Model-based iterative reconstruction for radial fast spin-echo MRI

Accelerated MR parameter mapping with low-rank and sparsity constraints

PURPOSE

To enable accurate magnetic resonance (MR) parameter mapping with accelerated data acquisition, utilizing recent advances in constrained imaging with sparse sampling.

THEORY AND METHODS

A new constrained reconstruction method based on low-rank and sparsity constraints is proposed to accelerate MR parameter mapping. More specifically, the proposed method simultaneously imposes low-rank and joint sparse structures on contrast-weighted image sequences within a unified mathematical formulation. With a pre-estimated subspace, this formulation results in a convex optimization problem, which is solved using an efficient numerical algorithm based on the alternating direction method of multipliers.

RESULTS

To evaluate the performance of the proposed method, two application examples were considered: (i) T2 mapping of the human brain and (ii) T1 mapping of the rat brain. For each application, the proposed method was evaluated at both moderate and high acceleration levels. Additionally, the proposed method was compared with two state-of-the-art methods that only use a single low-rank or joint sparsity constraint. The results demonstrate that the proposed method can achieve accurate parameter estimation with both moderately and highly undersampled data. Although all methods performed fairly well with moderately undersampled data, the proposed method achieved much better performance (e.g., more accurate parameter values) than the other two methods with highly undersampled data.

CONCLUSIONS

Simultaneously imposing low-rank and sparsity constraints can effectively improve the accuracy of fast MR parameter mapping with sparse sampling.

Consideration of slice profiles in inversion recovery Look-Locker relaxation parameter mapping

PURPOSE

To include the flip angle distribution caused by the slice profile into the model used for describing the relaxation curves observed in inversion recovery Look-Locker FLASH T1 mapping for a more accurate determination of the relaxation parameters.

MATERIALS AND METHODS

For each inversion time, the flip angle dependent signal of the mono-exponential relaxation model is integrated across the slice profile. The resulting Consideration of Slice Profiles (CSP) relaxation curves are compared to the mono-exponential signal model in numerical simulations as well as in phantom and in-vivo experiments.

RESULTS

All measured relaxation curves showed systematic deviations from a mono-exponential curve increasing with flip angle and T1 but decreasing with repetition time. Additionally, the accuracy of T1 was found to be largely dependent on the temporal coverage of the relaxation curve. All these systematic errors were largely reduced by the CSP model.

CONCLUSION

The proposed CSP model represents a useful extension of the conventionally used mono-exponential relaxation model. Despite inherent model inaccuracies, the mono-exponential model was found to be sufficient for many T1 mapping situations. However, if only a poor temporal coverage of the relaxation process is achievable or a very precise modeling of the relaxation course is needed as in model-based techniques, the mono-exponential model leads to systematic errors and the CSP model should be used instead.

Fast T2 mapping with multiple echo, Caesar cipher acquisition and model-based reconstruction

PURPOSE

Fast, quantitative T2 mapping is of value to both clinical and research environments. However, many protocols utilizing fast spin echo (FSE) pulse sequences contain acceleration-induced artifacts that are compounded when fitting parameter maps, especially in the presence of imperfect refocusing. This work presents a B1 -corrected, model-based reconstruction and associated Cartesian FSE phase-encode ordering that provides enhanced accuracy in T2 estimates compared with other common accelerated protocols.

THEORY AND METHODS

The method, known as multiple echo, Caesar cipher acquisition and model-based reconstruction (ME-CAMBREC), directly fitted T2 , flip angle, and proton density maps on a row-by-row basis to k-space data using the extended phase graph model. Regularization was enforced in order to minimize noise amplification effects. ME-CAMBREC was evaluated in computational and physical phantoms, as well as human brain, and compared with other FSE-based T2 mapping protocols, DESPOT2, and parallel imaging acceleration.

RESULTS

In computational, phantom, and human experiments, ME-CAMBREC provided T2 maps with fewer artifacts and less or similar error compared with other methods tested at moderate-to-high acceleration factors. In vivo, ME-CAMBREC provided error rates approximately one-half those of other methods.

CONCLUSION

Directly fitting multi-echo data to k-space using the extended phase graph can increase fidelity of T2 maps significantly, especially when using an appropriate phase-encode ordering.

Rapid and accurate T2 mapping from multi-spin-echo data using Bloch-simulation-based reconstruction

PURPOSE

Quantitative T2 -relaxation-based contrast has the potential to provide valuable clinical information. Practical T2 -mapping, however, is impaired either by prohibitively long acquisition times or by contamination of fast multiecho protocols by stimulated and indirect echoes. This work presents a novel postprocessing approach aiming to overcome the common penalties associated with multiecho protocols, and enabling rapid and accurate mapping of T2 relaxation values.

METHODS

Bloch simulations are used to estimate the actual echo-modulation curve (EMC) in a multi-spin-echo experiment. Simulations are repeated for a range of T2 values and transmit field scales, yielding a database of simulated EMCs, which is then used to identify the T2 value whose EMC most closely matches the experimentally measured data at each voxel.

RESULTS

T2 maps of both phantom and in vivo scans were successfully reconstructed, closely matching maps produced from single spin-echo data. Results were consistent over the physiological range of T2 values and across different experimental settings.

CONCLUSION

The proposed technique allows accurate T2 mapping in clinically feasible scan times, free of user- and scanner-dependent variations, while providing a comprehensive framework that can be extended to model other parameters (e.g., T1 , B1 (+) , B0 , diffusion) and support arbitrary acquisition schemes.

Simple recipe for accurate T(2) quantification with multi spin-echo acquisitions

OBJECTIVE

The quantification of magnetic resonance relaxation parameters T 1 and T 2 have the potential for improved disease detection and classification over standard clinical weighted imaging. Performing a mono-exponential fit on multi spin-echo (MSE) data provides quantitative T 2 values in a clinically acceptable scan-time. However, due to technical imperfections of refocusing pulses, stimulated echo contributions to the signals lead to significant deviations in the resulting T 2 values. In this work, a simple auto-calibrating correction procedure is presented, allowing the accurate estimation of T 2 from MSE acquisitions.

MATERIALS AND METHODS

Correction factors for T 2 values obtained from MSE acquisitions with a mono-exponential fit are derived from simulations following the extended phase graph formulation. A closed formula is given for the calculation of the required correction factors directly from the measured data itself.

RESULTS

Simulations and phantom experiments show high accuracy of corrected T 2 values for a wide range of clinically relevant T 2 values and for different nominal refocusing flip angles. In addition, corrected T 2 maps of the human brain are presented.

CONCLUSION

A simple recipe is provided to correct T 2 values obtained from MSE acquisitions via a mono-exponential fit for the influence of stimulated echoes. Since all required parameters are extracted from the data themselves, no additional acquisitions are required.

PANDA-T1ρ: Integrating principal component analysis and dictionary learning for fast T1ρ mapping

PURPOSE

Long scanning time greatly hinders the widespread application of spin-lattice relaxation in rotating frame (T1ρ) in clinics. In this study, a novel method is proposed to reconstruct the T1ρ-weighted images from undersampled k-space data and hence accelerate the acquisition of T1ρ imaging.

METHODS

The proposed approach (PANDA-T1ρ) combined the benefit of PCA and dictionary learning when reconstructing image from undersampled data. Specifically, the PCA transform was first used to sparsify the image series along the parameter direction and then the sparsified images were reconstructed by means of dictionary learning and finally solved the images. A variation of PANDA-T1ρ was also developed for the heavy noise case. Numerical simulation and in vivo experiments were carried out with the accelerating factor from 2 to 4 to verify the performance of PANDA-T1ρ.

RESULTS

The reconstructed T1ρ maps using the PANDA-T1ρ method were found to be comparable to the reference at all verified acceleration factors. Moreover, the variation exhibited better performance than the original version when the k-space data were contaminated by heavy noise.

CONCLUSION

PANDA-T1ρ can significantly reduce the scanning time of T1ρ by integrating PCA and dictionary learning and provides better parameter estimation than the state-of-art methods for a fixed acceleration factor.

MODEL-BASED MR PARAMETER MAPPING WITH SPARSITY CONSTRAINT

MR parameter mapping (e.g., T1 mapping, T2 mapping, or [Formula: see text] mapping) is a valuable tool for tissue characterization. However, its practical utility has been limited due to long data acquisition time. This paper addresses this problem with a new model-based parameter mapping method, which utilizes an explicit signal model and imposes a sparsity constraint on the parameter values. The proposed method enables direct estimation of the parameters of interest from highly undersampled, noisy k-space data. An algorithm is presented to solve the underlying parameter estimation problem. Its performance is analyzed using estimation-theoretic bounds. Some representative results from T2 brain mapping are also presented to illustrate the performance of the proposed method for accelerating parameter mapping.

Rank awareness in group-sparse recovery of multi-echo MR images

This work addresses the problem of recovering multi-echo T1 or T2 weighted images from their partial K-space scans. Recent studies have shown that the best results are obtained when all the multi-echo images are reconstructed by simultaneously exploiting their intra-image spatial redundancy and inter-echo correlation. The aforesaid studies either stack the vectorised images (formed by row or columns concatenation) as columns of a Multiple Measurement Vector (MMV) matrix or concatenate them as a long vector. Owing to the inter-image correlation, the thus formed MMV matrix or the long concatenated vector is row-sparse or group-sparse respectively in a transform domain (wavelets). Consequently the reconstruction problem was formulated as a row-sparse MMV recovery or a group-sparse vector recovery. In this work we show that when the multi-echo images are arranged in the MMV form, the thus formed matrix is low-rank. We show that better reconstruction accuracy can be obtained when the information about rank-deficiency is incorporated into the row/group sparse recovery problem. Mathematically, this leads to a constrained optimization problem where the objective function promotes the signal's groups-sparsity as well as its rank-deficiency; the objective function is minimized subject to data fidelity constraints. The experiments were carried out on ex vivo and in vivo T2 weighted images of a rat's spinal cord. Results show that this method yields considerably superior results than state-of-the-art reconstruction techniques.

Model-based Acceleration of Parameter mapping (MAP) for saturation prepared radially acquired data

A reconstruction technique called Model-based Acceleration of Parameter mapping (MAP) is presented allowing for quantification of longitudinal relaxation time and proton density from radial single-shot measurements after saturation recovery magnetization preparation. Using a mono-exponential model in image space, an iterative fitting algorithm is used to reconstruct one well resolved and consistent image for each of the projections acquired during the saturation recovery relaxation process. The functionality of the algorithm is examined in numerical simulations, phantom experiments, and in-vivo studies. MAP reconstructions of single-shot acquisitions feature the same image quality and resolution as fully sampled reference images in phantom and in-vivo studies. The longitudinal relaxation times obtained from the MAP reconstructions are in very good agreement with the reference values in numerical simulations as well as phantom and in-vivo measurements. Compared to available contrast manipulation techniques, no averaging of projections acquired at different time points of the relaxation process is required in MAP imaging. The proposed technique offers new ways of extracting quantitative information from single-shot measurements acquired after magnetization preparation. The reconstruction simultaneously yields images with high spatiotemporal resolution fully consistent with the acquired data as well as maps of the effective longitudinal relaxation parameter and the relative proton density.

Improved multi B-value diffusion-weighted MRI of the body by simultaneous model estimation and image reconstruction (SMEIR)

Diffusion-weighted MRI images acquired with multiple b-values have the potential to improve diagnostic accuracy by increasing the conspicuity of lesions and inflammatory activity with background suppression. Unfortunately, the inherently low signal-to-noise ratio (SNR) of DW-MRI reduces enthusiasm for using these images for diagnostic purposes. Moreover, lengthy acquisition times limit our ability to improve the quality of multi b-value DW-MRI images by multiple excitations acquisition and signal averaging at each b-value. To offset these limitations, we propose the Simultaneous Model Estimation and Image Reconstruction (SMEIR) for DW-MRI, which substantially improves the quality of multi b-value DW-MRI images without increasing acquisition times. Our model introduces the physiological signal decay model of DW-MRI as a constraint in the reconstruction of the DW-MRI images. An in-vivo experiment using 6 low-quality DW-MRI datasets of a healthy subject showed that SMEIR reconstruction of low-quality data improved SNR by 55% in the liver and by 41% in the kidney without increasing acquisition times. We also demonstrated the clinical impact of our SMEIR reconstruction by increasing the conspicuity of inflamed bowel regions in DW-MRI of 12 patients with Crohn's disease. The contrast-to-noise ratio (CNR) of the inflamed regions in the SMEIR images was higher by 12.6% relative to CNR in the original DW-MRI images.

Accelerating MR parameter mapping using sparsity-promoting regularization in parametric dimension

MR parameter mapping requires sampling along additional (parametric) dimension, which often limits its clinical appeal due to a several-fold increase in scan times compared to conventional anatomic imaging. Data undersampling combined with parallel imaging is an attractive way to reduce scan time in such applications. However, inherent SNR penalties of parallel MRI due to noise amplification often limit its utility even at moderate acceleration factors, requiring regularization by prior knowledge. In this work, we propose a novel regularization strategy, which uses smoothness of signal evolution in the parametric dimension within compressed sensing framework (p-CS) to provide accurate and precise estimation of parametric maps from undersampled data. The performance of the method was demonstrated with variable flip angle T1 mapping and compared favorably to two representative reconstruction approaches, image space-based total variation regularization and an analytical model-based reconstruction. The proposed p-CS regularization was found to provide efficient suppression of noise amplification and preservation of parameter mapping accuracy without explicit utilization of analytical signal models. The developed method may facilitate acceleration of quantitative MRI techniques that are not suitable to model-based reconstruction because of complex signal models or when signal deviations from the expected analytical model exist.

T2 relaxometry with indirect echo compensation from highly undersampled data

PURPOSE

To develop an algorithm for fast and accurate T2 estimation from highly undersampled multi-echo spin-echo data.

METHODS

The algorithm combines a model-based reconstruction with a signal decay based on the slice-resolved extended phase graph (SEPG) model with the goal of reconstructing T2 maps from highly undersampled radial multi-echo spin-echo data with indirect echo compensation. To avoid problems associated with the nonlinearity of the SEPG model, principal component decomposition is used to linearize the signal model. The proposed CUrve Reconstruction via principal component-based Linearization with Indirect Echo compensation (CURLIE) algorithm is used to estimate T2 curves from highly undersampled data. T2 maps are obtained by fitting the curves to the SEPG model.

RESULTS

Results on phantoms showed T2 biases (1.9% to 18.4%) when indirect echoes are not taken into account. The T2 biases were reduced (< 3.2%) when the CURLIE reconstruction was performed along with SEPG fitting even for high degrees of undersampling (4% sampled). Experiments in vivo for brain, liver, and heart followed the same trend as the phantoms.

CONCLUSION

The CURLIE reconstruction combined with SEPG fitting enables accurate T2 estimation from highly undersampled multi-echo spin-echo radial data thus, yielding a fast T2 mapping method without errors caused by indirect echoes.

Model-based reconstruction of undersampled diffusion tensor k-space data

The practical utility of diffusion tensor imaging, especially for 3D high-resolution spin warp experiments of ex vivo specimens, has been hampered by long acquisition times. To accelerate the acquisition, a compressed sensing framework that uses a model-based formulation to reconstruct diffusion tensor fields from undersampled k-space data was presented and evaluated. Accuracies in brain specimen white matter fiber orientation, fractional anisotropy, and mean diffusivity mapping were compared with alternative methods achievable using the same scan time via reduced image resolution, fewer diffusion encoding directions, standard compressed sensing, or asymmetrical sampling reconstruction. The efficiency of the proposed approach was also compared with fully sampled cases across a range of the number of diffusion encoding directions. In general, the proposed approach was found to reduce the image blurring and noise and to provide more accurate fiber orientation, fractional anisotropy, and mean diffusivity measurements compared with the alternative methods. Moreover, depending on the degree of undersampling used and the diffusion tensor imaging parameter examined, the measurement accuracy of the proposed scheme was equivalent to fully sampled diffusion tensor imaging datasets that consist of 33-67% more encoding directions and require proportionally longer scan times. The findings show model-based compressed sensing to be promising for improving the resolution, accuracy, or scan time of diffusion tensor imaging.

Rapid 3D-imaging of phosphocreatine recovery kinetics in the human lower leg muscles with compressed sensing

The rate of phosphocreatine (PCr) resynthesis following physical exercise is an accepted index of mitochondrial oxidative metabolism and has been studied extensively with unlocalized (31)P-MRS methods and small surface coils. Imaging experiments using volume coils that measure several muscles simultaneously can provide new insights into the variability of muscle function in healthy and diseased states. However, they are limited by long acquisition times relative to the dynamics of PCr recovery. This work focuses on the implementation of a compressed sensing technique to accelerate imaging of PCr resynthesis following physical exercise, using a modified three-dimensional turbo-spin-echo sequence and principal component analysis as sparsifying transform. The compressed sensing technique was initially validated using 2-fold retrospective undersampling of fully sampled data from four volunteers acquired on a 7T MRI system (voxel size: 1.6 mL, temporal resolution: 24 s), which led to an accurate estimation of the mono-exponential PCr resynthesis rate constant (mean error <6.4%). Acquisitions with prospective 2-fold acceleration (temporal resolution: 12 s) demonstrated that three-dimensional mapping of PCr resynthesis is possible at a temporal resolution that is sufficiently high for characterizing the recovery curve of several muscles in a single measurement.

Parallel imaging with nonlinear reconstruction using variational penalties

A new approach based on nonlinear inversion for autocalibrated parallel imaging with arbitrary sampling patterns is presented. By extending the iteratively regularized Gauss-Newton method with variational penalties, the improved reconstruction quality obtained from joint estimation of image and coil sensitivities is combined with the superior noise suppression of total variation and total generalized variation regularization. In addition, the proposed approach can lead to enhanced removal of sampling artifacts arising from pseudorandom and radial sampling patterns. This is demonstrated for phantom and in vivo measurements.

Improved least squares MR image reconstruction using estimates of k-space data consistency

This study describes a new approach to reconstruct data that has been corrupted by unfavorable magnetization evolution. In this new framework, images are reconstructed in a weighted least squares fashion using all available data and a measure of consistency determined from the data itself. The reconstruction scheme optimally balances uncertainties from noise error with those from data inconsistency, is compatible with methods that model signal corruption, and may be advantageous for more accurate and precise reconstruction with many least squares-based image estimation techniques including parallel imaging and constrained reconstruction/compressed sensing applications. Performance of the several variants of the algorithm tailored for fast spin echo and self-gated respiratory gating applications was evaluated in simulations, phantom experiments, and in vivo scans. The data consistency weighting technique substantially improved image quality and reduced noise as compared to traditional reconstruction approaches.

T2 mapping from highly undersampled data by reconstruction of principal component coefficient maps using compressed sensing

Recently, there has been an increased interest in quantitative MR parameters to improve diagnosis and treatment. Parameter mapping requires multiple images acquired with different timings usually resulting in long acquisition times. While acquisition time can be reduced by acquiring undersampled data, obtaining accurate estimates of parameters from undersampled data is a challenging problem, in particular for structures with high spatial frequency content. In this work, principal component analysis is combined with a model-based algorithm to reconstruct maps of selected principal component coefficients from highly undersampled radial MRI data. This novel approach linearizes the cost function of the optimization problem yielding a more accurate and reliable estimation of MR parameter maps. The proposed algorithm--reconstruction of principal component coefficient maps using compressed sensing--is demonstrated in phantoms and in vivo and compared with two other algorithms previously developed for undersampled data.

Accelerating multi-echo T2 weighted MR imaging: analysis prior group-sparse optimization

This works addresses the problem of reconstructing multi-echo T2 weighted MR images from partially sampled K-space data. Previous studies in reconstructing MR images from partial samples of the K-space used Compressed Sensing (CS) techniques to exploit the spatial correlation of the images (leading to sparsity in transform domain). Such techniques can be employed to reconstruct the individual T2 weighted images. However, in the current context, the different images are not independent; they are images of the same cross section, and hence are highly correlated. In this work, we not only exploit the spatial correlation within the image, but also the correlation between the images to achieve even better reconstruction results. For individual MR images, CS based techniques lead to a sparsity promoting optimization problem in a transform domain. In this paper, we show how to extend the same framework in order to incorporate correlation between images leading to group sparsity promoting optimization. Group sparsity promoting optimization is popularly formulated as a synthesis prior problem. The synthesis prior formulation for group sparsity leads to superior reconstruction results compared to ordinary sparse reconstruction. However, in this paper we show that when group sparsity is framed as an analysis prior problem the reconstruction results are even better for proper choice of the sparsifying transform. An interesting observation of this work is that when the same sampling pattern is used to sample the K-space for all the T2 weighted echoes, group sparsity does not yield any noticeable improvement, but when different sampling patterns are used for different echoes, our proposed group sparsity promoting formulation yields significant improvement (in terms of Normalized Mean Squared Error) over previous CS based techniques.