Image-based EPI ghost correction using an algorithm based on projection onto convex sets (POCS)

Reconstruction for 7T high-resolution whole-brain diffusion MRI using two-stage N/2 ghost correction and L1-SPIRiT without single-band reference

PURPOSE

To combine a new two-stage N/2 ghost correction and an adapted L1-SPIRiT method for reconstruction of 7T highly accelerated whole-brain diffusion MRI (dMRI) using only autocalibration scans (ACS) without the need of additional single-band reference (SBref) scans.

METHODS

The proposed ghost correction consisted of a 3-line reference approach in stage 1 and the reference-free entropy method in stage 2. The adapted L1-SPIRiT method was formulated within the 3D k-space framework. Its efficacy was examined by acquiring two dMRI data sets at 1.05-mm isotropic resolutions with a total acceleration of 6 or 9 (i.e., 2-fold or 3-fold slice and 3-fold in-plane acceleration). Diffusion analysis was performed to derive DTI metrics and estimate fiber orientation distribution functions (fODFs). The results were compared with those of 3D k-space GRAPPA using only ACS, all in reference to 3D k-space GRAPPA using both ACS and SBref (serving as a reference).

RESULTS

The proposed ghost correction eliminated artifacts more robustly than conventional approaches. Our adapted L1-SPIRiT method outperformed 3D k-space GRAPPA when using only ACS, improving image quality to what was achievable with 3D k-space GRAPPA using both ACS and SBref scans. The improvement in image quality further resulted in an improvement in estimation performances for DTI and fODFs.

CONCLUSION

The combination of our new ghost correction and adapted L1-SPIRiT method can reliably reconstruct 7T highly accelerated whole-brain dMRI without the need of SBref scans, increasing acquisition efficiency and reducing motion sensitivity.

Nyquist ghost correction of breast diffusion weighted imaging using referenceless methods

PURPOSE

Correction of Nyquist ghosts for single-shot spin-echo EPI using the standard 3-line navigator often fails in breast DWI because of incomplete fat suppression, respiration, and greater B₀ inhomogeneity. The purpose of this work is to compare the performance of the 3-line navigator with 4 data-driven methods termed "referenceless methods," including 2 previously proposed in literature, 1 introduced in this work, and finally a combination of all 3, in breast DWI.

METHODS

Breast DWI was acquired for 41 patients with SS SE-EPI. Raw data was corrected offline with the standard 3-line navigator and 4 referenceless methods, which modeled the ghost as a linear phase error and minimized 3 unique cost functions as well as the median solution of all 3. Ghost levels were evaluated based on the signal intensity in the background region, defined by a mask auto-generated from a T₁ -weighted anatomical image. Ghost intensity measurements were fit to a linear mixed model including ghost correction method and b-value as covariates.

RESULTS

All 4 referenceless methods outperformed the standard 3-line navigator with statistical significance at all 4 b-values tested (b = 0, 100, 600, and 800 s/mm² ).

CONCLUSIONS

Referenceless methods provide a robust way to reduce Nyquist ghosts in breast DWI without the need for any additional calibration scan.

Ghost reduction in echo-planar imaging by joint reconstruction of images and line-to-line delays and phase errors

PURPOSE

To correct line-to-line delays and phase errors in echo-planar imaging (EPI).

THEORY AND METHODS

EPI-trajectory auto-corrected image reconstruction (EPI-TrACR) is an iterative maximum-likelihood technique that exploits data redundancy provided by multiple receive coils between nearby lines of k-space to determine and correct line-to-line trajectory delays and phase errors that cause ghosting artifacts. EPI-TrACR was efficiently implemented using a segmented FFT and was applied to in vivo brain data acquired at 7 T across acceleration (1×-4×) and multishot factors (1-4 shots), and in a time series.

RESULTS

EPI-TrACR reduced ghosting across all acceleration factors and multishot factors, compared to conventional calibrated reconstructions and the PAGE method. It also achieved consistently lower ghosting in the time series. Averaged over all cases, EPI-TrACR reduced root-mean-square ghosted signal outside the brain by 27% compared to calibrated reconstruction, and by 40% compared to PAGE.

CONCLUSION

EPI-TrACR automatically corrects line-to-line delays and phase errors in multishot, accelerated, and dynamic EPI. While the method benefits from additional calibration data for initialization, it was not a requirement for most reconstructions. Magn Reson Med 79:3114-3121, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Reference-free single-pass EPI Nyquist ghost correction using annihilating filter-based low rank Hankel matrix (ALOHA)

PURPOSE

MR measurements from an echo-planar imaging (EPI) sequence produce Nyquist ghost artifacts that originate from inconsistencies between odd and even echoes. Several reconstruction algorithms have been proposed to reduce such artifacts, but most of these methods require either additional reference scans or multipass EPI acquisition. This article proposes a novel and accurate single-pass EPI ghost artifact correction method that does not require any additional reference data.

THEORY AND METHODS

After converting a ghost correction problem into separate k-space data interpolation problems for even and odd phase encoding, our algorithm exploits an observation that the differential k-space data between the even and odd echoes is a Fourier transform of an underlying sparse image. Accordingly, we can construct a rank-deficient Hankel structured matrix, whose missing data can be recovered using an annihilating filter-based low rank Hankel structured matrix completion approach.

RESULTS

The proposed method was applied to EPI data for both single and multicoil acquisitions. Experimental results using in vivo data confirmed that the proposed method can completely remove ghost artifacts successfully without prescan echoes.

CONCLUSION

Owing to the discovery of the annihilating filter relationship from the intrinsic EPI image property, the proposed method successfully suppresses ghost artifacts without a prescan step. Magn Reson Med 76:1775-1789, 2016. © 2016 International Society for Magnetic Resonance in Medicine.

Iterative projection onto convex sets for quantitative susceptibility mapping

PURPOSE

Quantitative susceptibility map (QSM) reconstruction is ill posed due to the zero values on the "magic angle cone" that make the maps prone to streaking artifacts. We propose projection onto convex sets (POCS) in the method of steepest descent (SD) for QSM reconstruction.

METHODS

Two convex projections, an object-support projection in the image domain and a projection in k-space were used. QSM reconstruction using the proposed SD-POCS method was compared with SD and POCS alone as well as with truncated k-space division (TKD) for numerically simulated and 7 Tesla (T) human brain phase data.

RESULTS

The QSM reconstruction error from noise-free simulated phase data using SD-POCS is at least two orders of magnitude lower than using SD, POCS, or TKD and has reduced streaking artifacts. Using the l1 -TV reconstructed susceptibility as a gold standard for 7T in vivo imaging, SD-POCS showed better image quality comparing to SD, POCS, or TKD from visual inspection.

CONCLUSION

POCS is an alternative method for regularization that can be used in an iterative minimization method such as SD for QSM reconstruction.

A correction method for streak artifacts in gradient-echo EPI using spin-echo EPI reference data

OBJECTIVE

To analyze the streak artifacts in a gradient-echo echo planar imaging (GE-EPI) sequence and to propose a correction method for the Nyquist ghost artifacts that does not cause streak artifacts in the GE-EPI imaging.

MATERIALS AND METHODS

Several GE-EPI imaging experiments with various reference scans, using both GE-EPI and SE-EPI scan data, were performed to analyze the streak artifacts and to investigate the spin dephasing phenomena of the GE-EPI reference scan. In addition, the analysis based on the spin dephasing was undertaken in order to demonstrate that the SE-EPI reference data can be used for the correction of the GE-EPI main scan data.

RESULTS

The experimental results confirmed that the improvement of the reference data using either signal averaging or a large flip angle cannot guarantee perfect correction of the streak artifact if the noise is not completely removed. Due to the main field inhomogeneity, the spins of the GE-EPI reference data were dephased in multiple echo signals. The proposed correction method, which uses a SE-EPI reference scan for the GE-EPI images, eliminates the N/2 ghost artifacts without producing streak artifacts.

CONCLUSION

It is believed that the proposed phase error correction scheme can improve the EPI performance in high field MRIs with higher magnetic field inhomogeneities.

Two-dimensional phase correction method for single and multi-shot echo planar imaging

Ghost artifacts are a serious issue in single and multi-shot echo planar imaging. Because of these coherent artifacts, it is essential to consistently suppress the ghosts. In this article, we present a phase correction algorithm that achieves excellent ghost suppression for single and multi-shot echo planar imaging. The phase correction is performed along both the x (read) direction and y (phase) direction. To this end, we apply a double field of view prescan and compute the phase required for ghost suppression. This phase is fitted to a 2D polynomial. The fitted phase is used to correct the echo planar imaging images. The correction algorithm can be used with any readout gradient polarities and any number of shots. A flow chart of the correction method is provided to better clarify the full process. Finally, phantom and volunteer images demonstrate the improvement of artifact suppression obtained with this algorithm over conventional phase correction methods.

Robust 2D phase correction for echo planar imaging under a tight field-of-view

Nyquist ghost artifacts are a serious issue in echo planar imaging. These artifacts primarily originate from phase difference between even and odd echo images and can be removed or reduced using phase correction methods. The commonly used 1D phase correction can only correct phase difference along readout axis. 2D correction is, therefore, necessary when phase difference presents along both readout and phase encoding axes. However, existing 2D methods have several unaddressed issues that affect their practicality. These issues include uncharacterized noise behavior, image artifact due to unoptimized phase estimation, Gibbs ringing artifact when directly applying to partial k(y) data, and most seriously a new image artifact under tight field-of-view (i.e., field-of-view slightly smaller than object size). All these issues are addressed in this article. Specifically, theoretical analysis of noise amplification and effect of phase estimation error is provided, and tradeoff between noise and ghost is studied. A new 2D phase correction method with improved polynomial fitting, joint homodyne processing and phase correction, compatibility with tight field-of-view is then proposed. Various results show that the proposed method can robustly generate images free of Nyquist ghosts and other image artifacts even in oblique scans or when cross-term eddy current terms are significant.

POCS-enhanced correction of motion artifacts in parallel MRI

A new method for correction of MRI motion artifacts induced by corrupted k-space data, acquired by multiple receiver coils such as phased arrays, is presented. In our approach, a projections onto convex sets (POCS)-based method for reconstruction of sensitivity encoded MRI data (POCSENSE) is employed to identify corrupted k-space samples. After the erroneous data are discarded from the dataset, the artifact-free images are restored from the remaining data using coil sensitivity profiles. The error detection and data restoration are based on informational redundancy of phased-array data and may be applied to full and reduced datasets. An important advantage of the new POCS-based method is that, in addition to multicoil data redundancy, it can use a priori known properties about the imaged object for improved MR image artifact correction. The use of such information was shown to improve significantly k-space error detection and image artifact correction. The method was validated on data corrupted by simulated and real motion such as head motion and pulsatile flow.

Characterization of Nyquist ghost in EPI-fMRI acquisition sequences implemented on two clinical 1.5 T MR scanner systems: effect of readout bandwidth and echo spacing

In EPI‐fMRI acquisitions, various readout bandwidth (BW) values are used as a function of gradients' characteristics of the MR scanner system. Echo spacing (ES) is another fundamental parameter of EPI‐fMRI sequences, but the employed ES value is not usually reported in fMRI studies. Nyquist ghost is a typical EPI artifact that can degrade the overall quality of fMRI time series. In this work, the authors assessed the basic effect of BW and ES for two clinical 1.5 T MR scanner systems (scanner‐A, scanner‐B) on Nyquist ghost of gradient‐echo EPI‐fMRI sequences. BW range was: scanner‐A, 1953‐3906 Hz/pixel; scanner‐B, 1220‐2894 Hz/pixel. ES range was: scanner‐A, scanner‐B: 0.75‐1.33 ms. The ghost‐to‐signal ratio of time series acquisition (GSRts) and drift of ghost‐to‐signal ratio (DRGSR) were measured in a water phantom. For both scanner‐A (93% of variation) and scanner‐B (102% of variation) the mean GSRts significantly increased with increasing BW. GSRts values of scanner‐A did not significantly depended on ES. On the other hand, GSRts values of scanner‐B significantly varied with ES, showing a downward trend (81% of variation) with increasing ES. In addition, a GSRts spike point at ES=1.05ms indicating a potential resonant effect was revealed. For both scanners, no significant effect of ES on DRGSR was revealed. DRGSR values of scanner‐B did not significantly vary with BW, whereas DRGSR values of scanner‐A significantly depended on BW showing an upward trend from negative to positive values with increasing BW. GSRts and DRGSR can significantly vary with BW and ES, and the specific pattern of variation may depend on gradients performances, EPI sequence calibrations and functional design of radiofrequency coil. Thus, each MR scanner system should be separately characterized. In general, the employment of low BW values seems to reduce the intensity and temporal variation of Nyquist ghost in EPI‐fMRI time series. On the other hand, the use of minimum ES value might not be entirely advantageous when the MR scanner is characterized by gradients with low performances and suboptimal EPI sequence calibration.

PACS numbers: 87.61.‐c, 87.61.Qr, 87.61.Hk

A new distortion model for strong inhomogeneity problems in echo-planar MRI

This paper proposes a new distortion model for strong inhomogeneity problems in echo planar imaging (EPI). Fast imaging sequences in magnetic resonance imaging (MRI), such as EPI, are very important in applications where temporal resolution or short total acquisition time is essential. Unfortunately, fast imaging sequences are very sensitive to variations in the homogeneity of the main magnetic field. The inhomogeneity leads to geometrical distortions and intensity changes in the image reconstructed via fast Fourier transform. Also, under strong inhomogeneity, the accelerated intravoxel dephase may overly attenuate signals coming from regions with higher inhomogeneity variations. Moreover, coarse discretization schemes for the inhomogeneity are not able to cope with this problem, producing discretization artifacts when large inhomogeneity variations occur. Most of the existing models do not attempt to solve this problem. In this paper, we propose a modification of the discrete distortion model to incorporate the effects of the intravoxel inhomogeneity and to minimize the discretization artifacts. As a result, these problems are significantly reduced. Extensive experiments are shown to demonstrate the achieved improvements. Also, the performance of the new model is evaluated for conjugate phase, least squares method (minimized iteratively using conjugated gradients), and regularized methods (using a total variation penalty).

SNR phase order k-space encoding (SPOKE)

A method of determining the phase-encode order for MR Fourier-encoded imaging is described, which provides an additional option for optimizing images from samples with signals that change during data acquisition. Examples are in hyperpolarized helium gas imaging of the lungs where polarization is lost with each RF pulse or the signal changes observed in rapid dynamic studies with T(1) or T(2)* contrast agents when mixing is taking place. The method uses a single frequency-encoded projection in the proposed phase-encoding direction. The projection is subsequently sorted into signal-to-noise ratio (SNR) order. The indices of the sorted array are then used to create the phase-encode table to be used for the scan. This phase table is sorted in descending SNR order for signals that decrease during data acquisition and in ascending order for signals that increase during data acquisition. Simulations suggest that this technique can produce higher resolution than centric-ordered phase encoding at the expense of increased modulation (ghosting) artifact for dynamically changing signals. Initial practical implementation of the technique has been carried out on a dedicated 0.2-T Niche MR system, and the test object results agree well with simulations. Hyperpolarized 3-He lung images have also been acquired and postprocessed using the SNR phase order k-space encoding (SPOKE) methodology and show potential for improved imaging with high flip angles where polarization is rapidly lost. Applications may also be found for 3D volumetric acquisitions where two dimensions can be SPOKE encoded.

Image-based method for automated phase correction of ghost

One of the most common artifacts for echo planar imaging is the ghost artifact, typically overcome with the aid of a reference scan preceding the actual image acquisition. In this work, we describe an automated free-scan-reference method for reducing ghost artifact using image-based correction. The two dimensional Fourier transformation of an entire data of image matrix is used to reconstruct two new images, one is reconstructed only by even rows, the other is only by odd rows, with the remaining ones zero-filled. Phase shift between even echoes and odd echoes can be computed by using the two images. Unwrapped phase shift gained by Marquardt-Levenber unlinear fitting can be used to suppress the ghost effectively.

Correction for geometric distortion and N/2 ghosting in EPI by phase labeling for additional coordinate encoding (PLACE)

Echo-planar imaging (EPI) is vulnerable to geometric distortion and N/2 ghosting. These artifacts can be analyzed with an intuitive k-t space tool, and here we propose a simple method for their correction. In a slightly modified additional EPI acquisition, we sample the k-t space with a shift in k(y) by adding a small area to the phase-encoding (PE) gradient. Physically, the added gradient area creates a relative phase ramp across the object and directly encodes the undistorted original y-coordinate of each voxel into a phase difference between two distorted complex images, in a method called "phase labeling for additional coordinate encoding" (PLACE). The phase information is then used to map the mismapped signals back to their original locations for geometric and intensity correction. Smoothing of expanded complex data matrix effectively reduces noise in the differential phase map and allows subpixel warping. The two acquired images can also be averaged to effectively suppress the N/2 ghost. Efficient correction for both artifacts can be achieved with three acquisitions. These acquisitions can also serve as reference scans to correct for geometric distortion and/or N/2 ghost artifacts on all images in a time series. The technique was successfully demonstrated in phantom and animal studies.

Method of generalized projections algorithm for image-based reduction of artifacts in radial imaging

This work describes the method of generalized projections (MGP) as an image-based, postprocessing method to correct for phase inconsistencies caused by echo misalignments in radial imaging. Computer simulations show that MGP can correct for echo shifts, constant phase, and amplitude errors, but the accuracy of the correction is limited, and this accuracy is reduced by the addition of more degrees of freedom. In phantom experiments, MGP performed better than magnitude filtered backprojection and anti-parallel projections correction.

Calibration of echo-planar 2D-selective RF excitation pulses

Echo-planar radiofrequency (RF) pulses (EPP) are increasingly being used for 2D-selective excitation in MRI. Pulse schemes of this kind are susceptible to eddy-current effects, timing imperfections, and anisotropy of the gradient system. As a consequence, practical EPP implementations have been restricted to robust fly-back strategies that use only every other leg of the echo-planar trajectory for RF transmission. The present work is dedicated to enabling forward-backward EPP with RF transmission during each k-space segment, hence doubling the pulses' time efficiency. This is accomplished by comprehensive pulse calibration based on preparatory measurements of the system imperfections, including potential gradient anisotropy. The effectiveness of the method is demonstrated in vitro and in vivo. By doubling the speed of k-space coverage, the proposed method enhances the potential of EPP for numerous applications. For example, motion-sensitive techniques benefit from shorter feasible echo times (TEs) and improved excitation profiles resulting from reduced in-pulse motion. In sequences with fast repetition, shorter EPP help reduce the overall scan duration. Alternatively, the higher time efficiency of forward-backward EPP can enhance their spatial selectivity.

A method of generalized projections (MGP) ghost correction algorithm for interleaved EPI

Investigations into the method of generalized projections (MGP) as a ghost correction method for interleaved EPI are described. The technique is image-based and does not require additional reference scans. The algorithm was found to be more effective if a priori knowledge was incorporated to reduce the degrees of freedom, by modeling the ghosting as arising from a small number of phase offsets. In simulations with phase variation between consecutive shots for n-interleaved echo planar imaging (EPI), ghost reduction was achieved for n = 2 only. With no phase variation between shots, ghost reduction was obtained with n up to 16. Incorporating a relaxation parameter was found to improve convergence. Dependence of convergence on the region of support was also investigated. A fully automatic version of the method was developed, using results from the simulations. When tested on in vivo 2-, 16-, and 32-interleaved spin-echo EPI data, the method achieved deghosting and image restoration close to that obtained by both reference scan and odd/even filter correction, although some residual artifacts remained.

Reference-scan-free method for automated correction of Nyquist ghost artifacts in echoplanar brain images

One of the most common artifacts for echo-planar imaging is the Nyquist ghost, typically overcome with the aid of a reference scan preceding the actual image acquisition. In this work, a nonlinear phase correction obviating the need for a reference scan is proposed. The method is based on computing the second moments of the even and odd subdomains of the phase-encoding k-space data to retrieve the phase disparities between even and odd echoes. The method's underlying assumption is that the images are dominated by their low frequency and symmetric part. In vivo data demonstrate the effectiveness of the algorithm showing ghost suppression comparable to that achievable with the reference-scan method.

POCSENSE: POCS-based reconstruction for sensitivity encoded magnetic resonance imaging

A novel method for iterative reconstruction of images from undersampled MRI data acquired by multiple receiver coil systems is presented. Based on Projection onto Convex Sets (POCS) formalism, the method for SENSitivity Encoded data reconstruction (POCSENSE) can be readily modified to include various linear and nonlinear reconstruction constraints. Such constraints may be beneficial for reconstructing highly and overcritically undersampled data sets to improve image quality. POCSENSE is conceptually simple and numerically efficient and can reconstruct images from data sampled on arbitrary k-space trajectories. The applicability of POCSENSE for image reconstruction with nonlinear constraining was demonstrated using a wide range of simulated and real MRI data.