A kernel approach to parallel MRI reconstruction

Abstract

GRAPPA has been widely used as a k-space-based parallel MRI reconstruction technique. It linearly combines the acquired k-space signals to estimate the missing k-space signals where the coefficients are obtained by linear regression using auto-calibration signals. At high acceleration factors, GRAPPA reconstruction can suffer from a high level of noise even with a large number of autocalibration signals. In this work, we improve the GRAPPA model using a kernel approach. Specifically, the acquired kspace data are mapped through a nonlinear transform to a high-dimensional space and then linearly combined to estimate the missing k-space data. A polynomial kernel is investigated in this work. Experimental results using phantom and in vivo data demonstrate that the proposed kernel GRAPPA method can significantly improve the reconstruction quality over the existing methods.

Improve GRAPPA with Cross-sampled ACS Lines and Nonlinear Kernel Model

“…But, the proposed method, CSNL GRAPPA, mixes two characteristic methods, cross sampling [15] and nonlinear model [13], to separately reduce aliens and decrease noises. As seen in Fig.…”

“…After both data sets are co-registered, nonlinear GRAPPA method [13] is used for image reconstruction. In existing GRAPPA formulations, the weight coefficients used for the linear combination is fitting by the ACS data.…”

“…When the high outer reduction factor (R) is applied for GRAPPA, the reconstruction noises will increase distinctly. Therefore, an amount of reconstruction methods have been proposed to reduce aliasing artifacts and noised for improving image quality, such as, regularization [5], reweighted least squares [6], high-pass filtering [7], cross-validation [8], iterative optimization [9], virtual coil using conjugate symmetric signals [10], multi-slice weighting [11], an infinite impulse response model [12], nonlinear model [13], etc. Only a few methods modify the data acquisition procedure to improve GRAPPA, such as, variable density sampling [14], cross sampling [15], etc.…”

“…In this paper, we propose a new hybrid method of cross sampling [15] and nonlinear estimating weights [13] based on the conventional GRAPPA. The proposed method acquires the ACS lines along the direction orthogonal to that of the undersampled lines.…”

Self‐supervised learning of physics‐guided reconstruction neural networks without fully sampled reference data

“…[1][2][3] Compressed sensing is another method that uses the compressibility of images based on linear sparsifying transforms for a regularized reconstruction, [4][5][6][7][8][9] which can also be synergistically combined with multicoil acquisitions. [10][11][12] At high acceleration rates, parallel imaging suffers from noise amplification, [13][14][15] whereas compressed sensing may lead to residual artifacts. 16,17 Furthermore, compressed-sensing reconstruction is computationally lengthy in nature and typically requires empirical fine-tuning of regularization parameters, although recent approaches using rapid self-tuning show promise for principled parameter selection.…”