Fast and Calibrationless Low-Rank Parallel Imaging Reconstruction Through Unrolled Deep Learning Estimation of Multi-Channel Spatial Support Maps.

Low-rank technique has emerged as a powerful calibrationless alternative for parallel magnetic resonance (MR) imaging. Calibrationless low-rank reconstruction, such as low-rank modeling of local k-space neighborhoods (LORAKS), implicitly exploits both coil sensitivity modulations and the finite spatial support constraint of MR images through an iterative low-rank matrix recovery process. Although powerful, this slow iteration process is computationally demanding and reconstruction requires empirical rank optimization, hampering its robust applications for high-resolution volume imaging. This paper proposes a fast and calibrationless low-rank reconstruction of undersampled multi-slice MR brain data, based on the finite spatial support constraint reformulation with a direct deep learning estimation of spatial support maps. The iteration process of low-rank reconstruction is unrolled into a complex-valued network by training on fully-sampled multi-slice axial brain datasets acquired from the same MR coil system. To utilize coil-subject geometric parameters available for datasets, the model minimizes a hybrid loss on two sets of spatial support maps, corresponding to brain data at the original slice locations as actually acquired and nearby locations within the standard reference coordinate. This deep learning framework was integrated with LORAKS reconstruction and was evaluated with publically available gradient-echo T1-weighted brain datasets. It directly produced high-quality multi-channel spatial support maps from undersampled data, enabling rapid reconstruction without iteration. Moreover, it led to effective reductions of artifacts and noise amplification at high acceleration. In summary, our proposed deep learning framework offers a new strategy to advance the existing calibrationless low-rank reconstruction, rendering it computationally efficient, simple, and robust in practice.

Calibrationless reconstruction of uniformly-undersampled multi-channel MR data with deep learning estimated ESPIRiT maps.

PURPOSE: To develop a truly calibrationless reconstruction method that derives An Eigenvalue Approach to Autocalibrating Parallel MRI (ESPIRiT) maps from uniformly-undersampled multi-channel MR data by deep learning. METHODS: ESPIRiT, one commonly used parallel imaging reconstruction technique, forms the images from undersampled MR k-space data using ESPIRiT maps that effectively represents coil sensitivity information. Accurate ESPIRiT map estimation requires quality coil sensitivity calibration or autocalibration data. We present a U-Net based deep learning model to estimate the multi-channel ESPIRiT maps directly from uniformly-undersampled multi-channel multi-slice MR data. The model is trained using fully-sampled multi-slice axial brain datasets from the same MR receiving coil system. To utilize subject-coil geometric parameters available for each dataset, the training imposes a hybrid loss on ESPIRiT maps at the original locations as well as their corresponding locations within the standard reference multi-slice axial stack. The performance of the approach was evaluated using publicly available T1-weighed brain and cardiac data. RESULTS: The proposed model robustly predicted multi-channel ESPIRiT maps from uniformly-undersampled k-space data. They were highly comparable to the reference ESPIRiT maps directly computed from 24 consecutive central k-space lines. Further, they led to excellent ESPIRiT reconstruction performance even at high acceleration, exhibiting a similar level of errors and artifacts to that by using reference ESPIRiT maps. CONCLUSION: A new deep learning approach is developed to estimate ESPIRiT maps directly from uniformly-undersampled MR data. It presents a general strategy for calibrationless parallel imaging reconstruction through learning from the coil and protocol-specific data.

Parallel imaging reconstruction using spatial nulling maps.

PURPOSE: To develop a robust parallel imaging reconstruction method using spatial nulling maps (SNMs). METHODS: Parallel reconstruction using null operations (PRUNO) is a k-space reconstruction method where a k-space nulling system is derived using null-subspace bases of the calibration matrix. ESPIRiT reconstruction extends the PRUNO subspace concept by exploiting the linear relationship between signal-subspace bases and spatial coil sensitivity characteristics, yielding a hybrid-domain approach. Yet it requires empirical eigenvalue thresholding to mask the coil sensitivity information and is sensitive to signal- and null-subspace division. In this study, we combine the concepts of null-subspace PRUNO and hybrid-domain ESPIRiT to provide a more robust reconstruction method that extracts null-subspace bases of calibration matrix to calculate image-domain SNMs. Multi-channel images are reconstructed by solving an image-domain nulling system formed by SNMs that contain both coil sensitivity and finite image support information, therefore, circumventing the masking-related procedure. The proposed method was evaluated with multi-channel 2D brain and knee data and compared to ESPIRiT. RESULTS: The proposed hybrid-domain method produced quality reconstruction highly comparable to ESPIRiT with optimal manual masking. It involved no masking-related manual procedure and was tolerant of the actual division of null- and signal-subspace. Spatial regularization could be also readily incorporated to reduce noise amplification as in ESPIRiT. CONCLUSION: We provide an efficient hybrid-domain reconstruction method using multi-channel SNMs that are calculated from coil calibration data. It eliminates the need for coil sensitivity masking and is relatively insensitive to subspace separation, therefore, presenting a robust parallel imaging reconstruction procedure in practice.

Joint denoising of diffusion-weighted images via structured low-rank patch matrix approximation.

PURPOSE: To develop a joint denoising method that effectively exploits natural information redundancy in MR DWIs via low-rank patch matrix approximation. METHODS: A denoising method is introduced to jointly reduce noise in DWI dataset by exploiting nonlocal self-similarity as well as local anatomical/structural similarity within multiple 2D DWIs acquired with the same anatomical geometry but different diffusion directions. Specifically, for each small 3D reference patch sliding within 2D DWI, nonlocal but similar patches are searched by matching image contents within entire DWI dataset and then structured into a patch matrix. The resulting patch matrices are denoised by enforcing low-rankness via weighted nuclear norm minimization and finally are back-distributed to DWI space. The proposed procedure was evaluated with simulated and in vivo brain diffusion tensor imaging (DTI) datasets and then compared to existing Marchenko-Pastur principal component analysis denoising method. RESULTS: The proposed method achieved significant noise reduction while preserving structural details in all DWIs for both simulated and in vivo datasets. Quantitative evaluation of error maps demonstrated it consistently outperformed Marchenko-Pastur principal component analysis method. Further, the denoised DWIs led to substantially improved DTI parametric maps, exhibiting significantly less noise and revealing more microstructural details. CONCLUSION: The proposed method denoises DWI dataset by utilizing both nonlocal self-similarity and local structural similarity within DWI dataset. This weighted nuclear norm minimization-based low-rank patch matrix denoising approach is effective and highly applicable to various diffusion MRI applications, including DTI as a postprocessing procedure.

Calibrationless multi-slice Cartesian MRI via orthogonally alternating phase encoding direction and joint low-rank tensor completion.

We propose a multi-slice acquisition with orthogonally alternating phase encoding (PE) direction and subsequent joint calibrationless reconstruction for accelerated multiple individual 2D slices or multi-slice 2D Cartesian MRI. Specifically, multi-slice multi-channel data are first acquired with random or uniform PE undersampling while orthogonally alternating PE direction between adjacent slices. They are then jointly reconstructed through a recently developed low-rank multi-slice Hankel tensor completion (MS-HTC) approach. The proposed acquisition and reconstruction strategy was evaluated with human brain MR data. It effectively suppressed aliasing artifacts even at high acceleration factor, outperforming the existing MS-HTC approach, where PE direction is the same between adjacent slices. More importantly, the new strategy worked robustly with uniform undersampling or random undersampling without any consecutive central k-space lines. In summary, our proposed multi-slice MRI strategy exploits both coil sensitivity and image content similarities across adjacent slices. Orthogonally alternating PE direction among slices substantially facilitates the low-rank completion process and improves image reconstruction quality. This new strategy is applicable to uniform and random PE undersampling. It can be easily implemented in practice for Cartesian parallel imaging of multiple individual 2D slices without any coil sensitivity calibration.

Partial Fourier reconstruction of complex MR images using complex-valued convolutional neural networks.

PURPOSE: To provide a complex-valued deep learning approach for partial Fourier (PF) reconstruction of complex MR images. METHODS: Conventional PF reconstruction methods, such as projection onto convex sets (POCS), uses low-resolution image phase information from the central symmetrically sampled k-space for image reconstruction. However, this smooth phase constraint undermines the phase estimation accuracy in presence of rapid local phase variations, causing image artifacts and limiting the extent of PF reconstruction. Using both magnitude and phase characteristics in big complex image datasets, we propose a complex-valued deep learning approach with an unrolled network architecture for PF reconstruction that iteratively reconstructs PF sampled data and enforces data consistency. We evaluate our approach for reconstructing both spin-echo and gradient-echo data. RESULTS: The proposed method outperformed the iterative POCS PF reconstruction method. It produced better artifact suppression and recovery of both image magnitude and phase details in presence of local phase changes. No noise amplification was observed even for highly PF reconstruction. Moreover, the network trained on axial brain data could reconstruct sagittal and coronal brain and knee data. This method could be extended to 2D PF reconstruction and joint multi-slice PF reconstruction. CONCLUSION: Our proposed method can effectively reconstruct MR data even at low PF fractions, yielding high-fidelity magnitude and phase images. It presents a valuable alternative to conventional PF reconstruction, especially for phase-sensitive 2D or 3D MRI applications.

Joint calibrationless reconstruction of highly undersampled multicontrast MR datasets using a low-rank Hankel tensor completion framework.

PURPOSE: To jointly reconstruct highly undersampled multicontrast two-dimensional (2D) datasets through a low-rank Hankel tensor completion framework. METHODS: A multicontrast Hankel tensor completion (MC-HTC) framework is proposed to exploit the shareable information in multicontrast datasets with respect to their highly correlated image structure, common spatial support, and shared coil sensitivity for joint reconstruction. This is achieved by first organizing multicontrast k-space datasets into a single block-wise Hankel tensor. Subsequent low-rank tensor approximation via higher-order singular value decomposition (HOSVD) uses the image structural correlation by considering different contrasts as virtual channels. Meanwhile, the HOSVD imposes common spatial support and shared coil sensitivity by treating data from different contrasts as from additional k-space kernels. The missing k-space data are then recovered by iteratively performing such low-rank approximation and enforcing data consistency. This joint reconstruction framework was evaluated using multicontrast multichannel 2D human brain datasets (T1 -weighted, T2 -weighted, fluid-attenuated inversion recovery, and T1 -weighted-inversion recovery) of identical image geometry with random and uniform undersampling schemes. RESULTS: The proposed method offered high acceleration, exhibiting significantly less residual errors when compared with both single-contrast SAKE (simultaneous autocalibrating and k-space estimation) and multicontrast J-LORAKS (joint parallel-imaging-low-rank matrix modeling of local k-space neighborhoods) low-rank reconstruction. Furthermore, the MC-HTC framework was applied uniquely to Cartesian uniform undersampling by incorporating a novel complementary k-space sampling strategy where the phase-encoding direction among different contrasts is orthogonally alternated. CONCLUSION: The proposed MC-HTC approach presents an effective tensor completion framework to jointly reconstruct highly undersampled multicontrast 2D datasets without coil-sensitivity calibration.

Calibrationless parallel imaging reconstruction for multislice MR data using low-rank tensor completion.

PURPOSE: To provide joint calibrationless parallel imaging reconstruction of highly accelerated multislice 2D MR k-space data. METHODS: Adjacent image slices in multislice MR data have similar coil sensitivity maps, spatial support, and image content. Such similarities can be utilized to improve image quality by reconstructing multiple slices jointly with low-rank tensor completion. Specifically, the multichannel k-space data from multiple slices are constructed into a block-wise Hankel tensor and iteratively updated by promoting tensor low-rankness through higher-order SVD. This multislice block-wise Hankel tensor completion was implemented for 2D spiral and Cartesian k-space undersampling where sampling patterns vary between adjacent slices. The approach was evaluated with human brain MR data and compared to the traditional single-slice simultaneous autocalibrating and k-space estimation reconstruction. RESULTS: The proposed multislice block-wise Hankel tensor completion approach robustly reconstructed highly undersampled multislice 2D spiral and Cartesian data. It produced substantially lower level of artifacts compared to the traditional single-slice simultaneous autocalibrating and k-space estimation reconstruction. Quantitative evaluation using error maps and root mean square error demonstrated its significantly improved performance in terms of residual artifacts and root mean square error. CONCLUSION: Our proposed multislice block-wise Hankel tensor completion method exploits the similar coil sensitivity and image content within multislice MR data through a tensor completion framework. It offers a new and effective approach to acquire and reconstruct highly undersampled multislice MR data in a calibrationless manner.

PEC-GRAPPA reconstruction of simultaneous multislice EPI with slice-dependent 2D Nyquist ghost correction.

PURPOSE: To provide simultaneous multislice (SMS) EPI reconstruction with k-space implementation and robust Nyquist ghost correction. METHODS: 2D phase error correction SENSE (PEC-SENSE) was recently developed for Nyquist ghost correction in SMS EPI reconstruction for which virtual coil simultaneous autocalibration and k-space estimation (VC-SAKE) was used to remove slice-dependent Nyquist ghosts and intershot 2D phase variations in multi-shot EPI reference scan. However, masking coil sensitivity maps to exclude background region in PEC-SENSE and manually selecting slice-wise target ranks in VC-SAKE are cumbersome procedures in practice. To avoid masking, the concept of PEC-SENSE is extended to k-space implementation and termed as PEC-GRAPPA. Furthermore, a singular value shrinkage scheme is incorporated in VC-SAKE to circumvent the empirical slice-wise target rank selection. PEC-GRAPPA was evaluated and compared to PEC-SENSE with/without masking and 1D linear phase correction GRAPPA. RESULTS: PEC-GRAPPA robustly reconstructed SMS EPI images from 7T phantom and human brain data, effectively removing the phase error-induced artifacts. The resulting residual artifact level and temporal SNR were comparable to those by PEC-SENSE with careful tuning. PEC-GRAPPA outperformed PEC-SENSE without masking and 1D linear phase correction GRAPPA. CONCLUSION: Our proposed PEC-GRAPPA approach effectively removes the artifacts caused by Nyquist ghosts in SMS EPI without cumbersome tuning. This approach provides a robust and practical implementation of SMS EPI reconstruction in k-space with slice-dependent 2D Nyquist ghost correction.

Hydrogel-Based Fluorescent Dual pH and Oxygen Sensors Loaded in 96-Well Plates for High-Throughput Cell Metabolism Studies.

In this study, we developed fluorescent dual pH and oxygen sensors loaded in multi-well plates for in-situ and high-throughput monitoring of oxygen respiration and extracellular acidification during microbial cell growth for understanding metabolism. Biocompatible PHEMA-co-PAM materials were used as the hydrogel matrix. A polymerizable oxygen probe (OS2) derived from PtTFPP and a polymerizable pH probe (S2) derived from fluorescein were chemically conjugated into the matrix to solve the problem of the probe leaching from the matrix. Gels were allowed to cure directly on the bottom of 96-well plates at room-temperature via redox polymerization. The influence of matrix's composition on the sensing behaviors was investigated to optimize hydrogels with enough robustness for repeatable use with good sensitivity. Responses of the dual sensing hydrogels to dissolved oxygen (DO) and pH were studied. These dual oxygen-pH sensing plates were successfully used for microbial cell-based screening assays, which are based on the measurement of fluorescence intensity changes induced by cellular oxygen consumption and pH changes during microbial growth. This method may provide a real-time monitoring of cellular respiration, acidification, and a rapid kinetic assessment of multiple samples for cell viability as well as high-throughput drug screening. All of these assays can be carried out by a conventional plate reader.