K-space Interpolation Research Articles

Accelerated Simultaneous Multi-Slice MRI using Subject-Specific Convolutional Neural Networks.

Simultaneous multi-slice or multi-band (SMS/MB) imaging allows accelerated coverage in magnetic resonance imaging (MRI). Multiple slices are excited and acquired at the same time, and reconstructed using the redundancies in receiver coil arrays, similar to parallel imaging. SMS/MB reconstruction is currently performed with linear reconstruction techniques. Recently, a nonlinear reconstruction method for parallel imaging, Robust Artificial-neural-networks for k-space Interpolation (RAKI) was proposed and shown to improve upon linear methods. This method uses convolutional neural networks (CNN) trained solely on subject-specific calibration data. In this study, we sought to extend RAKI to SMS/MB imaging reconstruction. CNN training was performed on calibration data acquired prior to SMS/MB imaging, in a manner consistent with the existing linear methods. These CNNs were used to reconstruct a time series of functional MRI (fMRI) data. CNN network parameters were optimized using an extensive search of the parameter space. With these optimal parameters, RAKI substantially improves image quality compared to a commonly used linear reconstruction algorithm, especially for high acceleration rates.

Scan-specific robust artificial-neural-networks for k-space interpolation (RAKI) reconstruction: Database-free deep learning for fast imaging.

To develop an improved k-space reconstruction method using scan-specific deep learning that is trained on autocalibration signal (ACS) data. Robust artificial-neural-networks for k-space interpolation (RAKI) reconstruction trains convolutional neural networks on ACS data. This enables nonlinear estimation of missing k-space lines from acquired k-space data with improved noise resilience, as opposed to conventional linear k-space interpolation-based methods, such as GRAPPA, which are based on linear convolutional kernels. The training algorithm is implemented using a mean square error loss function over the target points in the ACS region, using a gradient descent algorithm. The neural network contains 3 layers of convolutional operators, with 2 of these including nonlinear activation functions. The noise performance and reconstruction quality of the RAKI method was compared with GRAPPA in phantom, as well as in neurological and cardiac in vivo data sets. Phantom imaging shows that the proposed RAKI method outperforms GRAPPA at high (≥4) acceleration rates, both visually and quantitatively. Quantitative cardiac imaging shows improved noise resilience at high acceleration rates (rate 4:23% and rate 5:48%) over GRAPPA. The same trend of improved noise resilience is also observed in high-resolution brain imaging at high acceleration rates. The RAKI method offers a training database-free deep learning approach for MRI reconstruction, with the potential to improve many existing reconstruction approaches, and is compatible with conventional data acquisition protocols.

Subject-Specific Convolutional Neural Networks for Accelerated Magnetic Resonance Imaging.

Magnetic Resonance Imaging (MRI) is one of the leading modalities for medical imaging, providing excellent soft-tissue contrast without exposure to ionizing radiation. Despite continuing advances in MRI, long scan times remain a major limitation in clinical applications. Parallel imaging is a technique for scan time acceleration in MRI, which utilizes the spatial variations in the reception profiles of receiver coil arrays to reconstruct images from undersampled Fourier space, i.e. k-space. One of the most commonly used parallel imaging techniques employs interpolation of missing k-space information by using linear shift-invariant convolutional kernels. These kernels are trained on a limited amount of autocalibration signal (ACS) for each scan. We propose a novel method for parallel imaging, Robust Artificial-neural-networks for k-space Interpolation (RAKI), which uses scan-specific convolutional neural networks (CNNs) to perform improved k-space interpolation. Three-layer CNNs are trained using only scan-specific ACS data, alleviating the need for large training databases. The proposed method was tested in ultra-high resolution brain MRI and quantitative cardiac MRI, acquired with various acceleration rates. Improved noise resilience as compared to existing parallel imaging methods was observed for high acceleration rates or in the presence of low signal-to-noise ratio (SNR). Furthermore, RAKI successfully reconstructed images for quantitative cardiac MRI, even when using the same CNN across images with varying contrasts. These results indicate that RAKI achieves improved noise performance without overfitting to specific image contents, and offers great promise for improved acceleration in a wide range of MRI applications.

Deep Residual Learning for Accelerated MRI Using Magnitude and Phase Networks.

Accelerated magnetic resonance (MR) image acquisition with compressed sensing (CS) and parallel imaging is a powerful method to reduce MR imaging scan time. However, many reconstruction algorithms have high computational costs. To address this, we investigate deep residual learning networks to remove aliasing artifacts from artifact corrupted images. The deep residual learning networks are composed of magnitude and phase networks that are separately trained. If both phase and magnitude information are available, the proposed algorithm can work as an iterative k-space interpolation algorithm using framelet representation. When only magnitude data are available, the proposed approach works as an image domain postprocessing algorithm. Even with strong coherent aliasing artifacts, the proposed network successfully learned and removed the aliasing artifacts, whereas current parallel and CS reconstruction methods were unable to remove these artifacts. Comparisons using single and multiple coil acquisition show that the proposed residual network provides good reconstruction results with orders of magnitude faster computational time than existing CS methods. The proposed deep learning framework may have a great potential for accelerated MR reconstruction by generating accurate results immediately.

A General Framework for Compressed Sensing and Parallel MRI Using Annihilating Filter Based Low-Rank Hankel Matrix

Parallel MRI (pMRI) and compressed sensing MRI (CS-MRI) have been considered as two distinct reconstruction problems. Inspired by recent k-space interpolation methods, an annihilating filter-based low-rank Hankel matrix approach is proposed as a general framework for sparsity-driven k-space interpolation method which unifies pMRI and CS-MRI. Specifically, our framework is based on a novel observation that the transform domain sparsity in the primary space implies the low-rankness of weighted Hankel matrix in the reciprocal space. This converts pMRI and CS-MRI to a k-space interpolation problem using a structured matrix completion. Experimental results using in vivo data for single/multicoil imaging as well as dynamic imaging confirmed that the proposed method outperforms the state-of-the-art pMRI and CS-MRI.

Plane-wave ultrasound beamforming using a nonuniform fast fourier transform

Beamforming of plane-wave ultrasound echo signals in the Fourier domain provides fast and accurate image reconstruction. Conventional implementations perform a k-space interpolation from the uniform sampled grid to a nonuniform acoustic dispersion grid. In this paper, we demonstrate that this step can be replaced by a nonuniform Fourier transform. We study the performance of the nonuniform fast Fourier transform (NUFFT) in terms of signal-to-noise ratio and computational cost, and show that the NUFFT offers an advantage in the trade-off between speed and accuracy, compared with other frequency-domain beamforming strategies.

Parallel magnetic resonance imaging using localized receive arrays with sinc interpolation (PILARS)

Large arrays with localized coil sensitivity make it possible to use parallel imaging to significantly accelerate MR imaging speed. However, the need for auto calibration signals limits the actual acceleration factors achievable with large arrays. This paper presents a novel method for parallel imaging with large arrays. The method uses Sinc kernels for k-space data interpolation that only requires one phase parameter to be estimated using a small size of calibration signals. Simulations based on synthetic array data and phantom experiments show that the new method can achieve higher actual acceleration factors with comparable reconstruction quality.

Spectral and Fermi surface properties from Wannier interpolation

We present an efficient first-principles approach for calculating Fermi surface averages and spectral properties of solids, and use it to compute the low-field Hall coefficient of several cubic metals and the magnetic circular dichroism of iron. The first step is to perform a conventional first-principles calculation and store the low-lying Bloch functions evaluated on a uniform grid of k-points in the Brillouin zone. We then map those states onto a set of maximally-localized Wannier functions, and evaluate the matrix elements of the Hamiltonian and the other needed operators between the Wannier orbitals, thus setting up an ``exact tight-binding model.'' In this compact representation the k-space quantities are evaluated inexpensively using a generalized Slater-Koster interpolation. Because of the strong localization of the Wannier orbitals in real space, the smoothness and accuracy of the k-space interpolation increases rapidly with the number of grid points originally used to construct the Wannier functions. This allows k-space integrals to be performed with ab-initio accuracy at low cost. In the Wannier representation, band gradients, effective masses, and other k-derivatives needed for transport and optical coefficients can be evaluated analytically, producing numerically stable results even at band crossings and near weak avoided crossings.

Time-resolved contrast-enhanced imaging with isotropic resolution and broad coverage using an undersampled 3D projection trajectory.

Time-resolved contrast-enhanced 3D MR angiography (MRA) methods have gained in popularity but are still limited by the tradeoff between spatial and temporal resolution. A method is presented that greatly reduces this tradeoff by employing undersampled 3D projection reconstruction trajectories. The variable density k-space sampling intrinsic to this sequence is combined with temporal k-space interpolation to provide time frames as short as 4 s. This time resolution reduces the need for exact contrast timing while also providing dynamic information. Spatial resolution is determined primarily by the projection readout resolution and is thus isotropic across the FOV, which is also isotropic. Although undersampling the outer regions of k-space introduces aliased energy into the image, which may compromise resolution, this is not a limiting factor in high-contrast applications such as MRA. Results from phantom and volunteer studies are presented demonstrating isotropic resolution, broad coverage with an isotropic field of view (FOV), minimal projection reconstruction artifacts, and temporal information. In one application, a single breath-hold exam covering the entire pulmonary vasculature generates high-resolution, isotropic imaging volumes depicting the bolus passage.