Dynamic image reconstruction for CT applications

Standard 3D dynamic positron emission tomographic (PET) imaging consists of independent image reconstructions of individual frames followed by application of appropriate kinetic model to the time activity curves at the voxel or region-of-interest (ROI). The emerging field of 4D PET reconstruction, by contrast, seeks to move beyond this scheme and incorporate information from multiple frames within the image reconstruction task. Here we propose a novel reconstruction framework aiming to enhance quantitative accuracy of parametric images via introduction of priors based on voxel kinetics, as generated via clustering of preliminary reconstructed dynamic images to define clustered neighborhoods of voxels with similar kinetics. This is then followed by straightforward maximum a posteriori (MAP) 3D PET reconstruction as applied to individual frames; and as such the method is labeled ‘3.5D’ image reconstruction. The use of cluster-based priors has the advantage of further enhancing quantitative performance in dynamic PET imaging, because: (a) there are typically more voxels in clusters than in conventional local neighborhoods, and (b) neighboring voxels with distinct kinetics are less likely to be clustered together. Using realistic simulated 11C-raclopride dynamic PET data, the quantitative performance of the proposed method was investigated. Parametric distribution-volume (DV) and DV ratio (DVR) images were estimated from dynamic image reconstructions using (a) maximum-likelihood expectation maximization (MLEM), and MAP reconstructions using (b) the quadratic prior (QP-MAP), (c) the Green prior (GP-MAP) and (d, e) two proposed cluster-based priors (CP-U-MAP and CP-W-MAP), followed by graphical modeling, and were qualitatively and quantitatively compared for 11 ROIs. Overall, the proposed dynamic PET reconstruction methodology resulted in substantial visual as well as quantitative accuracy improvements (in terms of noise versus bias performance) for parametric DV and DVR images. The method was also tested on a 90 min 11C-raclopride patient study performed on the high-resolution research tomography. The proposed method was shown to outperform the conventional method in visual as well as quantitative accuracy improvements (in terms of noise versus regional DVR value performance).

Purpose:Dynamic imaging (DI) provides additional diagnostic information in emission tomography in comparison to conventional static imaging at the cost of being computationally more challenging. Dynamic SPECT (Single Photon Emission Computed Tomography) reconstruction is particularly difficult because of the limitations in the sampling geometry present in most existing scanners. We have developed an algorithm Spline Initialized Factor Analysis of Dynamic Structures (SIFADS) that is a matrix factorization method for reconstructing the dynamics of tracers in tissues and blood directly from the projections in dynamic cardiac SPECT, without first resorting to any 3D reconstruction.Methods:SIFADS is different from “pure” FADS in that it employs a dedicated spline-based pre-initialization. In this paper, we analyze the convergence properties of SIFADS and FADS using multiple metrics. The performances of the two approaches are evaluated for numerically simulated data and for real dynamic SPECT data from canine and human subjects.Results:Most metrics analyzed for reconstruction algorithm convergence show better features of the metric curves versus iterations, In addition, SIAFDS provides better tissue segmentations than that from pure FADS. Measured computational times are also typically better for SIFADS implementations than those with pure FADS.Conclusion:The analysis supports the utility of the pre-initialization of a factorization algorithm for better dynamic SPECT image reconstruction.

Recursive Procedures in Sire Evaluation

We propose a recovery approach for highly subsampled dynamic parallel MRI image without auto-calibration signals (ACSs) or prior knowledge of coil sensitivity maps. By exploiting the between-frame redundancy of dynamic parallel MRI data, we first introduce a new low-rank matrix recovery-based model, termed as calibration using spatial---temporal matrix (CUSTOM), for ACSs recovery. The recovered ACSs from data are used for estimating coil sensitivity maps and further dynamic image reconstruction. The proposed non-convex and non-smooth minimization for the CUSTOM step is solved by a proximal alternating linearized minimization method, and we provide its convergence result for this specific minimization problem. Numerical experiments on several highly subsampled test data demonstrate that the proposed overall approach outperforms other state-of-the-art methods for calibrationless dynamic parallel MRI reconstruction.

The article proposes an integrated approach to modeling the initial stage of tracking air targets in radar systems based on a combination of a probabilistic-temporal model of the GERT type and a recursive state estimation procedure using the Kalman filter. At the macro level, the process of interaction "radar-tracked object" is described by an exponential GERT network using moment generating functions, which allows analytically forming an equivalent W-function, determining the distribution and probability density functions of the interaction time, as well as taking into account multivariate transition trajectories, returns to previous states, and detection confirmation delays. It is shown that the GERT model effectively reproduces global temporal-probabilistic regularities of the process, but does not provide recursive correction of coordinates and velocities estimates in real time and minimization of the mean square error. To overcome these limitations, it is proposed to integrate the Kalman filter as a micro-level tool for trajectory estimation. A discrete linear stochastic model in the state space is formulated, a two-step recursion "prediction-correction", principles of selection of motion models (CV, CA, CT), structures of noise covariance matrices and tuning procedures based on RMSE and NEES criteria are presented. It is shown that the time characteristics obtained from GERT can be used to initialize the initial state and covariances, as well as for adaptive tuning of the sampling step and process noise parameters. The modeling results demonstrate the complementarity of the approaches: GERT forms a structural-probabilistic framework of the tracking process, while the Kalman filter provides smoothing of measurements, reduction of the spread of estimates and a significant reduction of RMSE compared to the macro-level estimate. The proposed integration framework "GERT → Kalman" creates a methodological basis for building a comprehensive model of goal tracking in a cluttered environment, combining the analysis of the temporal-probabilistic structure of the process with highly accurate recursive real-time state estimation.

Due to sensor cost and installment accessibility, it is not practical to instrument sensors on every point of a structure and the measured set of dynamic responses is thus usually incomplete, thus the need to perform dynamic response reconstruction always arises, especially for a large civil structure. This study presents the novel Kalman filter (KF) based response reconstruction methods under known and unknown excitations. The underlying state estimation theories under known and unknown excitation are first introduced. Then dynamic response reconstruction methods are developed based on the state estimation in the framework of KF. For easy explanation and demonstration, a simple 4-story shear-type frame is employed in numerical study. The performances of the proposed KF based response reconstruction are examined. The effect of process and measurement noises covariance and spatial location of the measurement sensors to the reconstruction accuracy is investigated and discussed.

Dynamic F-18 FDG PET imaging along with tracer kinetic modeling can provide parametric images of physiologically important parameters for characterization of tumor and other diseases. This technique often requires a 1-hour long scanning time, which is less practical in clinic; a more practical method is to use a shortened dynamic scan time of thirty or forty minutes. However, a shortened dynamic scan acquires less data and tracer kinetic modeling becomes more sensitive to high noise in dynamic PET. To address the noise challenge, the kernel method has been developed for efficient dynamic PET image reconstruction. Previous kernel approaches use a single kernel type, which exploits either nonlocal or local spatial correlations from image priors but does not explore the full potential of the kernel framework. In this work, we propose a new dualkernel approach to further enhance kernel-based dynamic PET image reconstruction. The dual kernel combines the existing non-local kernel with a local convolutional kernel that can be easily trained from image priors. We evaluated the new kernel approach for shortened dynamic FDG-PET imaging using a digital brain phantom. Simulation results have demonstrated that the dual-kernel approach can achieve better image quality than standard reconstruction approach and the single kernel approach.

It has been previously shown that an image with motion ghost artifacts can be decomposed into a ghost mask superimposed over a ghost-free image. The present study demonstrates that the ghost components carry useful dynamic information and should not be discarded. Specifically, ghosts of different orders indicate the intensity and phase of the corresponding harmonics contained in the quasi-periodically varying spin-density distribution. A summation of the ghosts weighted by appropriate temporal phase factors can give a time-dependent dynamic image that is a movie of the object motion. This dynamic image reconstruction technique does not necessarily require monitoring of the motion and thus is easy to implement and operate. It also has a shorter imaging time than point-by-point imaging of temporal variation, because the periodic motion is more efficiently sampled with a limited number of harmonics recorded in the motion ghosts. This technique was tested in both moving phantoms and volunteers. It is believed to be useful for dynamic imaging of time-varying anatomic structures, such as in the cardiovascular system.

Previous studies show that Kalman filter (KF)-based dynamic response reconstruction of a structure has distinct advantages in the aspects of combining the system model with limited measurement information and dealing with system model errors and measurement Gaussian noises. However, because the recursive KF aims to achieve a least-squares estimate of state vector by minimizing a quadratic criterion, observation outliers could dramatically deteriorate the estimator’s performance and considerably reduce the response reconstruction accuracy. This study addresses the KF-based online response reconstruction of a structure in the presence of observation outliers. The outlier-robust Kalman filter (OKF), in which the outlier is discerned and reweighted iteratively to achieve the generalized maximum likelihood (ML) estimate, is used instead of KF for online dynamic response reconstruction. The influences of process noise and outlier duration to response reconstruction are investigated in the numerical study of a simple 5-story frame structure. The experimental work on a simply-supported overhanging steel beam is conducted to testify the effectiveness of the proposed method. The results demonstrate that compared with the KF-based response reconstruction, the proposed OKF-based method is capable of dealing with the observation outliers and producing more accurate response construction in presence of observation outliers.

Based on a 3D pre-treatment magnetic resonance (MR) scan, we developed DREME-MR to jointly reconstruct the reference patient anatomy and solve a data-driven, patient-specific cardiorespiratory motion model. Via a motion encoder simultaneously learned during the reconstruction, DREME-MR further enables real-time volumetric MR imaging and cardiorespiratory motion tracking with minimal intra-treatment k-space data.&#xD;&#xD;Approach: DREME-MR integrates dynamic MRI reconstruction and real-time MR imaging into a unified, dual-task learning framework. From a 3D radial-spoke-based pre-treatment MR scan, DREME-MR uses spatiotemporal implicit-neural-representation (INR) to reconstruct pre-treatment dynamic volumetric MR images (learning task 1). The INR-based reconstruction takes a joint image reconstruction and deformable registration approach, yielding a reference anatomy and a corresponding cardiorespiratory motion model. The motion model adopts a low-rank, multi-resolution representation to approximate motion fields as products of motion coefficients and motion basis components (MBCs). Via a progressive, frequency-guided strategy, DREME-MR decouples cardiac MBCs from respiratory MBCs to resolve the two distinct motion modes. Simultaneously with the pre-treatment dynamic MRI reconstruction, DREME-MR also trains a multilayer perceptron (MLP)-based motion encoder to infer cardiorespiratory motion coefficients directly from the raw k-space data (learning task 2), allowing real-time, intra-treatment volumetric MR imaging and motion tracking with minimal k-space data (20-30 spokes) acquired after the pre-treatment MRI scan.&#xD;&#xD;Main results: Evaluated using data from a digital phantom (XCAT) and a human scan, DREME-MR solves real-time 3D cardiorespiratory motion with a latency of < 165 ms (= 150-ms data acquisition + 15-ms inference time), fulfilling the temporal constraint of real-time imaging. The XCAT study achieves mean(±S.D.) center-of-mass tracking errors of 0.73±0.38mm for a lung tumor and 1.69±1.12mm for the left ventricle. The human study shows good motion correlations (liver: 0.96; left ventricle: 0.65) between DREME-MR-solved motion and extracted surrogate signals.&#xD;&#xD;Significance: DREME-MR allows real-time 3D MRI and cardiorespiratory motion tracking with low latency, advancing intra-treatment MR-guided adaptive radiotherapy, including real-time multileaf collimator (MLC) tracking.

Multiscale fuzzy Kalman filtering

Parallel magnetic resonance imaging (MRI) is an imaging technique by acquiring a reduced amount of data in Fourier domain with multiple receiver coils. To recover the underlying imaging object, one often needs the explicit knowledge of coil sensitivity maps, or some additional fully acquired data blocks called the auto-calibration signals (ACS). In this paper, we show that by exploiting the between-frame redundancy of dynamic parallel MRI data, it is possible to achieve simultaneous coil sensitivity map estimation and image sequence reconstruction. Specially, we introduce a novel two-stage approach for dynamic parallel MRI reconstruction without pre-calibrating the coil sensitivity maps nor additionally acquiring any fully sampled ACS. Numerical experiments demonstrate that, the performance of the proposed approach is better than other state-of-the-art approaches for calibrationless dynamic parallel MRI reconstruction.

A recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings. This estimator has a similar form as that of the Kalman filter with intermittent observations, but its parameters should be adjusted when a plant output measurement arrives. A new recursive form is derived for the pseudo-covariance matrix of estimation errors, which plays important roles in analyzing its asymptotic properties. Based on a Riemannian metric for positive definite matrices, some necessary and sufficient conditions have been obtained for the strict contractiveness of an iteration of this recursion. It has also been proved that under some controllability and observability conditions, as well as some weak requirements on measurement arrival probability, the gain matrix of this recursive robust state estimator converges in probability one to a stationary distribution. Numerical simulation results show that estimation accuracy of the suggested procedure is more robust against parametric modelling errors than the Kalman filter.

The presence of fixed and stochastic parameters in a mixed linear regression model has been dealt with for the case where the stochastic parameters follow a stationary process. The solution is given either by Generalized Least Squares (e.g. Rao, 1965, p. 192) or by a recursive state space estimation procedure such as the Kalman filter and smoother (e.g. Sallas and Harville 1981). The estimation of non-stationary stochastic parameters has been mainly approached in the state space framework, either as an initial condition problem (see among others, Ansley and Kohn, 1985, 1989; Kohn and Ansley, 1986; Bell and Hillmer, 1991 and De Jong, 1989, 1991); or as a hierarchical model with “fixed” effects in the hierarchy given a flat prior distribution (see Sallas and Harville, 1981, 1988; Tsimikas and Ledolter, 1994).KeywordsKalman FilterTime Series AnalysisAmerican Statistical AssociationARIMA ModelGeneralize Little SquareThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Addresses the identification of nonlinear systems from output time series, which we have called dynamic modeling. We start by providing the mathematical basis for dynamic modeling and show that it is equivalent to a multivariate nonlinear prediction problem in the reconstructed space. We address the importance of dynamic reconstruction for dynamic modeling. Recognizing that dynamic reconstruction is an ill-defined inverse problem, we describe a regularized radial basis function network for solving the dynamic reconstruction problem. Prior knowledge in the form of smoothness of the mapping is imposed on the solution via regularization. We also show that, in time-series analysis, some form of regularization can be accomplished by using the structure of the time series instead of imposing a smoothness constraint on the cost function. We develop a methodology based on iterated prediction to train the network weights with an error derived through trajectory learning. This method provides a robust performance because during learning the weights are constrained to follow a trajectory. The dynamic invariants estimated from the generated time series are similar to the ones estimated from the original time series, which means that the properties of the attractor have been captured by the neural network. We finally raise the question that generalized delay operators may have advantages in dynamic reconstruction, primarily in cases where the time series is corrupted by noise. We show how to set the recursive parameter of the gamma operator to attenuate noise and preserve the dynamics.