteration-based approaches, which yield results that are dependent on the algorithm, initialization, and number of iterations. We also explore extensions of some of these methods to a range of special contexts, including dynamic and motion-compensated image reconstruction. While most of the discussed techniques were developed for emission tomography, the general methods are extensible to other imaging modalities as well. In addition to enabling image characterization, these analysis techniques allow us to control and enhance imaging system performance. We review practical applications where performance improvement is achieved by applying these ideas to the contexts of both hardware (optimizing scanner design) and image reconstruction (designing regularization functions that produce uniform resolution or maximize task-specific figures of merit).

Self‐adapting cyclic registration for motion‐compensated cone‐beam CT in image‐guided radiation therapy

In image-guided radiation therapy an additional kV imaging system next to the linear particle accelerator provides information for an accurate patient positioning. However, the acquisition time of the system is much longer than the patient's breathing cycle due to the low gantry rotation speed. Our purpose is a cyclic registration in the context of motion-compensated image reconstruction that provides high quality respiratory-correlated 4D volumes for on-board flat panel detector cone-beam CT scans. Based on the small motion assumption, widely used within registration algorithms, a strategy is developed for motion estimation. In this strategy temporal restrictions are incorporated, for example, the cyclic motion patterns of respiration. The resultant cyclic registration method is to show less sensitivity on image artifacts, in particular on artifacts due to projection data sparsification. Using a new cyclic registration method a motion estimation is performed on respiratory-correlated reconstructions, and the obtained motion vector fields are used for motion compensation. The proposed cyclic registration is evaluated in the context of motion-compensated image reconstruction using simulated data and patient data. Motion artifacts of 3D standard reconstructions can be significantly reduced by the resulting cyclic motion compensation. The method outperforms the respiratory-correlated reconstructions regarding sparse-view artifacts and maintains the high temporal resolution at the same time. Image artifacts show only minor to almost no effect on the motion estimation using the cyclic registration. The cyclic motion compensation approach provides respiratory-correlated volumes with high image quality. The cyclic motion estimation is of such low sensitivity to sparse-view artifacts, that it is capable to determine high quality motion vector fields based on reconstructions of low sampled data.

Analysis and comparison of two methods for motion correction in PET imaging

Although there have been various proposed methods for positron emission tomography (PET) motion correction, there is not sufficient evidence to answer which method is better in practice. This investigation aims to characterize the behavior of the two main motion-correction approaches in terms of convergence and image properties. For the first method, reconstruct-transform-average (RTA), reconstructions of each gate are transformed to a reference gate and averaged. In the second method, motion-compensated image reconstruction (MCIR), motion information is incorporated within the reconstruction. Both techniques studied were based on the ordered subsets expectation maximization algorithm. Motion information was obtained from a dynamic MR acquisition performed on a human volunteer and concurrent PET data were simulated from the dynamic MR data. The two approaches were assessed statistically using multiple realizations to accurately define the noise properties of the reconstructed images. MCIR successfully recovers the true values of all regions, whereas RTA has high bias due to the limited count-statistics and interpolation errors during the transformation step. In addition, RTA noise is very small and stabilized, whereas in MCIR noise becomes progressively greater with the number of iterations and therefore MCIR outperforms RTA in terms of MSE only if noise is treated. For example, MCIR with postfiltering results in MSE up to 42% lower than RTA. This study indicates that MCIR may provide superior performance overall to RTA if noise is minimized. However, in applications where quantification is not the main objective RTA can be a practical and simple method to correct for motion.

Fast simulation of x-ray projections of spline-based surfaces using an append buffer**The software and source code that was created for this paper can be found at http://conrad.stanford.edu.

Many scientists in the field of x-ray imaging rely on the simulation of x-ray images. As the phantom models become more and more realistic, their projection requires high computational effort. Since x-ray images are based on transmission, many standard graphics acceleration algorithms cannot be applied to this task. However, if adapted properly, the simulation speed can be increased dramatically using state-of-the-art graphics hardware. A custom graphics pipeline that simulates transmission projections for tomographic reconstruction was implemented based on moving spline surface models. All steps from tessellation of the splines, projection onto the detector and drawing are implemented in OpenCL. We introduced a special append buffer for increased performance in order to store the intersections with the scene for every ray. Intersections are then sorted and resolved to materials. Lastly, an absorption model is evaluated to yield an absorption value for each projection pixel. Projection of a moving spline structure is fast and accurate. Projections of size 640 × 480 can be generated within 254 ms. Reconstructions using the projections show errors below 1 HU with a sharp reconstruction kernel. Traditional GPU-based acceleration schemes are not suitable for our reconstruction task. Even in the absence of noise, they result in errors up to 9 HU on average, although projection images appear to be correct under visual examination. Projections generated with our new method are suitable for the validation of novel CT reconstruction algorithms. For complex simulations, such as the evaluation of motion-compensated reconstruction algorithms, this kind of x-ray simulation will reduce the computation time dramatically.

Noise Properties of Motion-Compensated Tomographic Image Reconstruction Methods

Motion-compensated image reconstruction (MCIR) methods incorporate motion models to improve image quality in the presence of motion. MCIR methods differ in terms of how they use motion information and they have been well studied separately. However, there have been less theoretical comparisions of different MCIR methods. This paper compares the theoretical noise properties of three popular MCIR methods assuming known nonrigid motion. We show the relationship among three MCIR methods-motion-compensated temporal regularization (MTR), the parametric motion model (PMM), and post-reconstruction motion correction (PMC)-for penalized weighted least square cases. These analyses show that PMM and MTR are matrix-weighted sums of all registered image frames, while PMC is a scalar-weighted sum. We further investigate the noise properties of MCIR methods with Poisson models and quadratic regularizers by deriving accurate and fast variance prediction formulas using an "analytical approach." These theoretical noise analyses show that the variances of PMM and MTR are lower than or comparable to the variance of PMC due to the statistical weighting. These analyses also facilitate comparisons of the noise properties of different MCIR methods, including the effects of different quadratic regularizers, the influence of the motion through its Jacobian determinant, and the effect of assuming that total activity is preserved. Two-dimensional positron emission tomography simulations demonstrate the theoretical results.

A fully four-dimensional, iterative motion estimation and compensation method for cardiac CT.

To develop a new fully four-dimensional (4D), iterative image reconstruction algorithm for cardiac CT that alternates the following two methods: estimation of a time-dependent motion vector field (MVF) of the heart from image data and reconstruction of images using the estimated MVF and projection data. Volumetric image data at different cardiac phase points were obtained using electrocardiogram-gated CT. Motion estimation (ME) and motion-compensated image reconstruction (MCR) were performed alternately until convergence was achieved. The ME method estimated the cardiac MVF using 4D nonrigid image registration between a cardiac reference phase and all the other phases. The nonrigid deformation of the heart was modeled using cubic B-splines. The cost function consisted of a sum of squared weighted differences and spatial and temporal regularization terms. A nested conjugate gradient optimization algorithm was applied to minimize the cost function and estimate the MVFs. Cardiac images were reconstructed using a motion-tracking algorithm that utilized the MVFs estimated by the ME method. The reconstructed images supplied the input to the ME of the next iteration. The performance of the proposed method was evaluated using four patient data sets acquired with a 64-slice CT scanner. The heart rates of the patients ranged from 52 to 71 beats/min. Motion artifacts were significantly reduced, and the image quality increased with the number of iterations. Without MCR, the right coronary artery (RCA) was deformed into an arc in axial images of rapid phases. With the proposed method the RCA appeared sharper and was reconstructed similar in shape to the reconstruction at the quiescent phase at mid-diastole. The boundary between the interventricular septum and the right ventricle was also clearer and sharper using the proposed algorithm. The steepness of the transition range at a rapid phase (35% R-R) was increased from 6.8 HU∕pixel to 11.5 HU∕pixel. The ME-MCR algorithm converged in just four iterations. We developed a fully 4D image reconstruction method that alternates ME and MCR algorithms in an iterative fashion. Performance tests using clinical patient data resulted in reduced motion artifacts.

Spatial Resolution Properties of Motion-Compensated Tomographic Image Reconstruction Methods

Many motion-compensated image reconstruction (MCIR) methods have been proposed to correct for subject motion in medical imaging. MCIR methods incorporate motion models to improve image quality by reducing motion artifacts and noise. This paper analyzes the spatial resolution properties of MCIR methods and shows that nonrigid local motion can lead to nonuniform and anisotropic spatial resolution for conventional quadratic regularizers. This undesirable property is akin to the known effects of interactions between heteroscedastic log-likelihoods (e.g., Poisson likelihood) and quadratic regularizers. This effect may lead to quantification errors in small or narrow structures (such as small lesions or rings) of reconstructed images. This paper proposes novel spatial regularization design methods for three different MCIR methods that account for known nonrigid motion. We develop MCIR regularization designs that provide approximately uniform and isotropic spatial resolution and that match a user-specified target spatial resolution. Two-dimensional PET simulations demonstrate the performance and benefits of the proposed spatial regularization design methods.

Registration-weighted motion correction for PET

Patient motion during a positron emission tomography (PET) scan can lead to significant resolution loss. Two of the main motion correction techniques employed to ameliorate the loss of image quality due to respiratory motion in the torso are postreconstruction registration (PRR) and motion-compensated image reconstruction (MCIR). In this study, the authors investigated whether versions of these methods that utilize registration-based weighting of the constituent respiratory gated data offer any advantage over the standard versions that use equal weighting. The registration-based weights were designed to penalize gates that were poorly registered to the reference gate. SimSET was used to simulate data from the NCAT phantom with six lesions added in the lung and liver. Images were reconstructed using registration-weighted PRR and MCIR algorithms, where the registration weighting was based on the mutual information (MI) of each registered gate and the reference gate. More specifically, relative to equal weighting, for which the weight for each gate is the inverse of the number of gates, the weights were increased for MI greater than the average MI and reduced for gates with MI less than the average MI. A scale factor was used to increase the range of the weights, and PRR and MCIR images were produced for a range of scale factor values. At the optimal values of the scale factor, registration-weighted PRR produced significantly higher contrast-to-noise ratio (CNR) for each lesion than PRR (p < 0.001), with average lesion CNR increasing significantly from (2.10 ± 0.05) to (2.70 ± 0.06) for 3 mm postsmoothing (p < 0.001) and from (2.03 ± 0.06) to (2.77 ± 0.05) for 6 mm postsmoothing (p < 0.001). Likewise, for MCIR registration weighting significantly increased the average CNR from (2.38 ± 0.04) to (2.62 ± 0.07) for 3 mm postsmoothing (p < 0.001) and from (2.56 ± 0.05) to (2.84 ± 0.08) for 6 mm postsmoothing (p < 0.001). These gains in lesion CNR were obtained despite corresponding reductions in signal-to-noise ratio, as expected from the use of unequal weighting of gated data with comparable variance. Registration weighting can significantly improve lesion CNR in motion corrected images, especially for PRR.

Cone Beam CT using motion-compensated algebraic reconstruction methods with limited data

Cone Beam Computed Tomography (CBCT) is widely used in radiation therapy for verifying treatment areas, since it provides three-dimensional image reconstruction of those tumour regions under inspection. However, organ motion is problematic during the scanning process, it causes motion artefacts on the CBCT image and can lead to mispositioning for the subsequent treatment. Moreover, patient dose is also considerable and there is a need for methods which yield acceptable image quality with as few X-ray images as possible. Although methods have been developed to handle limited projection data, such as the Algebraic Reconstruction Technique (ART); Simultaneous ART (SART); and Ordered-Subset SART (OS-SART), this study applied motion compensation to these reconstruction techniques. Root Mean Square Error (RMSE) of image is calculated to study the convergence of reconstructed images compared with the truth image. When motion was applied to a phantom and the motion compensation was used to account for the motion, the results showed that motion compensation improved the quality of CBCT image, when compared to uncompensated images. Furthermore, the experiments suggested that minimising phase error, for breathing models, was more important than minimising amplitude error.