We introduce an automated, data-driven coil combination method for high-quality phase and susceptibility imaging that obviates the need for an additional reference acquisition. The technique is shown to perform similarly to SNR-optimal Roemer combination (1,2) that requires additional body and head coil acquisitions. For tissue phase estimation, an inverse problem using the spherical mean value (SMV) property was adopted (3,4), and extended to allow single-step Quantitative Susceptibility Mapping (QSM) (5–7). Our reconstruction approach is shown to enable streamlined phase and QSM processing of multi-coil images from routinely acquired 2D, 3D and Simultaneous MultiSlice (SMS) protocols.

The magnetic field created by background susceptibility sources is harmonic inside the brain boundary, hence can be filtered out using an SMV kernel (3). Denoting the total and tissue phase as φ_tot and φ_tis, this can be expressed as M(s*L(φ_tot))=M(s*φ_tis), where M is the brain mask, s is an SMV filter and L is Laplacian unwrapping operator (8,9). RESHARP technique formulates SMV filtering as a regularized inverse problem (10):

min_φtis ||M(s*L(φ_tot)) - M(s*φ_tis)||₂² + α·||φ_tis||₂²

Expressing the convolution operations as multiplication with k-space kernel S=Fs, this formulation is readily extended to single-step QSM:

min_χ ||M(F'SFL(φ_tot)) - M(F'SDFχ)||₂² + λ·TV(χ)

Here, the susceptibility distribution χ is related to the tissue phase φ_tis via DFχ=φ_tis and λ is the Total Variation parameter. Nonlinear conjugate gradients (11) were employed for optimization.

Optimal-SNR coil combination requires estimation of coil sensitivities as well as the receiver phase offsets, which need to be removed from the coil images for constructive addition (1,2). This necessitates additional reference images acquired with the body coil and head coil array, where the head coil images are normalized by the body coil to remove anatomical information from the receiver phase estimates. Virtual body coil concept (12) derives a homogenous reference from the head array data, thus averting the need for an additional body coil acquisition. This is achieved by computing the singular value decomposition (SVD) across channels, and taking the dominant singular vector as the body coil reference, similar to a “uniform-mode birdcage combination”. We propose to combine this concept with ESPIRiT (13) for automated calibration of sensitivities. In ESPIRiT, the relative receiver phase offset is arbitrary; hence the first coil channel is assumed to be the reference. To make use of the virtual body coil concept, we apply SVD compression (14) on the head array, and sort the virtual channels in decreasing order of eigenvalues. This way, the first virtual channel corresponds to the dominant singular vector, and therefore is the virtual body coil. Supplying the SVD compressed data to ESPIRiT then uses the virtual body coil as the reference, thus allowing coil sensitivity estimation without an additional acquisition (Fig.1).

Three volunteers were scanned with informed consent. Following BET brain masking (15) and Laplacian unwrapping, tissue phase and QSM images were reconstructed using α and λ chosen with L-curve (16). A 32-channel head array was used for reception and coil sensitivities were estimated from the central 16×16×16 k-space points of the acquired data using the proposed ESPIRiT with virtual body coil concept. The following datasets were acquired:

(i) 3D-GRE at 3T with 1mm isotropic resolution (Fig.2): FOV=240×192×120mm³, TE/TR=24.8/35ms. For comparison against Roemer combination, additional reference acquisitions with body and head coils were processed with ESPIRiT to compute coil sensitivities.

(ii) 2D-GRE at 3T with 1.5mm isotropic resolution (Fig.3): FOV=192×192×144mm³, TE/TR=20/2630ms.

(iii) SMS-EPI with blipped-CAIPI (17) at 7T with 2mm isotropic resolution (Fig.4): MultiBand 3× accelerated data were acquired at 3× in-plane acceleration with FOV=200×200×126mm³ and TE/TR=15/2040ms. To mitigate SMS slice-group boundary artifacts stemming from large acquisition time differences between adjacent slices at the slice-group boundaries, Laplacian unwrapping was applied separately for each slice-group.

Fig.2 demonstrates high-quality phase and QSM reconstructions where the difference from Roemer combination is 2.6% and 2.3% RMSE respectively. Fig.3 shows high-fidelity QSM images free of dipole artifacts. Arrows in Fig.4 point to the slice-group boundary artifacts in the SMS phase images, which were largely mitigated in the tissue phase and susceptibility results. Herein, an automated coil sensitivity estimation technique that does not require additional reference scans has been proposed. This is shown to yield detailed phase and QSM images with nearly identical quality as the Roemer combination. This approach can be particularly useful in cases where an adequate body coil reference is not available, such as ultra-high field scanners. The technique is applicable to raw coil images from 2D, 3D and SMS acquisitions and performs in a data-driven fashion from as few as 16×16 central k-space lines of the acquired data.