Constrained magnetic resonance image reconstruction from incomplete frequency measurements

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.

A novel method for highly-undersampled Magnetic Resonance Image (MRI) reconstruction is presented. One of the principal challenges faced in clinical MR imaging is the fundamental linear relation between net exam duration and admissible spatial resolution. Increased scan duration diminishes patient comfort while increasing the risk of susceptibility to motion artifact and limits the ability to depict many physiological events at high temporal rates. With the recent development of Compressive Sampling theory, several authors have successfully demonstrated that clinical MR images possessing a sparse representation in some transform domain can be accurately reconstructed even when sampled at rates well below the Nyquist limit by casting the recovery as a convex ℓ₁-minimization problem. While ℓ₁-based techniques offer a sizeable advantage over Nyquist-limited methods, they nonetheless require a modest degree of over-sampling above the true theoretical minimum sampling rate in order to guarantee the achievability of exact reconstruction. In this work, we present a reconstruction model based on homotopic approximation of the ℓ₀ quasi-norm and discuss the ability of this technique to reconstruct undersampled MR images at rates even lower than are achievable than with ℓ₁-minimization and arbitrarily close to the true minimum sampling rate. A semi-implicit numerical solver is presented for efficient numerical computation of the reconstruction process and several examples depicting the capability for accurate MRI reconstructions from highly-undersampled K-space data are presented.

Cardiac x-ray CT imaging is still challenging due to heart motion, which cannot be ignored even with the current rotation speed of the equipment. In response, many algorithms have been developed to compensate remaining motion artifacts by estimating the motion using projection data or reconstructed images. In these algorithms, accurate motion estimation is critical to the compensated image quality. In addition, since the scan range is directly related to the radiation dose, it is preferable to minimize the scan range in motion estimation. In this paper, the authors propose a novel motion estimation and compensation algorithm using a sinogram with a rotation angle of less than 360°. The algorithm estimates the motion of the whole heart area using two opposite 3D partial angle reconstructed (PAR) images and compensates the motion in the reconstruction process. A CT system scans the thoracic area including the heart over an angular range of 180° + α + β, where α and β denote the detector fan angle and an additional partial angle, respectively. The obtained cone-beam projection data are converted into cone-parallel geometry via row-wise fan-to-parallel rebinning. Two conjugate 3D PAR images, whose center projection angles are separated by 180°, are then reconstructed with an angular range of β, which is considerably smaller than a short scan range of 180° + α. Although these images include limited view angle artifacts that disturb accurate motion estimation, they have considerably better temporal resolution than a short scan image. Hence, after preprocessing these artifacts, the authors estimate a motion model during a half rotation for a whole field of view via nonrigid registration between the images. Finally, motion-compensated image reconstruction is performed at a target phase by incorporating the estimated motion model. The target phase is selected as that corresponding to a view angle that is orthogonal to the center view angles of two conjugate PAR images. To evaluate the proposed algorithm, digital XCAT and physical dynamic cardiac phantom datasets are used. The XCAT phantom datasets were generated with heart rates of 70 and 100 bpm, respectively, by assuming a system rotation time of 300 ms. A physical dynamic cardiac phantom was scanned using a slowly rotating XCT system so that the effective heart rate will be 70 bpm for a system rotation speed of 300 ms. In the XCAT phantom experiment, motion-compensated 3D images obtained from the proposed algorithm show coronary arteries with fewer motion artifacts for all phases. Moreover, object boundaries contaminated by motion are well restored. Even though object positions and boundary shapes are still somewhat different from the ground truth in some cases, the authors see that visibilities of coronary arteries are improved noticeably and motion artifacts are reduced considerably. The physical phantom study also shows that the visual quality of motion-compensated images is greatly improved. The authors propose a novel PAR image-based cardiac motion estimation and compensation algorithm. The algorithm requires an angular scan range of less than 360°. The excellent performance of the proposed algorithm is illustrated by using digital XCAT and physical dynamic cardiac phantom datasets.

Intrafractional organ motion imposes considerable challenges to scanned ion beam therapy and demands for a thorough verification of the applied treatment. At the Heidelberg Ion-Beam Therapy Center (HIT), the scanned ion beam delivery is verified by means of postirradiation positron-emission-tomography (PET) imaging. This work presents a first clinical evaluation of PET-based treatment monitoring in ion beam therapy under consideration of target motion. Three patients with mobile liver lesions underwent scanned carbon ion irradiation at HIT and postirradiation PET/CT (x-ray-computed-tomography) imaging with a commercial scanner. Respiratory motion was recorded during irradiation and subsequent image acquisition. This enabled a time-resolved (4D) calculation of the expected irradiation-induced activity pattern and, for one patient where an additional 4D CT was acquired at the PET/CT scanner after treatment, a motion-compensated PET image reconstruction. For the other patients, PET data were reconstructed statically. To verify the treatment, calculated prediction and reconstructed measurement were compared with a focus on the ion beam range. Results in the current three patients suggest that for motion amplitudes in the order of 2 mm there is no benefit from incorporating respiratory motion information into PET-based treatment monitoring. For a target motion in the order of 10 mm, motion-related effects become more severe and a time-resolved modeling of the expected activity distribution can lead to an improved data interpretation if a sufficient number of true coincidences is detected. Benefits from motion-compensated PET image reconstruction could not be shown conclusively at the current stage. The feasibility of clinical PET-based treatment verification under consideration of organ motion has been shown for the first time. Improvements in noise-robust 4D PET image reconstruction are deemed necessary to enhance the clinical potential.

Respiratory motion during positron emission tomography (PET)/computed tomography (CT) imaging can cause significant image blurring and underestimation of tracer concentration for both static and dynamic studies. In this paper, with the aim to eliminate both intra-cycle and inter-cycle motions, and apply to dynamic imaging, we developed a non-rigid event-by-event (NR-EBE) respiratory motion-compensated list-mode reconstruction algorithm. The proposed method consists of two components: the first component estimates a continuous non-rigid motion field of the internal organs using the internal-external motion correlation. This continuous motion field is then incorporated into the second component, non-rigid MOLAR (NR-MOLAR) reconstruction algorithm to deform the system matrix to the reference location where the attenuation CT is acquired. The point spread function (PSF) and time-of-flight (TOF) kernels in NR-MOLAR are incorporated in the system matrix calculation, and therefore are also deformed according to motion. We first validated NR-MOLAR using a XCAT phantom with a simulated respiratory motion. NR-EBE motion-compensated image reconstruction using both the components was then validated on three human studies injected with 18F-FPDTBZ and one with 18F-fluorodeoxyglucose (FDG) tracers. The human results were compared with conventional non-rigid motion correction using discrete motion field (NR-discrete, one motion field per gate) and a previously proposed rigid EBE motion-compensated image reconstruction (R-EBE) that was designed to correct for rigid motion on a target lesion/organ. The XCAT results demonstrated that NR-MOLAR incorporating both PSF and TOF kernels effectively corrected for non-rigid motion. The 18F-FPDTBZ studies showed that NR-EBE out-performed NR-Discrete, and yielded comparable results with R-EBE on target organs while yielding superior image quality in other regions. The FDG study showed that NR-EBE clearly improved the visibility of multiple moving lesions in the liver where some of them could not be discerned in other reconstructions, in addition to improving quantification. These results show that NR-EBE motion-compensated image reconstruction appears to be a promising tool for lesion detection and quantification when imaging thoracic and abdominal regions using PET.

Fourier phase retrieval problem is equivalent to the recovery of a two-dimensional image from its autocorrelation measurements. This problem is generally nonlinear and nonconvex. Good initialization and prior information about the support or sparsity of the target image are often critical for a robust recovery. In this paper, we show that the presence of a known reference image can help us solve the nonlinear phase retrieval problem as a sequence of small linear inverse problems. Instead of recovering the entire image at once, our sequential method recovers a small number of rows or columns by solving a linear deconvolution problem at every step. Existing methods for the reference-based (holographic) phase retrieval either assume that the reference and target images are sufficiently separated so that the recovery problem is linear or recover the image via nonlinear optimization. In contrast, our proposed method does not require the separation condition. We performed an extensive set of simulations to demonstrate that our proposed method can successfully recover images from autocorrelation data under different settings of reference placement and noise.

Reducing acquisition time is a major challenge in high-resolution MRI that has been successfully addressed by Compressed Sensing (CS) theory. While the scan time has been massively accelerated by a factor up to 20 in 2D imaging, the complexity of image recovery algorithms has strongly increased, resulting in slower reconstruction processes. In this work we propose an online approach to shorten image reconstruction times in the CS setting. We leverage the segmented acquisition in multiple shots of k-space data to interleave the MR acquisition and image reconstruction steps. This approach is particularly appealing for 2D high-resolution T * 2-weighted anatomical imaging as the largest timing interval (i.e. Time of Repetition) between consecutive shots arises for this kind of imaging. During the scan, acquired shots are stacked together to form mini-batches and image reconstruction may start from incomplete data. For each newly available mini-batch, the previous partial solution is used as warm restart for the next sub-problem to be solved in a timing window compatible with the given TR and the number of shots stacked in a mini-batch. We demonstrate the interest and time savings of using online MR image reconstruction for Cartesian and non-Cartesian sampling strategies combined with a single receiver coil. Next, we extend the online formalism to address the more general multi-receiver phased array acquisition scenario. In this setting, calibrationless image reconstruction is adopted to remain compatible with the timing constraints of online delivery. Our retrospective and prospective results on ex-vivo 2D T * 2-weighted brain imaging show that high-quality MR images are recovered by the end of acquisition for single receiver acquisition and that additional iterations are required when parallel imaging is adopted. Overall, our approach implemented through the Gadgetron framework may be compatible with the data workflow on the scanner to provide the physician with reliable MR images for diagnostic purposes.

This paper presents a three-dimensional method to reconstruct moving objects from cone-beam X-ray projections using an iterative reconstruction algorithm and a given motion vector field. For the image representation, adapted blobs are used, which can be implemented efficiently as basis functions. Iterative reconstruction requires the calculation of line integrals (forward projections) through the image volume, which are compared with the actual measurements to update the image volume. In the existence of a divergent motion vector field, a change in the volumes of the blobs has to be taken into account in the forward and backprojections. An efficient method to calculate the line integral through the adapted blobs is proposed. It solves the problem, how to compensate for the divergence in the motion vector field on a grid of basis functions. The method is evaluated on two phantoms, which are subject to three different known motions. Moreover, a motion-compensated filtered back-projection reconstruction method is used, and the reconstructed images are compared. Using the correct motion vector field with the iterative motion-compensated reconstruction, sharp images are obtained, with a quality that is significantly better than gated reconstructions.

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.

Integrated PET/MR systems are becoming increasingly popular in clinical and research applications. Quantitative PET reconstruction requires correction for γ-photon attenuations using an attenuation coefficient map (μ map) that is a measure of the electron density. One challenge of PET/MR, in contrast to PET/CT, lies in the accurate computation of μ maps. Unlike CT, MR imaging measures physical properties not directly related to electron density. Previous approaches have computed the attenuation coefficients using a segmentation of MR images or using deformable registration of atlas CT images to the space of the subject MR images. In this work, we propose a patch-based method to generate whole-head μ maps from ultrashort echo-time (UTE) MR imaging sequences. UTE images are preferred to other MR sequences because of the increased signal from bone. To generate a synthetic CT image, we use patches from a reference dataset, which consists of dual-echo UTE images and a coregistered CT scan from the same subject. Matching of patches between the reference and target images allows corresponding patches from the reference CT scan to be combined via a Bayesian framework. No registration or segmentation is required. For evaluation, UTE, CT, and PET data acquired from 5 patients under an institutional review board-approved protocol were used. Another patient (with UTE and CT data only) was selected to be the reference to generate synthetic CT images for these 5 patients. PET reconstructions were attenuation-corrected using the original CT, our synthetic CT, Siemens Dixon-based μ maps, Siemens UTE-based μ maps, and deformable registration-based CT. Our synthetic CT-based PET reconstruction showed higher correlation (average ρ = 0.996, R(2) = 0.991) to the original CT-based PET, as compared with the segmentation- and registration-based methods. Synthetic CT-based reconstruction had minimal bias (regression slope, 0.990), as compared with the segmentation-based methods (regression slope, 0.905). A peak signal-to-noise ratio of 35.98 dB in the reconstructed PET activity was observed, compared with 29.767, 29.34, and 27.43 dB for the Siemens Dixon-, UTE-, and registration-based μ maps. A patch-matching approach to synthesize CT images from dual-echo UTE images leads to significantly improved accuracy of PET reconstruction as compared with actual CT scans. The PET reconstruction is improved over segmentation- (Dixon and Siemens UTE) and registration-based methods, even in subjects with pathologic findings.

Purpose: To improve the quality and specificity of metabolic imaging with hyperpolarized pyruvate using prior information from dynamic contrast-enhanced MRI (DCE-MRI). Background: Dynamic nuclear polarization (DNP) and MR spectroscopic imaging of [1-13C]-pyruvate shows tremendous promise for imaging aerobic glycolysis with sensitivity, specificity, and resolution that was previously impossible. Exogeneous, enriched hyperpolarized (HP) pyruvate is injected as a bolus and traverses multiple biological barriers before it is exposed to intracellular enzymes that mediate its fate. Preservation of the spin label through chemical reaction allows visualization of pyruvate and its chemical endpoints (lactate, alanine, and carbon dioxide/bicarbonate). We have previously observed a strong correlation between tumor perfusion and the normalized area under the curve for HP lactate, the chemical endpoint associated with aerobic glycolysis. A pharmacokinetic model of HP substrate evolution that balances physiological accuracy and computational burden includes two physical pools (intravascular/extravascular) and two chemical pools (pyruvate/lactate). In the analytical solution for this model, terms for substrate extravasation and the fractional intravascular volume can be recognized as analogues for KTRANS and Vb that are derived from analysis of DCE-MRI data using the extended Tofts model. Use of these DCE-MRI parameters as prior information could eliminate unknowns in the measurement of HP agents and improve the specificity of quantitative estimates for kPL, the apparent conversion rate for HP pyruvate into lactate. Experimental Procedures: Athymic nude mice bearing orthotopic anaplastic thyroid cancer tumors were anesthetized and scanned using a 7T Biospec small animal MR system (Bruker Biospin Corp.). A dual-tuned 1H/13C volume resonator was used for anatomic imaging and for 13C excitation, and a surface coil was used for 13C detection. HP pyruvate was prepared using a HyperSense DNP system (Oxford Instruments). Dynamic 13C spectroscopic imaging data was acquired using a radial multi-band frequency encoding sequence beginning prior to intravascular administration of HP pyruvate via tail-vein catheter. DCE-MRI data was acquired after HP measurements, using a fast spoiled gradient echo sequence. DCE-MRI data was fit to the extended Tofts model on a pixel-by-pixel basis using software developed in Matlab (The Mathworks). Parametric maps for perfusion and vascular blood volume fraction were resampled to the resolution of HP 13C scans and used as priors in a constrained reconstruction algorithm that enforces consistency between undersampled 13C projection data, the kinetic model, and prior information from 1H MRI. Results: With prior information about extravasation and fractional intravascular blood volume, the constrained reconstruction algorithm needs only solve for a global parameterized vascular input function and values for chemical conversion (kPL) and signal relaxation/loss for each voxel in the imaging volume. Elimination of nuisance parameters with strongly correlated effects reduces the computational burden of constrained reconstruction and clarifies interpretation of changes in biomarkers due to disease progression or response to therapy. Conclusions: The combination of DCE-MRI with constrained reconstruction reduces the number of unknowns in quantitative metabolic imaging using HP pyruvate, eases the computational burden, and decouples correlated effects of perfusion and chemical exchange. Citation Format: James A. Bankson, Christopher M. Walker, Yunyun Chen, Stephen Y. Lai, John D. Hazle. Metabolic imaging with hyperpolarized [1-13C]-pyruvate and DCE-MRI. [abstract]. In: Proceedings of the AACR Special Conference: Metabolism and Cancer; Jun 7-10, 2015; Bellevue, WA. Philadelphia (PA): AACR; Mol Cancer Res 2016;14(1_Suppl):Abstract nr B51.

We propose a technique that estimates both the image and the respiratory motion states of all PET gates during PET reconstruction. This is done using a gradient analytically-derived from the Poisson log-likelihood, and involves a parameterised motion model. This is incorporated into reconstruction using the motion-compensated image reconstruction (MCIR) framework, coupled with optimisation of the analytical gradient. The use of the motion model in this way reduces the number of additional parameters to be optimised for motion correction to one per PET gate. This was tested using a 3D PET simulation derived from segmented UTE MR image volumes, warped using real MR-derived motion measurements.

Both parallel MRI and compressed sensing (CS) are emerging techniques to accelerate conventional MRI by reducing the number of acquired data. The combination of parallel MRI and CS for further acceleration is of great interest. In this paper, we propose a novel method to combine sensitivity encoding (SENSE), one of the standard methods for parallel MRI, and compressed sensing for rapid MR imaging (SparseMRI), a recently proposed method for applying CS in MR imaging with Cartesian trajectories. The proposed method, named CS-SENSE, sequentially reconstructs a set of aliased reduced-field-of-view images in each channel using SparseMRI and then reconstructs the final image from the aliased images using Cartesian SENSE. The results from simulations and phantom and in vivo experiments demonstrate that CS-SENSE can achieve a reduction factor higher than those achieved by SparseMRI and SENSE individually and outperform the existing method that combines parallel MRI and CS.

Hyperpolarized [1-(13)C]-pyruvate has shown tremendous promise as an agent for imaging tumor metabolism with unprecedented sensitivity and specificity. Imaging hyperpolarized substrates by magnetic resonance is unlike traditional MRI because signals are highly transient and their spatial distribution varies continuously over their observable lifetime. Therefore, new imaging approaches are needed to ensure optimal measurement under these circumstances. Constrained reconstruction algorithms can integrate prior information, including biophysical models of the substrate/target interaction, to reduce the amount of data that is required for image analysis and reconstruction. In this study, we show that metabolic MRI with hyperpolarized pyruvate is biased by tumor perfusion and present a new pharmacokinetic model for hyperpolarized substrates that accounts for these effects. The suitability of this model is confirmed by statistical comparison with alternates using data from 55 dynamic spectroscopic measurements in normal animals and murine models of anaplastic thyroid cancer, glioblastoma, and triple-negative breast cancer. The kinetic model was then integrated into a constrained reconstruction algorithm and feasibility was tested using significantly undersampled imaging data from tumor-bearing animals. Compared with naïve image reconstruction, this approach requires far fewer signal-depleting excitations and focuses analysis and reconstruction on new information that is uniquely available from hyperpolarized pyruvate and its metabolites, thus improving the reproducibility and accuracy of metabolic imaging measurements.

Compressive Sensing (CS) is a new method for sparse images reconstruction using incomplete measurements. In this study our goal is to reconstruct a High Resolution (HR), MR image from a single Low Resolution (LR) image. Our proposed method applies the CS theory to Super Resolution (SR) single Magnetic Resonance Imaging (MRI). We first use a LR image generated by applying a Gaussian filter on the original image (for k-space under-sampling) and then generate the HR image by using CS theory. The formulation of CS theory emphasizes on maximizing image sparsity on known sparse transform domain and minimizing fidelity. For satisfying sparsity, finite difference is applied as a sparsifying transform. We propose and compare the Non-Linear Conjugate Gradients (NLCG) and Split Bregman (SB) algorithms as two different image reconstructing methods in CS. The result images are compared with three types of images: Original image which is used as the input of experiments, low quality of original image and the image which is generated by Zero Filling (ZF) algorithm. The following measures are used for evaluation: SNR, PSNR, SSIM and MSE. Experiments show that the SB algorithm outperforms ZF and NLCG for reconstructing MR images.