Undersampling Pattern Research Articles

Volumetric abdominal perfusion measurement using a pseudo-randomly sampled 3D fast-spin-echo (FSE) arterial spin labeling (ASL) sequence and compressed sensing reconstruction.

To improve image quality and spatial coverage for abdominal perfusion imaging by implementing an arterial spin labeling (ASL) sequence that combines variable-density 3D fast-spin-echo (FSE) with Cartesian trajectory and compressed-sensing (CS) reconstruction. A volumetric FSE sequence was modified to include background-suppressed pseudo-continuous ASL labeling and to support variable-density (VD) Poisson-disk sampling for acceleration. We additionally explored the benefits of center oversampling and variable outer k-space sampling. Fourteen healthy volunteers were scanned on a 3T scanner to test acceleration factors as well as the various sampling schemes described under synchronized-breathing to limit motion issues. A CS reconstruction was implemented using the BART toolbox to reconstruct perfusion-weighted ASL volumes, assessing the impact of acceleration, different reconstruction, and sampling strategies on image quality. CS acceleration is feasible with ASL, and a strong renal perfusion signal could be observed even at very high acceleration rates (≈15). We have shown that ASL k-space complex subtraction was desirable before CS reconstruction. Although averaging of multiple highly accelerated images helped to reduce artifacts from physiologic fluctuations, superior image quality was achieved by interleaving of different highly undersampled pseudo-random spatial sampling patterns and using 4D-CS reconstruction. Combination of these enhancements produces high-quality ASL volumes in under 5 min. High-quality isotropic ASL abdominal perfusion volumes can be obtained in healthy volunteers with a VD-FSE and CS reconstruction. This lays the groundwork for future developments toward whole abdomen free-breathing non-contrast perfusion imaging.

ACCELERATED CORONARY MRI USING 3D SPIRIT-RAKI WITH SPARSITY REGULARIZATION.

Coronary MRI is a non-invasive radiation-free imaging tool for the diagnosis of coronary artery disease. One of its limitations is the long scan time, due to the need for high resolution imaging in the presence of respiratory and cardiac motions. Machine learning (ML) methods have been recently utilized to accelerate MRI. In particular, a scan-specific ML technique, called Robust Artifical-neural-network for k-space Interpolation (RAKI) has shown promise in cardiac MRI. However, it requires uniform undersampling. In this study, we sought to extend this approach to arbitrary sampling patterns, using coil self-consistency. This technique, called SPIRiT-RAKI, utilizes scan-specific convolutional neural networks to nonlinearly enforce coil self-consistency. Additionally, regularization terms can also be incorporated. SPIRiT-RAKI was used to accelerate right coronary MRI. Reconstructions were compared to SPIRiT for different undersampling patterns and acceleration rates. Results show SPIRiT-RAKI reduces residual aliasing and blurring artifacts compared to SPIRiT.

Undersampling patterns in k-space for compressed sensing MRI using two-dimensional Cartesian sampling.

In compressed sensing magnetic resonance imaging (CS-MRI), undersampling of k-space is performed to achieve faster imaging. For this process, it is important to acquire data randomly, and an optimal random undersampling pattern is required. However, random undersampling is difficult in two-dimensional (2D) Cartesian sampling. In this study, the effect of random undersampling patterns on image reconstruction was clarified using phantom and in vivo MRI, and a sampling pattern relevant for 2D Cartesian sampling in CS-MRI is suggested. The precision of image restoration was estimated with various acceleration factors and extents for the fully sampled central region of k-space. The root-mean-square error, structural similarity index, and modulation transfer function were measured, and visual assessments were also performed. The undersampling pattern was shown to influence the precision of image restoration, and an optimal undersampling pattern should be used to improve image quality; therefore, we suggest that the ideal undersampling pattern in CS-MRI for 2D Cartesian sampling is one with a high extent for the fully sampled central region of k-space.

Lung morphometry using hyperpolarized 129 Xe multi-b diffusion MRI with compressed sensing in healthy subjects and patients with COPD.

To demonstrate the feasibility of compressed sensing (CS) to accelerate the acquisition of hyperpolarized (HP) 129 Xe multi-b diffusion MRI for quantitative assessments of lung microstructural morphometry. Six healthy subjects and six chronic obstructive pulmonary disease (COPD) subjects underwent HP 129 Xe multi-b diffusion MRI (b=0, 10, 20, 30, and 40s/cm2 ). First, a fully sampled (FS) acquisition of HP 129 Xe multi-b diffusion MRI was conducted in one healthy subject. The acquired FS dataset was retrospectively undersampled in the phase encoding direction, and an optimal twofold undersampled pattern was then obtained by minimizing mean absolute error (MAE) between retrospective CS (rCS) and FS MR images. Next, the FS and CS acquisitions during separate breath holds were performed on five healthy subjects (including the above one). Additionally, the FS and CS synchronous acquisitions during a single breath hold were performed on the sixth healthy subject and one COPD subject. However, only CS acquisitions were conducted in the rest of the five COPD subjects. Finally, all the acquired FS, rCS and CS MR images were used to obtain morphometric parameters, including acinar duct radius (R), acinar lumen radius (r), alveolar sleeve depth (h), mean linear intercept (Lm ), and surface-to-volume ratio (SVR). The Wilcoxon signed-rank test and the Bland-Altman plot were employed to assess the fidelity of the CS reconstruction. Moreover, the t-test was used to demonstrate the effectiveness of the multi-b diffusion MRI with CS in clinical applications. The retrospective results demonstrated that there was no statistically significant difference between rCS and FS measurements using the Wilcoxon signed-rank test (P>0.05). Good agreement between measurements obtained with the CS and FS acquisitions during separate breath holds was demonstrated in Bland-Altman plots of slice differences. Specifically, the mean biases of the R, r, h, Lm , and SVR between the CS and FS acquisitions were 1.0%, 2.6%, -0.03%, 1.5%, and -5.5%, respectively. Good agreement between measurements with the CS and FS acquisitions was also observed during the single breath-hold experiments. Furthermore, there were significant differences between the morphometric parameters for the healthy and COPD subjects (P<0.05). Our study has shown that HP 129 Xe multi-b diffusion MRI with CS could be beneficial in lung microstructural assessments by acquiring less data while maintaining the consistent results with the FS acquisitions.

Stable and efficient retrospective 4D-MRI using non-uniformly distributed quasi-random numbers

The purpose of this work is the development of a robust and reliable three-dimensional (3D) Cartesian imaging technique for fast and flexible retrospective 4D abdominal MRI during free breathing. To this end, a non-uniform quasi random (NU-QR) reordering of the phase encoding (ky–kz) lines was incorporated into 3D Cartesian acquisition. The proposed sampling scheme allocates more phase encoding points near the k-space origin while reducing the sampling density in the outer part of the k-space. Respiratory self-gating in combination with SPIRiT-reconstruction is used for the reconstruction of abdominal data sets in different respiratory phases (4D-MRI). Six volunteers and three patients were examined at 1.5 T during free breathing. Additionally, data sets with conventional two-dimensional (2D) linear and 2D quasi random phase encoding order were acquired for the volunteers for comparison. A quantitative evaluation of image quality versus scan times (from 70 s to 626 s) for the given sampling schemes was obtained by calculating the normalized mutual information (NMI) for all volunteers. Motion estimation was accomplished by calculating the maximum derivative of a signal intensity profile of a transition (e.g. tumor or diaphragm).The 2D non-uniform quasi-random distribution of phase encoding lines in Cartesian 3D MRI yields more efficient undersampling patterns for parallel imaging compared to conventional uniform quasi-random and linear sampling. Median NMI values of NU-QR sampling are the highest for all scan times. Therefore, within the same scan time 4D imaging could be performed with improved image quality.The proposed method allows for the reconstruction of motion artifact reduced 4D data sets with isotropic spatial resolution of 2.1 × 2.1 × 2.1 mm3 in a short scan time, e.g. 10 respiratory phases in only 3 min. Cranio-caudal tumor displacements between 23 and 46 mm could be observed.NU-QR sampling enables for stable 4D-MRI with high temporal and spatial resolution within short scan time for visualization of organ or tumor motion during free breathing. Further studies, e.g. the application of the method for radiotherapy planning are needed to investigate the clinical applicability and diagnostic value of the approach.

Sparse recovery of undersampled intensity patterns for coherent diffraction imaging at high X-ray energies

Coherent X-ray photons with energies higher than 50 keV offer new possibilities for imaging nanoscale lattice distortions in bulk crystalline materials using Bragg peak phase retrieval methods. However, the compression of reciprocal space at high energies typically results in poorly resolved fringes on an area detector, rendering the diffraction data unsuitable for the three-dimensional reconstruction of compact crystals. To address this problem, we propose a method by which to recover fine fringe detail in the scattered intensity. This recovery is achieved in two steps: multiple undersampled measurements are made by in-plane sub-pixel motion of the area detector, then this data set is passed to a sparsity-based numerical solver that recovers fringe detail suitable for standard Bragg coherent diffraction imaging (BCDI) reconstruction methods of compact single crystals. The key insight of this paper is that sparsity in a BCDI data set can be enforced by recognising that the signal in the detector, though poorly resolved, is band-limited. This requires fewer in-plane detector translations for complete signal recovery, while adhering to information theory limits. We use simulated BCDI data sets to demonstrate the approach, outline our sparse recovery strategy, and comment on future opportunities.

The Empirical Effect of Gaussian Noise in Undersampled MRI Reconstruction

In Fourier-based medical imaging, sampling below the Nyquist rate results in an underdetermined system, in which a linear reconstruction will exhibit artifacts. Another consequence is lower signal-to-noise ratio (SNR) because of fewer acquired measurements. Even if one could obtain information to perfectly disambiguate the underdetermined system, the reconstructed image could still have lower image quality than a corresponding fully sampled acquisition because of reduced measurement time. The coupled effects of low SNR and underdetermined system during reconstruction makes it difficult to isolate the impact of low SNR on image quality. To this end, we present an image quality prediction process that reconstructs fully sampled, fully determined data with noise added to simulate the SNR loss induced by a given undersampling pattern. The resulting prediction image empirically shows the effects of noise in undersampled image reconstruction without any effect from an underdetermined system. We discuss how our image quality prediction process simulates the distribution of noise for a given undersampling pattern, including variable density sampling that produces colored noise in the measurement data. An interesting consequence of our prediction model is that recovery from an underdetermined nonuniform sampling is equivalent to a weighted least squares optimization that accounts for heterogeneous noise levels across measurements. Through experiments with synthetic and in vivo datasets, we demonstrate the efficacy of the image quality prediction process and show that it provides a better estimation of reconstruction image quality than the corresponding fully sampled reference image.

High spatio‐temporal resolution in functional MRI with 3D echo planar imaging using cylindrical excitation and a CAIPIRINHA undersampling pattern

The combination of 3D echo planar imaging (3D-EPI) with a 2D-CAIPIRINHA undersampling scheme provides high flexibility in the optimization for spatial or temporal resolution. This flexibility can be increased further with the addition of a cylindrical excitation pulse, which exclusively excites the brain regions of interest. Here, 3D-EPI was combined with a 2D radiofrequency pulse to reduce the brain area from which signal is generated, and hence, allowing either reduction of the field of view or reduction of parallel imaging noise amplification. 3D-EPI with cylindrical excitation and 4 × 3-fold undersampling in a 2D-CAIPIRINHA sampling scheme was used to generate functional MRI (fMRI) data with either 2-mm or 0.9-mm in-plane resolution and 1.1-s temporal resolution over a 5-cm diameter cylinder placed over both temporal lobes for an auditory fMRI experiment. Significant increases in image signal-to-noise ratio (SNR) and temporal SNR (tSNR) were found for both 2-mm isotropic data and the high-resolution protocol when using the cylindrical excitation pulse. Both protocols yielded highly significant blood oxygenation level-dependent responses for the presentation of natural sounds. The higher tSNR of the cylindrical excitation 3D-EPI data makes this sequence an ideal choice for high spatiotemporal resolution fMRI acquisitions. Magn Reson Med 79:2589-2596, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Accelerated three-dimensional multispectral MRI with robust principal component analysis for separation of on- and off-resonance signals.

To enable highly accelerated distortion-free MRI near metal by separating on- and off-resonance to exploit the redundancy of slice-phase encoding for the dominant on-resonance component. Multispectral MRI techniques resolve off-resonance distortions by a combination of limited excitation bins and additional encoding. Inspired by robust principal component analysis, a novel compact representation of multispectral images as a sum of rank-one and sparse matrices corresponding to on- and off-resonance respectively is described. This representation is used in a calibration-free and model-free reconstruction for data with an undersampling pattern that varies between bins. Retrospective undersampling was used to compare the proposed reconstruction and bin-by-bin compressed sensing. Hip images were acquired in eight patients with standard and prospectively undersampled three-dimensional multispectral imaging, and image quality was evaluated by two radiologists on a 5-point scale. Experiments with retrospective undersampling showed that the enhanced sparsity afforded by the separation greatly reduces reconstruction errors and artifacts. Images from prospectively undersampled multispectral imaging offered 2.6-3.4-fold (18-24-fold overall) acceleration compared to standard multispectral imaging with parallel imaging and partial-Fourier acceleration with equivalence in all qualitative assessments within a tolerance of one point (P < 0.004). Three-dimensional multispectral imaging can be highly accelerated by varying undersampling between bins and separating on- and off-resonance. Magn Reson Med 79:1495-1505, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Denoising Algorithm for CFA Image Sensors Considering Inter-Channel Correlation.

In this paper, a spatio-spectral-temporal filter considering an inter-channel correlation is proposed for the denoising of a color filter array (CFA) sequence acquired by CCD/CMOS image sensors. Owing to the alternating under-sampled grid of the CFA pattern, the inter-channel correlation must be considered in the direct denoising process. The proposed filter is applied in the spatial, spectral, and temporal domain, considering the spatio-tempo-spectral correlation. First, nonlocal means (NLM) spatial filtering with patch-based difference (PBD) refinement is performed by considering both the intra-channel correlation and inter-channel correlation to overcome the spatial resolution degradation occurring with the alternating under-sampled pattern. Second, a motion-compensated temporal filter that employs inter-channel correlated motion estimation and compensation is proposed to remove the noise in the temporal domain. Then, a motion adaptive detection value controls the ratio of the spatial filter and the temporal filter. The denoised CFA sequence can thus be obtained without motion artifacts. Experimental results for both simulated and real CFA sequences are presented with visual and numerical comparisons to several state-of-the-art denoising methods combined with a demosaicing method. Experimental results confirmed that the proposed frameworks outperformed the other techniques in terms of the objective criteria and subjective visual perception in CFA sequences.

Accelerated whole-heart MR angiography using a variable-density poisson-disc undersampling pattern and compressed sensing reconstruction.

To accelerate whole-heart three-dimension MR angiography (MRA) by using a variable-density Poisson-disc undersampling pattern and a compressed sensing (CS) reconstruction algorithm, and compare the results with sensitivity encoding (SENSE). For whole-heart MRA, a prospective variable-density Poisson-disc k-space undersampling pattern was developed in which 1-2% of central part of k-space was fully sampled, and sampling in the remainder decreased exponentially toward the periphery. The undersampled data were then estimated using CS reconstruction. In patients, images using this sequence with an undersampling rate of ≈6 were compared with those using a SENSE rate of 2 (n = 15) and a SENSE rate of 6 (n = 13). Compared with SENSE rate 2, CS rate 6 images had similar objective border sharpness, significantly lower subjective image quality scores at all four locations (all P < 0.01), and shorter scan times (P < 0.05). Compared with SENSE rate 6, CS rate 6 had similar objective border sharpness at all four locations, significantly better subjective image quality scores at three of four locations (all P < 0.01), and similar scan times (P = 0.24). Compared with SENSE with a comparable acceleration rate, a variable-density Poisson-disc undersampling pattern and CS reconstruction achieved better subjective image quality and similar border sharpness. Magn Reson Med 79:761-769, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Compressed sensing based simultaneous black- and gray-blood carotid vessel wall MR imaging

ObjectiveIn this study, we sought to demonstrate the blood suppression performance, image quality and morphological measurements for compressed sensing (CS) based simultaneous 3D black- and gray-blood imaging sequence (CS-siBLAG) in carotid vessel wall MR imaging. Materials and methodsSeven healthy volunteers and five patients were recruited. Healthy subjects underwent five CS-siBLAG scans with 1, 2, 3, 4 and 5-fold accelerations. Signal-to-tissue ratio (STR) and contrast-to-tissue ratio (CTR) were computed as the measures of flowing signal suppression performance and the image quality for black-blood imaging of the technique. Vessel lumen area (LA) and wall area (WA) were compared between fully sampled acquisition and each accelerated acquisition. Patients underwent three CS-siBLAG scans with 1, 3 and 5-fold accelerations as well as a 3D time of flight (3D TOF) scan. Two radiologists reviewed the under-sampled black- and gray-blood image quality. ResultsSTR and CTR values obtained with 2 to 5-fold accelerations were not significantly different from those with full acquisition. LA and WA measured at 2×, 3×, 4× and 5× were all highly correlated to the corresponding values at 1×. For patients imaging, two radiologists both found that the dual-contrast images at 3× acceleration exhibited comparable image quality to that of the fully sampled acquisition, and that the images at 5× exhibited slightly blurred vessel wall and outer vessel wall boundaries. ConclusionBy combining the CS under-sampling pattern and reconstruction, pseudo-centric phase encoding order and dual blood contrast sequences, this technique provides spatially registered black- and gray-blood images and excellent visualization for vessel wall imaging and gray-blood imaging in a short scan time.

Correlation between k-space sampling pattern and MTF in compressed sensing MRSI.

To investigate the relationship between the k-space sampling patterns used for compressed sensing MR spectroscopic imaging (CS-MRSI) and the modulation transfer function (MTF) of the metabolite maps. This relationship may allow the desired frequency content of the metabolite maps to be quantitatively tailored when designing an undersampling pattern. Simulations of a phantom were used to calculate the MTF of Nyquist sampled (NS) 32 × 32 MRSI, and four-times undersampled CS-MRSI reconstructions. The dependence of the CS-MTF on the k-space sampling pattern was evaluated for three sets of k-space sampling patterns generated using different probability distribution functions (PDFs). CS-MTFs were also evaluated for three more sets of patterns generated using a modified algorithm where the sampling ratios are constrained to adhere to PDFs. Strong visual correlation as well as high R2 was found between the MTF of CS-MRSI and the product of the frequency-dependant sampling ratio and the NS 32 × 32 MTF. Also, PDF-constrained sampling patterns led to higher reproducibility of the CS-MTF, and stronger correlations to the above-mentioned product. The relationship established in this work provides the user with a theoretical solution for the MTF of CS MRSI that is both predictable and customizable to the user's needs.

(2 + 1)D-CAIPIRINHA accelerated MR spectroscopic imaging of the brain at 7T.

PurposeTo compare a new parallel imaging (PI) method for multislice proton magnetic resonance spectroscopic imaging (1H‐MRSI), termed (2 + 1)D‐CAIPIRINHA, with two standard PI methods: 2D‐GRAPPA and 2D‐CAIPIRINHA at 7 Tesla (T).Methods(2 + 1)D‐CAIPIRINHA is a combination of 2D‐CAIPIRINHA and slice‐CAIPIRINHA. Eight healthy volunteers were measured on a 7T MR scanner using a 32‐channel head coil. The best undersampling patterns were estimated for all three PI methods. The artifact powers, g‐factors, Cramér–Rao lower bounds (CRLB), and root mean square errors (RMSE) were compared quantitatively among the three PI methods. Metabolic maps and spectra were compared qualitatively.Results(2 + 1)D‐CAIPIRINHA allows acceleration in three spatial dimensions in contrast to 2D‐GRAPPA and 2D‐CAIPIRINHA. Thus, this sequence significantly decreased the RMSE of the metabolic maps by 12.1 and 6.9%, on average, for 4 < R < 11, compared with 2D‐GRAPPA and 2D‐CAIPIRINHA, respectively. The artifact power was 22.6 and 8.4% lower, and the CRLB were 3.4 and 0.6% lower, respectively.Conclusion(2 + 1)‐CAIPIRINHA can be implemented for multislice MRSI in the brain, enabling higher accelerations than possible with two‐dimensional (2D) parallel imaging methods. An eight‐fold acceleration was still feasible in vivo with negligible PI artifacts with lipid decontamination, thus decreasing the measurement time from 120 to 15 min for a 64 × 64 × 4 matrix. Magn Reson Med 78:429–440, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

Chemical exchange saturation transfer (CEST) imaging with fast variably-accelerated sensitivity encoding (vSENSE).

The widespread clinical use of chemical exchange saturation transfer (CEST) imaging is hampered by relatively long scan times due to its requirement that multiple saturation-offset image frames be acquired. Here, a novel variably-accelerated sensitivity encoding (vSENSE) method is proposed that provides faster CEST acquisition than conventional SENSE. The vSENSE method fully samples one CEST saturation frame, then undersamples the other frames variably. The fully-sampled frame, in conjunction with newly proposed incoherence absorption and artifact suppression strategies, improves the accuracy of sensitivity maps and permits higher acceleration factors for the other undersampled frames than regular SENSE. vSENSE is validated in a phantom, a normal volunteer and eight brain tumor patients at 3 Tesla. vSENSE with an acceleration factor of four generated a 3-6 times smaller error on average than conventional SENSE (P ≤ 0.02), with acceleration factors of 2-4, as compared with full k-space reconstruction. vSENSE permitted four-fold acceleration for amide proton transfer-weighted images, while regular SENSE could only provide a factor of two. When conventional SENSE is used with vSENSE's variable undersampling pattern, erroneous (∼9%) z-spectra result. The vSENSE method enabled twice the acceleration and generated more accurate images than conventional SENSE. Magn Reson Med 77:2225-2238, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

SU-G-JeP1-15: Sliding Window Prior Data Assisted Compressed Sensing for MRI Lung Tumor Tracking

Purpose: Prior Data Assisted Compressed Sensing (PDACS) is a partial k-space acquisition and reconstruction method for mobile tumour (i.e. lung) tracking using on-line MRI in radiotherapy. PDACS partially relies on prior data acquired at the beginning of dynamic scans, and is therefore susceptible to artifacts in longer duration scan due to slow drifts in MR signal. A novel sliding window strategy is presented to mitigate this effect. Methods: MRI acceleration is simulated by retrospective removal of data from the fully sampled sets. Six lung cancer patients were scanned (clinical 3T MRI) using a balanced steady state free precession (bSSFP) sequence for 3 minutes at approximately 4 frames per second, for a total of 650 dynamics. PDACS acceleration is achieved by undersampling of k-space in a single pseudo-random pattern. Reconstruction iteratively minimizes the total variations while constraining the images to satisfy both the currently acquired data and the prior data in missing k-space. Our novel sliding window technique (SW-PDACS), uses a series of distinct pseudo-random under-sampling patterns of partial k-space – with the prior data drawn from a sliding window of the most recent data available. Under-sampled data, simulating 2 – 5x acceleration are reconstructed using PDACS and SW-PDACS. Three quantitative metrics: artifact power, centroid error and Dice's coefficient are computed for comparison. Results: Quantitively metric values from all 6 patients are averaged in 3 bins, each containing approximately one minute of dynamic data. For the first minute bin, PDACS and SW-PDACS give comparable results. Progressive decline in image quality metrics in bins 2 and 3 are observed for PDACS. No decline in image quality is observed for SW-PDACS. Conclusion: The novel approach presented (SW-PDACS) is a more robust for accelerating longer duration (>1 minute) dynamic MRI scans for tracking lung tumour motion using on-line MRI in radiotherapy. B.G. Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization).

Compressed Sensing 3-Dimensional Time-of-Flight Magnetic Resonance Angiography for Cerebral Aneurysms: Optimization and Evaluation.

The aims of this study were to optimize parameters for Nesterov algorithm (NESTA) in reconstruction of 3-dimensional time-of-flight (TOF) magnetic resonance angiography (MRA) at 3 T by performing an exhaustive search and to validate the performance of compressed sensing (CS) by applying it to data from cerebral aneurysms and evaluating diagnostic quality. Three-dimensional TOF-MRA was obtained using a 3 T MR system with a 32-channel head coil for both healthy volunteers and 10 patients (11 aneurysms). No undersampling was applied for imaging parameters, including parallel imaging or other partial Fourier sampling. In the first step, the experimental setup was for healthy subjects to optimize CS parameters of NESTA and the undersampling mask pattern, so 24,696 different reconstruction conditions were surveyed for sampling rates of 8.0X and 5.0X. Mean square error (MSE) was calculated for each image reconstructed with the undersampling pattern and CS parameter sets. Evaluation was by normalized MSE, edge sharpness for MRA reconstructed using fully sampled data (MRA-full), zero-filled MRA (ZF-MRA) with Poisson disk undersampling mask, and CS-MRA (5.0X and 8.0X) with iterations of 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. CS-MRA (5.0X and 8.0X) with 5, 10, and 50 iterations of the sampling pattern and CS parameter set with the lowest MSE were visually inspected by 2 neuroradiologists to check the diagnostic quality. The sampling pattern and CS parameter set with the lowest MSE were identical for both CS-MRA 5.0X and CS-MRA 8.0X. At the initial 5 to 15 iterations, MSE of both sampling rates greatly decreased from that of ZF-MRA. For subsequent iterations, the decrease in MSE was relatively small. For CS-MRA, sharpness greatly increased from that of ZF-MRA within the initial 5 to 15 iterations, followed by slight increases with further iterations. Two neuroradiologists graded most aneurysms as excellent, with the exception of 1 to 4 aneurysms recognized as good by 1 observer in CS-MRA (8.0X). Optimization of NESTA in the reconstruction of 3-dimensional TOF-MRA was conducted, and the parameters and undersampling mask with the lowest MSE were determined. Caliber measurement should be performed with CS (5.0X) with 25 or 30 iterations. Most cerebral aneurysms were sufficiently recognized using CS-MRA (5.0X) or CS-MRA (8.0X) with 10 iterations.

Hybrid-Space SENSE Reconstruction for Simultaneous Multi-Slice MRI.

Simultaneous Multi-Slice (SMS) magnetic resonance imaging (MRI) is a rapidly evolving technique for increasing imaging speed. Controlled aliasing techniques utilize periodic undersampling patterns to help mitigate the loss in signal-to-noise ratio (SNR) in SMS MRI. To evaluate the performance of different undersampling patterns, a quantitative description of the image SNR loss is needed. Additionally, eddy current effects in echo planar imaging (EPI) lead to slice-specific Nyquist ghosting artifacts. These artifacts cannot be accurately corrected for each individual slice before or after slice-unaliasing. In this work, we propose a hybrid-space sensitivity encoding (SENSE) reconstruction framework for SMS MRI by adopting a three-dimensional representation of the SMS acquisition. Analytical SNR loss maps are derived for SMS acquisitions with arbitrary phase encoding undersampling patterns. Moreover, we propose a matrix-decoding correction method that corrects the slice-specific Nyquist ghosting artifacts in SMS EPI acquisitions. Brain images demonstrate that the proposed hybrid-space SENSE reconstruction generates images with comparable quality to commonly used split-slice-generalized autocalibrating partially parallel acquisition reconstruction. The analytical SNR loss maps agree with those calculated by a Monte Carlo based method, but require less computation time for high quality maps. The analytical maps enable a fair comparison between the performances of coherent and incoherent SMS undersampling patterns. Phantom and brain SMS EPI images show that the matrix-decoding method performs better than the single-slice and slice-averaged Nyquist ghosting correction methods under the hybrid-space SENSE reconstruction framework.

Comparison of MRI Under-Sampling Techniques for Compressed Sensing with Translation Invariant Wavelets Using FastTestCS: A Flexible Simulation Tool

A sparsifying transform for use in Compressed Sensing (CS) is a vital piece of image reconstruction for Magnetic Resonance Imaging (MRI). Previously, Translation Invariant Wavelet Transforms (TIWT) have been shown to perform exceedingly well in CS by reducing repetitive line pattern image artifacts that may be observed when using orthogonal wavelets. To further establish its validity as a good sparsifying transform, the TIWT is comprehensively investigated and compared with Total Variation (TV), using six under-sampling patterns through simulation. Both trajectory and random mask based under-sampling of MRI data are reconstructed to demonstrate a comprehensive coverage of tests. Notably, the TIWT in CS reconstruction performs well for all varieties of under-sampling patterns tested, even for cases where TV does not improve the mean squared error. This improved Image Quality (IQ) gives confidence in applying this transform to more CS applications which will contribute to an even greater speed-up of a CS MRI scan. High vs low resolution time of flight MRI CS re-constructions are also analyzed showing how partial Fourier acquisitions must be carefully addressed in CS to prevent loss of IQ. In the spirit of reproducible research, novel software is introduced here as FastTestCS. It is a helpful tool to quickly develop and perform tests with many CS customizations. Easy integration and testing for the TIWT and TV minimization are exemplified. Simulations of 3D MRI datasets are shown to be efficiently distributed as a scalable solution for large studies. Comparisons in reconstruction computation time are made between the Wavelab toolbox and Gnu Scientific Library in FastTestCS that show a significant time savings factor of 60×. The addition of FastTestCS is proven to be a fast, flexible, portable and reproducible simulation aid for CS research.

Pixel super-resolution using wavelength scanning.

Undersampling and pixelation affect a number of imaging systems, limiting the resolution of the acquired images, which becomes particularly significant for wide-field microscopy applications. Various super-resolution techniques have been implemented to mitigate this resolution loss by utilizing sub-pixel displacements in the imaging system, achieved, for example, by shifting the illumination source, the sensor array and/or the sample, followed by digital synthesis of a smaller effective pixel by merging these sub-pixel-shifted low-resolution images. Herein, we introduce a new pixel super-resolution method that is based on wavelength scanning and demonstrate that as an alternative to physical shifting/displacements, wavelength diversity can be used to boost the resolution of a wide-field imaging system and significantly increase its space-bandwidth product. We confirmed the effectiveness of this new technique by improving the resolution of lens-free as well as lens-based microscopy systems and developed an iterative algorithm to generate high-resolution reconstructions of a specimen using undersampled diffraction patterns recorded at a few wavelengths covering a narrow spectrum (10–30 nm). When combined with a synthetic-aperture-based diffraction imaging technique, this wavelength-scanning super-resolution approach can achieve a half-pitch resolution of 250 nm, corresponding to a numerical aperture of ~1.0, across a large field of view (>20 mm2). We also demonstrated the effectiveness of this approach by imaging various biological samples, including blood and Papanicolaou smears. Compared with displacement-based super-resolution techniques, wavelength scanning brings uniform resolution improvement in all directions across a sensor array and requires significantly fewer measurements. This technique would broadly benefit wide-field imaging applications that demand larger space-bandwidth products.