Phase Offset Correction Research Articles

Multi-source off-grid DOA estimation using iterative phase offset correction in coarray domain

Direction-of-arrival (DOA) estimation performance degrades when arrival angles of incident signals do not locate exactly on the discretized grid points. Existing off-grid DOA estimation algorithms either suffer from high computational complexity or are restricted to uniform linear arrays (ULAs). In order to overcome these disadvantages, we propose a simple but effective off-grid DOA estimation method, referred to as iterative phase offset correction (IPOC), for non-uniform linear arrays (NLAs) in this work. The proposed IPOC first transforms the received signal into the coarray domain and then iteratively corrects the phase offset between the coarray data and presumed model caused by angle biases according to a closed-form formula. In the case of multiple sources, we separate these sources using generalized inner product and then utilize IPOC to sequentially estimate the off-grid angle of one source in each iteration. The spectral leakage between multiple sources is reduced as well by subtracting cross-correlation terms, thus overcoming the shortage of requiring a large number of training snapshots. We calculate the mean squared error (MSE) of the proposed method theoretically. Simulation results demonstrate the effectiveness and efficacy of the proposed method for off-grid DOA estimation using NLAs with very few snapshots.

MRI phase offset correction method impacts quantitative susceptibility mapping

Individual channel ultra-high field (7T) phase images have to be phase offset corrected prior to the mapping of magnetic susceptibility of tissue. Whilst numerous methods have been proposed for gradient recalled echo MRI phase offset correction, it remains unclear how they affect quantitative magnetic susceptibility values derived from phase images. Methods already proposed either employ a single or multiple echo time MRI data. In terms of the latter, offsets can be derived using an ultra-short echo time acquisition, or by estimating the offset based on two echo points with the assumption of linear phase evolution with echo time. Our evaluation involved 32 channel multi-echo time 7T GRE (Gradient Recalled Echo) and ultra-short echo time PETRA (Pointwise Encoding Time Reduction with Radial Acquisition) MRI data collected for a susceptibility phantom and three human brains. The combined phase images generated using four established offset correction methods (two single and two multiple echo time) were analysed, followed by an assessment of quantitative susceptibility values obtained for a phantom and human brains. The effectiveness of each method in removing the offsets was shown to reduce with increased echo time, decreased signal intensity and reduced overlap in coil sensitivity profiles. Quantitative susceptibility values and how they change with echo time were found to be method specific. Phase offset correction methods based on single echo time data have a tendency to produce more accurate and less noisy quantitative susceptibility maps in comparison with methods employing multiple echo time data.

In-vivo validation of interpolation-based phase offset correction in cardiovascular magnetic resonance flow quantification: a multi-vendor, multi-center study

BackgroundA velocity offset error in phase contrast cardiovascular magnetic resonance (CMR) imaging is a known problem in clinical assessment of flow volumes in vessels around the heart. Earlier studies have shown that this offset error is clinically relevant over different systems, and cannot be removed by protocol optimization. Correction methods using phantom measurements are time consuming, and assume reproducibility of the offsets which is not the case for all systems. An alternative previously published solution is to correct the in-vivo data in post-processing, interpolating the velocity offset from stationary tissue within the field-of-view. This study aims to validate this interpolation-based offset correction in-vivo in a multi-vendor, multi-center setup.MethodsData from six 1.5 T CMR systems were evaluated, with two systems from each of the three main vendors. At each system aortic and main pulmonary artery 2D flow studies were acquired during routine clinical or research examinations, with an additional phantom measurement using identical acquisition parameters. To verify the phantom acquisition, a region-of-interest (ROI) at stationary tissue in the thorax wall was placed and compared between in-vivo and phantom measurements. Interpolation-based offset correction was performed on the in-vivo data, after manually excluding regions of spatial wraparound. Correction performance of different spatial orders of interpolation planes was evaluated.ResultsA total of 126 flow measurements in 82 subjects were included. At the thorax wall the agreement between in-vivo and phantom was − 0.2 ± 0.6 cm/s. Twenty-eight studies were excluded because of a difference at the thorax wall exceeding 0.6 cm/s from the phantom scan, leaving 98. Before correction, the offset at the vessel as assessed in the phantom was − 0.4 ± 1.5 cm/s, which resulted in a − 5 ± 16% error in cardiac output. The optimal order of the interpolation correction plane was 1st order, except for one system at which a 2nd order plane was required. Application of the interpolation-based correction revealed a remaining offset velocity of 0.1 ± 0.5 cm/s and 0 ± 5% error in cardiac output.ConclusionsThis study shows that interpolation-based offset correction reduces the offset with comparable efficacy as phantom measurement phase offset correction, without the time penalty imposed by phantom scans.Trial registrationThe study was registered in The Netherlands National Trial Register (NTR) under TC 4865. Registered 19 September 2014. Retrospectively registered.

Visualizing and quantifying flow stasis in abdominal aortic aneurysms in men using 4D flow MRI

PurposeTo examine methods for visualizing and quantifying flow stasis in abdominal aortic aneurysms (AAA) using 4D Flow MRI. MethodsThree methods were investigated: conventional volumetric residence time (VRT), mean velocity analysis (MVA), and particle travel distance analysis (TDA). First, ideal 4D Flow MRI data was generated using numerical simulations and used as a platform to explore the effects of noise and background phase-offset errors, both of which are common 4D Flow MRI artifacts. Error-free results were compared to noise or offset affected results using linear regression. Subsequently, 4D Flow MRI data for thirteen (13) subjects with AAA was acquired and used to compare the stasis quantification methods against conventional flow visualization. ResultsVRT (R2 = 0.69) was more sensitive to noise than MVA (R2 = 0.98) and TDA (R2 = 0.99) at typical non-contrast signal-to-noise ratio levels (SNR = 20). VRT (R2 = 0.14) was more sensitive to background phase-offsets than MVA (R2 = 0.99) and TDA (R2 = 0.96) when considering a 95% effective background phase-offset correction. Qualitatively, TDA outperformed MVA (Wilcoxon p < 0.005, mean score improvement 1.6/5), and had good agreement (median score 4/5) with flow visualizations. ConclusionFlow stasis can be quantitatively assessed using 4D Flow MRI. While conventional residence time calculations fail due to error accumulation as a result of imperfect measured velocity fields, methods that do not require lengthy particle tracking perform better. MVA and TDA are less sensitive to measurement errors, and TDA generates results most similar to those obtained using conventional flow visualization.

In-vivo validation of interpolation-based phase offset correction in MR flow quantification: a multi-vendor, multi-center study

In-vivo validation of interpolation-based phase offset correction in MR flow quantification: a multi-vendor, multi-center study

Influence of eddy current, Maxwell and gradient field corrections on 3D flow visualization of 3D CINE PC-MRI data

The measurement of velocities based on phase contrast MRI can be subject to different phase offset errors which can affect the accuracy of velocity data. The purpose of this study was to determine the impact of these inaccuracies and to evaluate different correction strategies on three-dimensional visualization. Phase contrast MRI was performed on a 3 T system (Siemens Trio) for in vitro (curved/straight tube models; venc: 0.3 m/s) and in vivo (aorta/intracranial vasculature; venc: 1.5/0.4 m/s) data. For comparison of the impact of different magnetic field gradient designs, in vitro data was additionally acquired on a wide bore 1.5 T system (Siemens Espree). Different correction methods were applied to correct for eddy currents, Maxwell terms, and gradient field inhomogeneities. The application of phase offset correction methods lead to an improvement of three-dimensional particle trace visualization and count. The most pronounced differences were found for in vivo/in vitro data (68%/82% more particle traces) acquired with a low venc (0.3 m/s/0.4 m/s, respectively). In vivo data acquired with high venc (1.5 m/s) showed noticeable but only minor improvement. This study suggests that the correction of phase offset errors can be important for a more reliable visualization of particle traces but is strongly dependent on the velocity sensitivity, object geometry, and gradient coil design.

Performance Analysis of Blind Adaptive Phase Offset Correction Based on Dispersion Minimization

This paper presents an analysis of the performance and behavior of a blind adaptive carrier phase offset recovery scheme based on dispersion minimization (DM). The algorithm, called the DM-derotator, is a kind of simple equalizer that attempts to correct the carrier phase offset by minimizing the dispersion of the projection of the real part of the (complex) data signal. The recent application of this algorithm to digital broadcasting signals motivates our analysis. This paper classifies the stationary points of the DM-derotator for a variety of source signals including digital vestigial side band (VSB) and quadrature amplitude modulation (QAM) and discusses initialization strategies. The analysis is extended to a variety of situations including i) its behavior in the presence of intersymbol interference, ii) its behavior when there is statistical dependence between the in-phase and quadrature components, and iii) its tracking ability.