In RASER (rapid acquisition with sequential excitation and refocusing) (1,2), a 2D-image in a single shot is acquired similar to EPI (Fig. 1). The phase-encoding in the echo-planar imaging (EPI) readout train is replaced spatiotemporal encoding (SPEN) in RASER. A low bandwidth-time product (R-value) of the frequency-swept excitation pulse causes blurring along the SPEN-dimension. Superresolution (SR) eliminates the blurring providing high spatial resolution (3,4). SR-reconstruction fails in the presence of spatial phase variations which are inevitably produced by the B₁-fields of all ultra-high field radio-frequency (RF)-coils. A novel iterative self-calibrated phasing algorithm, which determines the spatial phase distribution directly from experimental RASER data, is developed. Benefits of SR-reconstruction, such as, increased signal-to-noise ratio (SNR) and improved spatial resolution, are quantified in RASER images acquired at 7 T.

SPEN in RASER is performed using a frequency-swept chirp-pulse for excitation in combination with appropriate balancing of the gradients resulting in a quadratic phase profile imprinted on the transverse magnetization during the echo readout. Spatial localization of the echo signal is based on dephasing of the transverse magnetization in regions of large phase variations outside the vicinity of the vertex of the quadratic phase profile producing the so-called signal attenuation function. The acquired series of echoes originates from subsequent locations along the spatial coordinate.

SR-reconstruction can also be described as the matrix multiplication of the SPEN vector S_x corresponding to a line in the low-resolution 2D-image at position x in frequency-encoded dimension with the so-called pulse encoding matrix (PEM) A (3-5)

$$I_{x} = u S_{x}$$

$$u = {\left(A^{T} A\right)}^{-1}A^{T}$$

generating the high-resolution image vector I_x. The superscript T represents the conjugate transpose. Spatial phase variations P, which are not represented in the PEM A, are obtained iteratively ($$$j \rightarrow j+1$$$) from the experimental data $$$S_{x} = P_x^S \mid S_{x} \mid$$$ and the reconstructed image $$$I_{x} = P_x^I \mid I_{x} \mid$$$. The elements of PEM A_μν are corrected according to

$$A_{\mu\nu}^{mod} = P_{x\nu}^{T} A_{\mu\nu} P_{x\nu}$$

$$P_{x,j+1} = P_{x,j}\sqrt{P_x^S P_x^I}$$

The SNR is determined by measuring the standard deviation in a noise scan acquired with blanked RF-amplifiers and signal intensity in RASER images of a homogenous saline phantom. Simulations of SNR are based on the method in reference (6). The theoretical SNR before SR-reconstruction is derived from the SNR of a spin echo (SE)-EPI image which is normalized by the square root of the number of phase-encoding steps (5).

Fig. 2 shows RASER and for comparison gradient echo (GRE) images of a high-resolution LEGO phantom in gray. The labels ‘before’ and ‘after’ correspond to iteration and after convergence of the phase-correction algorithm applied to the RASER images of each channel of a 32-channel RF head coil. The spatial phase variation distributions are shown in color. The reduction of striping artifacts in the RASER images achieved with the phase-correction algorithm is evident.

Fig. 3 depicts the SNR-values for various R-values obtained from the experimental RASER data (blue: before SR-reconstruction, green: after SR-reconstruction) and SE-EPI image (yellow) as well as the theoretical SNR-values before SR-reconstruction (red). The SNR of the RASER images before SR-reconstruction (lores) increases with lower R-values confirming the theoretically predicted gains (red). The SNR after SR-reconstruction (hires) also increases with lower R-values, but is lower than in low-resolution images. This finding suggest that there are two competing mechanisms for noise propagation in SR-reconstruction present: first, noise enhancement as a result of matrix inversion reduces SNR. Secondly, averaging of the noise weighted by the signal attenuation function across the field-of-view (FOV) reduces the noise level.

Fig. 4 shows images of the calcarine sulcus of a subject. The RASER images are reconstructed using the SR-algorithm with self-calibrated phasing. Similar image quality and spatial resolution are achieved with RASER data acquired with the three different R-values. For comparison, segmented gradient echo (GE)-EPI, segmented SE-EPI and T₁-weighted (T₁)-GRE were acquired from the same slice. The yellow box marks the extent and location of the RASER images. The details of sulci are depicted in the RASER images equally well to the T₁-GRE (inverted contrast) and the SE-EPI images. The GE-EPI provides T₂^*-weighted contrast while RASER and SE-EPI produce T₂-weighted images accounting for the different gray-white matter contrast.

In summary, self-calibrated phasing algorithm which enables SR-reconstruction of SPEN data exhibiting strong phase variations was developed. The proposed phase-correction algorithm is shown to substantially improve the quality of RASER-images acquired at 7 T. It is concluded that this capability is essential to be able to perform SR-reconstruction of data acquired at ultrahigh magnetic field providing high spatial resolution and increased SNR.