General Series Model Research Articles

Accelerated 3D metabolite T1 mapping of the brain using variable-flip-angle SPICE.

To develop a practical method to enable 3D T1 mapping of brain metabolites. Due to the high dimensionality of the imaging problem underlying metabolite T1 mapping, measurement of metabolite T1 values has been currently limited to a single voxel or slice. This work achieved 3D metabolite T1 mapping by leveraging a recent ultrafast MRSI technique called SPICE (spectroscopic imaging by exploiting spatiospectral correlation). The Ernst-angle FID MRSI data acquisition used in SPICE was extended to variable flip angles, with variable-density sparse sampling for efficient encoding of metabolite T1 information. In data processing, a novel generalized series model was used to remove water and subcutaneous lipid signals; a low-rank tensor model with prelearned subspaces was used to reconstruct the variable-flip-angle metabolite signals jointly from the noisy data. The proposed method was evaluated using both phantom and healthy subject data. Phantom experimental results demonstrated that high-quality 3D metabolite T1 maps could be obtained and used for correction of T1 saturation effects. In vivo experimental results showed metabolite T1 maps with a large spatial coverage of 240 × 240 × 72 mm3 and good reproducibility coefficients (< 11%) in a 14.5-min scan. The metabolite T1 times obtained ranged from 0.99 to 1.44 s in gray matter and from 1.00 to 1.35 s in white matter. We successfully demonstrated the feasibility of 3D metabolite T1 mapping within a clinically acceptable scan time. The proposed method may prove useful for both T1 mapping of brain metabolites and correcting the T1-weighting effects in quantitative metabolic imaging.

High-resolution sodium imaging using anatomical and sparsity constraints for denoising and recovery of novel features.

To develop and evaluate a novel method for reconstruction of high-quality sodium MR images from noisy, limited k-space data. A novel reconstruction method was developed for reconstruction of high-quality sodium images from noisy, limited k-space data. This method is based on a novel image model that contains a motion-compensated generalized series model and a sparse model. The motion-compensated generalized series model enables effective use of anatomical information from a proton image for denoising and resolution enhancement of sodium data, whereas the sparse model enables high-resolution reconstruction of sodium-dependent novel features. The underlying model estimation problems were solved efficiently using convex optimization algorithms. The proposed method has been evaluated using both simulation and experimental data obtained from phantoms, healthy human volunteers, and tumor patients. Results showed a substantial improvement in spatial resolution and SNR over state-of-the-art reconstruction methods, including compressed sensing and anatomically constrained reconstruction methods. Quantitative tissue sodium concentration maps were obtained from both healthy volunteers and brain tumor patients. These tissue sodium concentration maps showed improved lesion fidelity and allowed accurate interrogation of small targets. A new method has been developed to obtain high-resolution sodium images with good SNR at 3 T. The proposed method makes effective use of anatomical prior information for denoising, while using a sparse model synergistically to recover sodium-dependent novel features. Experimental results have been obtained to demonstrate the feasibility of achieving high-quality tissue sodium concentration maps and their potential for improved detection of spatially heterogeneous responses of tumor to treatment.

Incorporating reference in parallel imaging and compressed sensing.

To develop a new compressed sensing parallel imaging technique called READ-PICS that can effectively incorporate prior information from a reference scan for MR image reconstruction from highly undersampled multichannel measurements. READ-PICS incorporates information from a high-spatial-resolution reference prior using the generalized series model, to achieve increased image sparsity and mitigated noise amplification simultaneously. To further improve the ill-conditioning of the parallel imaging system, an annular area in the central residual k-space is used for calibration. Additionally, the mixed L1-L2 norm of the coefficients from the prior component and residual component is used to enforce joint sparsity. The evaluations on parametric imaging and multiscan experiment demonstrate superior performance of READ-PICS in terms of detail preservation and noise suppression compared to state-of-the-art technique, L1-Iterative self-consistent parallel imaging reconstruction, and prescan required method, correlation imaging. The proposed method can significantly increase signal sparsity and improve the ill-conditioning of the parallel imaging system using reference adaptive regularization. This technique can be easily adapted to other imaging applications where multiple images need to be acquired sequentially and a reference prior is also available.

A Framework for generalized reference image reconstruction methods including HYPR-LR, PR-FOCUSS, and k-t FOCUSS

To investigate the relationships among highly constrained back projection (HYPR)-LR, projection reconstruction focal underdetermined system solver (PR-FOCUSS), and k-t FOCUSS by showing how each method relates to a generalized reference image reconstruction method. That is, the generalized series model employs a fixed reference image and multiplicative corrections-that model is extended here to consider reference images more broadly, both in image space and in transform spaces (x-t and x-f spaces), and that can evolve with iteration. Theoretical relationships between the methods were derived. Computer simulations were done to compare HYPR-LR to one iteration of PR-FOCUSS. The generalized reference approaches applied in the x-t or x-f domain were compared using computer simulation, five cardiac cine imaging datasets, and six myocardial perfusion datasets. PR-FOCUSS and HYPR-LR gave comparable errors, with PR-FOCUSS slightly outperforming HYPR-LR. The baseline image is important to the performance of k-t FOCUSS and x-t FOCUSS, as demonstrated by results from cardiac cine imaging. For cardiac perfusion reconstructions with the use of a temporal average image as the baseline image, k-t FOCUSS gave lower errors than x-t FOCUSS. HYPR-LR and PR-FOCUSS are closely related: both work for radial sampling and use reference images in the x-t domain; HYPR-LR is an approximate implementation of the generalized reference framework, while PR-FOCUSS is a conjugate gradient implementation of the generalized reference framework. The superiority of generalized reference approaches applied in the x-t or x-f domain was sensitive to the characteristics of the acquired data and to the baseline image used.

A variational approach to Boussinesq modelling of fully nonlinear water waves

In this paper we present a new method to derive Boussinesq-type equations from a variational principle. These equations are valid for nonlinear surface-water waves propagating over bathymetry. The vertical structure of the flow, required in the Hamiltonian, is approximated by a (series of) vertical shape functions associated with unknown parameter(s). It is not necessary to make approximations with respect to the nonlinearity of the waves. The resulting approximate Hamiltonian is positive definite, contributing to the good dynamical behaviour of the resulting equations. The resulting flow equations consist of temporal equations for the surface elevation and potential, as well as a (set of) elliptic equations for some auxiliary parameter(s). All equations only contain low-order spatial derivatives and no mixed time–space derivatives. Since one of the parameters, the surface potential, can be associated with a uniform shape function, the resulting equations are very well suited for wave–current interacting flows.The variational method is applied to two simple models, one with a parabolic vertical shape function and the other with a hyperbolic-cosine vertical structure. For both, as well as the general series model, the flow equations are derived. Linear dispersion and shoaling are studied using the average Lagrangian. The model with a parabolic vertical shape function has improved frequency dispersion, as compared to classical Boussinesq models. The model with a hyperbolic-cosine vertical structure can be made to have exact phase and group velocity, as well as shoaling, for a certain frequency.For the model with a parabolic vertical structure, numerical computations are done with a one-dimensional pseudo-spectral code. These show the nonlinear capabilities for periodic waves over a horizontal bed and an underwater bar. Further some long-distance computations for soliton wave groups over bathymetry are presented.

A data‐consistent linear prediction method for image reconstruction from finite Fourier samples

Linear prediction (LP) methods have been widely used for high-resolution spectral estimation from finite Fourier samples. Their application to image reconstruction, on the other hand, has been markedly less successful. In this article, we present an improved LP method for high-resolution image reconstruction. The distinguishing feature of the proposed method is its use of a generalized series model to enforce the data consistency constraint to compensate for reconstruction error resulting from LP modeling. Several reconstruction examples from magnetic resonance imaging data are included to demonstrate the performance of the method. © 1996 John Wiley & Sons, Inc.