Wave encoding is a controlled aliasing strategy which allows better utilization of the spatial degrees of freedom in multi-channel receive arrays. This enables high acceleration rates in parallel imaging without incurring significant g-factor penalty. Conventional spin-warp acquisitions can be augmented to utilize wave encoding using simple sequence modifications. However, this requires a dedicated image reconstruction that captures these modifications on the k-space trajectory. We will focus on wave acquisition and reconstruction techniques as well as the trade-offs in image calculation time, trajectory estimation and potential artifacts, and how these could be mitigated to enable translation of this efficient imaging technique.
The Sequence
Wave is an extreme Controlled Aliasing In Parallel Imaging (CAIPI) strategy which has been applied to structural imaging acquisitions with 3D and Simultaneous MultiSlice (SMS) encoding (1–5). This involves playing sinusoidal Gy and Gz gradient waveforms during the acquisition of each k-space “line”, which leads to a helical k-space trajectory. The effect of this non-Cartesian trajectory is to spread the image aliasing in all directions, including the conventionally “fully-sampled” readout axis. Utilizing coil sensitivity variations in all three spatial dimensions thus provides substantial reduction in g-factor noise amplification, especially at high acceleration factors. We will focus on the application of wave gradients in a range of sequences commonly used in clinical imaging.The Reconstruction
It is possible to represent the voxel spreading effect of the non-Cartesian trajectory via convolution with a point spread function (PSF). This way, wave encoding can be formulated in Cartesian space and admits a generalized SENSE reconstruction (6). In addition to the coil sensitivities, such reconstruction also requires the estimation of the actual wave gradient waveforms that were played out during the acquisition. Wave reconstruction also benefits from additional regularizers that enforce sparsity (7) and low rank structure (8), which allow for further acceleration.
It is also possible to perform k-space based parallel imaging reconstruction using the GRAPPA formalism (9). This requires multiple kernels to represent the relations between k-space points on the non-Cartesian sinusoidal trajectory, but has the advantage of obviating the need for explicit coil sensitivity estimation (10,11). We will talk about both image and k-space domain reconstruction techniques as well as their pros and cons.
The Trade-Offs
As with most non-Cartesian acquisitions, trajectory errors lead to image artifacts in wave-CAIPI. As such, calibration of the sinusoidal waveforms, and the resulting “experimental” PSF is crucial for high quality wave imaging. Since the wave forward model includes both the coil sensitivities and the PSF, which both need to be estimated, auto-calibration of wave acquisition is difficult. A fully-sampled autocalibration signal (ACS) region could be utilized, and the “theoretical” PSF could be used to deconvolve the voxel spreading. This demodulated ACS data could then allow for the estimation of coil sensitivities, after which the PSF estimates could also be refined iteratively (12).
Another approach is to use a separate fully-sampled, low-resolution, Cartesian acquisition to estimate the coil sensitivities. Having estimated the receive profiles, PSFs and the image content can be simultaneously solved for using a joint parallel imaging reconstruction (13). This data driven “auto-PSF” approach finds the trajectory and the image that is most consistent with the acquired k-space data. Another data driven approach for PSF calibration is to use an auto-focusing loss function to find the PSF parameters that provide the most crisp image reconstruction (12). We will touch upon these calibration techniques and talk about their computational efficiency.
Influence of the sinusoidal gradients can lead to image artifacts due to physiological and relaxation effects. For gradient echo acquisitions at late echo times, unwanted flow encoding performed by the wave trajectory can be alleviated by additional flow compensation gradients. Echo train acquisitions such as MPRAGE (14) use an inversion module for contrast preparation. The combination of T1 recovery and sinusoidal k-space trajectory can lead to additional ringing artifacts. We will talk about how to mitigate these artifacts by designing the wave trajectory appropriately so as to retain the large g-factor benefit.
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