Echo planar imaging (EPI) [1] encompasses a family of fast and flexible acquisition techniques in magnetic resonance imaging (MRI), serving as a workhorse readout strategy for a variety of imaging applications. A challenge with EPI is its low effective bandwidth along the phase-encoding dimension, yielding extensive phase evolution during prolonged readouts. The EPI signal is very sensitive to off-resonance effects originating in the imaged sample through susceptibility changes, as well as system non-idealities including B0 inhomogeneity, eddy currents, and concomitant fields. As a result, standard Fourier reconstructions which do not explicitly account for these effects commonly exhibit artifacts manifesting as geometric distortion and signal pile-up along this axis, particularly in regions of magnetic susceptibility.

A variety of methods encompassing acquisition and/or reconstruction have been proposed to surmount these challenges. In acquisition, shortening the readout window reduces the time over which off-resonance effects manifest. Parallel imaging is often employed for this purpose. Use of high-performance imaging systems, such as the compact 3T scanner in this study [2], facilitate further echo spacing reductions. Segmented or interleaved multi-shot acquisition also shortens the intra-shot readout window and can reduce distortion, but shot-to-shot phase variations may need to be addressed especially for diffusion imaging. In reconstruction, multiplexed sensitivity encoding (MUSE [3]) is an example of a multi-shot EPI technique improving image quality, giving navigator-free correction for shot-to-shot phase variations through extended sensitivity encoding (SENSE [4]) operations, but does not completely mitigate distortion. Direct handling of off-resonance effects can be accomplished with the use of field map data in reconstruction [5,6], but this requires additional calibration, and consideration of phase wrapping and resolution differences between EPI and field map data as well as map accuracy and noise. Collection of readouts at alternate polarities with subsequent iterative correction is a popular alternative, but may degrade resolution as a dedicated image-based technique given discretization effects and gives incomplete correction [7]. Subsequently, a hybrid-space SENSE approach has shown success for dual-polarity EPI [8]. Acquisition of EPI readouts at differing echo times combined with structured low-rank matrix completion in reconstruction is an additional calibration-free multi-shot approach to reduce sensitivity to off-resonance [9].

Point spread function (PSF)-encoded EPI [[10], [11], [12]] is a multi-shot EPI technique employing identical readouts within each shot, each preceded by preemptive auxiliary phase-encoding. An abbreviated pulse sequence diagram for spin-echo PSF-EPI in Fig. 1 illustrates gradient evolution as well as visualizations of sampling variants utilized in this work. At a single channel, PSF-EPI yields a 3-dimensional k-space data volume along readout, phase encoding, and auxiliary (PSF) encoding. From here, one may generate a pixel shift map for correction of distorted echo planar images via interpolation, which has been a common historical approach [11], itself the subject of prior model-based study [13]. Alternatively if imaging directly with PSF-EPI, this data volume can (following standard methods) can be projected into a distortion-free image after inverse Fourier transforms. Direct imaging with PSF-EPI, which is the focus of this work, has become more practical in terms of scan time with recent advancements in acceleration and/or sampling [12,14]. Recent implementations employ acceleration with parallel imaging along the primary phase-encoding axis as well as reduced field of view (rFOV) acceleration along the PSF-encoding axis to reduce scan time [11,12,15]. Partial Fourier encoding along the PSF axis further reduces scan time, as each encoding comprises a TR. In contrast to use of PSF-EPI as a calibration method for distortion correction, this work focuses on image reconstruction for direct T2-weighted imaging via the PSF-EPI sequence.

There are certain advantages motivating emerging clinical and scientific interest for direct imaging with PSF-EPI over alternative techniques. The oversampling inherent to PSF-EPI acquisition translates to enhanced SNR through signal averaging effects. Direct PSF-EPI imaging is a viable and increasingly practical technique in scenarios for which undistorted, high-SNR images are a priority, particularly when EPI-based acquisitions are desired. Clinical scenarios with pathology adjacent to regions with high magnetic susceptibility (e.g., the sinuses) are one example. Neuroscientific applications investigating brain regions which are commonly distorted when using standard EPI-based techniques are another.

Conventional multi-shot EPI techniques acquiring a distinct subset of k-space each shot provide limited oversampling, and present tradeoffs between distortion reduction and SNR efficiency. To enhance SNR with (e.g.) interleaved EPI, additional shots could be acquired while holding fixed a number of echoes, but prolonged readouts will beget distortion if off-resonance is not considered in reconstruction. Conversely, increasing shots while reducing echoes per shot shortens the readout echo train, but reduces both distortion and SNR efficiency [17]. Associated SNR tradeoffs can be compensated for with a multi-shot, multi-echo acquisition by increasing the number of acquired shots and then averaging, accepting a scan time increase. The benefits of that approach necessitate application-specific evaluation. In prior work, readout-segmented EPI reduced distortion to a much lesser degree than a direct PSF-EPI imaging method, and showed reduced SNR in diffusion-weighted imaging in vivo relative to PSF-EPI even with matched scan time [12]. Moreover, in a recent comparison MUSE showed exacerbated distortion and dropout artifacts relative to direct PSF-EPI imaging in clinical comparisons [18]. Direct imaging with PSF-EPI enables robustly distortion-free imaging with image quality that is difficult to match with conventional multi-shot EPI.

Beyond PSF-EPI, alternative multi-shot EPI techniques have emerged enabling high-resolution distortion-free imaging with practical scan times, albeit with explicit reliance on ΔB0 estimates in reconstruction. Echo planar time-resolved imaging (EPTI) as originally introduced [19] and with subspace reconstruction [20] enables multi-contrast distortion-free imaging, but requires integrated estimation of ΔB0. A self-navigated diffusion EPTI with regularized reconstruction has also been introduced, similarly requiring estimation of ΔB0-induced phases using calibration data [21]. Blip-up/down acquisition (BUDA) enables distortion-free and quantitative imaging with EPI readouts at alternating phase-encoding polarities and regularized reconstruction [22,23], though is reliant on field map estimates obtained preceding reconstruction. As an alternative to methods requiring ΔB0 estimation, a key element of the reconstruction proposed in this work is a phasor decomposition enabling direct reconstruction of an undistorted volume of images. With our proposed reconstruction, T2-weighted PSF-EPI provides high-SNR, undistorted images without a need for field maps, and with absolute scan times comparable to alternative advanced methods that require calibration scans.

While direct imaging with PSF-EPI confers SNR advantages via oversampling inherent to PSF-EPI acquisition, its scan time remains a barrier to widespread adoption, even with acceleration applied along multiple axes. The number of shots required to obtain a PSF volume producing high-quality undistorted images—and correspondingly, scan time—remains relatively high with standard methods. The introduction of tilted-CAIPI sampling with generalized autocalibrating partially parallel acquisition (GRAPPA) [24] reconstruction of PSF-encoded data considerably reduces shots required [14], but requires a calibration scan which is itself PSF-encoded and time-consuming to acquire. As an alternative, the purpose of this work is to improve image quality and reduce scan time for T2-weighted direct PSF-EPI imaging through advanced reconstruction. If absolute scan time can be reduced, PSF-EPI's affinity to provide high-SNR undistorted images could make it better suited for wider use. Furthermore, a model-based reconstruction built for T2-weighted PSF-EPI can serve as a foundation for future extensions to other forms of PSF-EPI.

In this work, we investigate model-based iterative reconstruction (MBIR) [25] for direct T2-weighted imaging with PSF-EPI. In MBIR, known acquisition physics and signal characteristics are incorporated into image reconstruction along with suitable priors, and the signal model's algebraic structure may be leveraged for performance enhancements. Advantages have been shown in a variety of scenarios [6,26]. We present a fully discrete signal model for accelerated PSF-EPI, and furnish an efficient and regularized variable splitting solution. We demonstrate superior image quality for direct PSF-EPI images relative to standard reconstructions through a neuroradiologists' assessment. As an extension, we demonstrate that our signal model allows for nonuniform as well as random sampling along the PSF axis, enabling reconstruction of images from less than one minute of scan data following retrospective subsampling. This work extends precursory efforts [27] with a subspace model, variable splitting, random PSF sampling, and a neuroradiologists' evaluation. Preliminary material for these extensions has been presented [28,29]. This paper is organized to briefly overview essential theory before experimental descriptions and presentation of results. Detailed mathematical descriptions of the signal model and reconstruction mechanics are provided in the Appendices.