Linogram reconstruction for magnetic resonance imaging (MRI)

Undersampled linogram trajectory for fast imaging (ULTI): experiments at 3 T and 7 T

In this study, the performance of linogram acquisition was investigated for the reconstruction of images from undersampled data using parallel imaging methods. The point spread function (PSF) of linogram sampling was analyzed for image sharpness and artifacts. Generalized auto-calibrating partially parallel acquisition was implemented for this new sampling scheme, and images were reconstructed with high acceleration rates. The results were compared with conventional radial sampling methods using simulations and phantom experiments at 3 T. Additionally, a human volunteer was scanned at 7 T. The results demonstrated that the PSF was sharper and the mean artifact power was lower for linogram sampling compared with radial sampling. Results of simulations and phantom experiments were in accord with the findings of the PSF analysis. In simulations, errors in the reconstructed images were lower for linogram sampling. In phantom experiments, fine details and sharp edges were preserved for linogram sampling, while details were blurred for radial sampling. The in vivo human study demonstrated that linogram sampling could provide high quality images of anatomy, even at high acceleration rates. Linogram sampling not only possesses the advantages of radial sampling, such as reduced sensitivity to motion and higher acceleration rates, but it also provides sharper images with fewer artifacts. Moreover, it is less prone to off-resonance artifacts compared with radial sampling. Copyright © 2016 John Wiley & Sons, Ltd.

Cardiovascular magnetic resonance artefacts

The multitude of applications offered by CMR make it an increasing popular modality to study the heart and the surrounding vessels. Nevertheless the anatomical complexity of the chest, together with cardiac and respiratory motion, and the fast flowing blood, present many challenges which can possibly translate into imaging artefacts. The literature is wide in terms of papers describing specific MR artefacts in great technical detail. In this review we attempt to summarise, in a language accessible to a clinical readership, some of the most common artefacts found in CMR applications. It begins with an introduction of the most common pulse sequences, and imaging techniques, followed by a brief section on typical cardiovascular applications. This leads to the main section on common CMR artefacts with examples, a short description of the mechanisms behind them, and possible solutions.

Reconstruction of MR images from data acquired on a general nonregular grid by pseudoinverse calculation

A minimum-norm least-squares image-reconstruction method for the reconstruction of magnetic resonance images from non-Cartesian sampled data is proposed. The method is based on a general formalism for continuous-to-discrete mapping and pseudoinverse calculation. It does not involve any regridding or interpolation of the data and therefore the methodology differs fundamentally from existing regridding-based methods. Moreover, the method uses a continuous representation of objects in the image domain instead of a discretized representation. Simulations and experiments show the possibilities of the method in both radial and spiral imaging. Simulations revealed that minimum-norm least-squares image reconstruction can result in a drastic decrease of artifacts compared with regridding-based reconstruction. Besides, both in vivo and phantom experiments showed that minimum-norm least-squares image reconstruction leads to contrast improvement and increased signal-to-noise ratio compared with image reconstruction based on regridding. As an appendix, an analytical calculation of the raw data corresponding to the well-known Shepp and Logan software head phantom is presented.

Reduced circular field-of-view imaging

A rapid dynamic imaging technique based on polar k-space sampling is presented. A gain in temporal resolution is achieved by angular undersampling. A detailed analysis of the point spread function of angular undersampled polar imaging reveals a reduced diameter of the corresponding circular field of view. Under the assumption that dynamic changes are restricted to a local circular field of view, angular undersampled dynamic imaging allows the recording of rapid changes at high temporal and spatial resolution. The theoretical and experimental details of the technique are presented.

Elimination of Nyquist ghosts in MRI by using fast linogram imaging

Timing inaccuracies between the even and odd echoes lead to the formation of Nyquist ghosts in conventional (blipped) echo-planar imaging (EPI). A fast radial scanning method based on the linogram sampling geometry was designed and implemented. No ghosting effects are seen with this scheme, and correction for timing inaccuracies is performed using simple postprocessing steps before reconstruction.

A dual approach to linogram imaging for MRI

An alternate scheme for linogram image reconstruction, which is more logical from the viewpoint of its applicability to MRI data, is presented here. As a result, an intermediate step for this method, the direct Fourier method (DFM) gives the same results as the earlier developed general reconstruction algorithm labeled as the linogram method (LM). However, the two differ in the pathways taken to the solution. As a result, an intermediate step for DFM corresponds directly with the geometry of linogram data collected for MRI, in contrast to the LM reconstruction. The two reconstruction methods are delineated within the context of MRI data reconstruction, and applied to reconstruct images from linogram spin-echo data of a physical phantom, obtained on a clinical 1.5 T scanner.

Characterization of and correction for artifacts in linogram MRI

Chemical shift differences, field inhomogeneity, and gradient nonlinearity result in artifacts in magnetic resonance imaging. Three artifacts are characterized for linogram imaging and it is shown that, based on computer simulations and theory, linogram MRI behaves similarly to 2DFT. A correction technique similar to a scheme for 2DFT imaging based on the Dixon technique and coordinate transform methods is proposed. The algorithm is applied to correct for field inhomogeneity and gradient nonlinearity-induced artifacts in both simulations and images of a clinical phantom. The results show good correlation with the theory. It is concluded that linogram imaging offers certain attractive features of both 2DFT and PR imaging techniques, and is a potentially viable alternative to PR imaging in the presence of field inhomogeneity.

Fully three-dimensional reconstruction from data collected on concentric cubes in Fourier space: implementation and a sample application to MRI

An algorithm is proposed for rapid and accurate reconstruction from data collected in Fourier space at points arranged on a grid of concentric cubes. The Fourier transform of the object to be reconstructed is decomposed into the sum of three functions by subdividing its domain into three non-overlapping mutually orthogonal double pyramids. Each of the three functions is zero-valued outside one of the double pyramids and has values inside that double pyramid which are the same as those of Fourier transform of the object to be reconstructed at the same points. Inverse Fourier transforms of these individual functions can be calculated using the chirp z-transform. The outputs of these inverse transforms for the three functions are estimates of their values at points of the same rectangular grid. The function to be reconstructed is estimated for this grid by adding together the three inverse transforms. The whole process has computational complexity of the same order as required for the 3D fast Fourier transform and so (for medically relevant sizes of the data set) it is faster than backprojection into the same size rectangular grid. The design of the algorithm ensures that no interpolations are needed, in contrast to methods involving backprojection with their unavoidable interpolations. As an application, a 3D data collection method for MRI has been designed which directly samples the Fourier transform of the object to be reconstructed on concentric cubes as needed for the algorithm.