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

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Three‐dimensional (3D) multispectral imaging (MSI) techniques that use slice phase encoding correct most distortion in MRI near metallic implants. In slice encoding for metal artifact correction 1, two‐dimensional slices are excited and imaged with 3D phase encoding to resolve slice distortion induced by off‐resonance, while in‐plane distortion is corrected using a view‐angle tilting technique 2. Although a frequency‐selective approach, multi‐acquisition variable‐resonance image combination 3, can also provide distortion‐free images near metal, slice encoding for metal artifact correction, and the multi‐acquisition variable‐resonance image combination‐slice encoding for metal artifact correction hybrid 4, use spatially‐selective excitation to limit the required amount of phase encoding and reduce scan time 5. In 3D MSI, a bin refers to one of multiple excited volumes (e.g., two‐dimensional slices or frequency offsets) that are encoded in 3D and combined to form a volumetric image with reduced distortion. The additional bin dimension required to resolve metal‐induced slice distortion results in significantly longer scan times than two‐dimensional or 3D fast spin echo techniques not offering metal artifact suppression.
Most existing methods for constrained 3D MSI offer approximately 2‐fold acceleration and are limited as they do not exploit the redundancy between bins 6. One approach has been proposed to exploit the redundancy between bins in 3D MSI methods based on slice phase encoding, and it explicitly represents the nonlinear relationship between quantitative parameters (e.g., magnetization, field map, profile width) and undersampled k‐space data 10. However, model‐based reconstruction can be less robust due to modeling errors that are specific to sequence parameters and faces a challenging nonconvex optimization problem. Existing methods also do not exploit the redundancy of slice phase encoding associated with the dominant on‐resonance signal. Other work has exploited the spatial distribution of off‐resonance in multi‐acquisition variable‐resonance image combination using a calibration procedure across bins but has limited generality 11.
A second challenge is to effectively combine complementary acceleration methods. Signal loss from field‐inhomogeneity‐related dephasing is reduced in 3D MSI with spin echo sequences (fast spin echo, turbo spin echo, rapid imaging with refocused echoes), which produce images with slow phase variation and thus are typically accelerated with partial Fourier. Parallel imaging offers additional acceleration, but estimating coil sensitivities in 3D MSI is challenging, and robust data‐driven parallel imaging is generally required 12. However, the required calibration for parallel imaging and partial Fourier introduces significant overhead ( JOURNAL/mrim/04.02/01445475-201803000-00027/math_27MM1/v/2018-01-24T161827Z/r/image-png of fully sampled scan time), as through‐plane resolution is often limited (e.g., 24 slices), and to reduce these requirements, methods have been proposed using external calibration 13. Existing acceleration methods have not demonstrated their efficacy in combination with both parallel imaging and partial Fourier reconstruction.
This work first addresses the challenges of partial Fourier and parallel imaging with the use of a novel calibration‐free technique and a flexible optimization framework. With these tools, a novel calibration‐free and model‐free technique to accelerate 3D MSI is proposed to exploit the redundancy of slice‐phase encoding for the dominant on‐resonance signal. Inspired by robust principal component analysis 14 (RPCA), our technique is based on a compact representation of multispectral images as a sum of rank‐one and sparse matrices corresponding to on‐ and off‐resonance signals. The representation is data‐dependent, making it independent of many sequence parameters, and it relies only on the sparsity of off‐resonance and signal separability of the on‐resonance signal. It is also built on an optimization framework that enables integration with other constraints such as parallel imaging and partial Fourier acceleration.

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