Spiral trajectories with long readout times improve scan efficiency, but exhibit blurring in reconstructed images due to chemical shift and field inhomogeneity. Image quality is restored by joint deblurring and water-fat separation provided an accurate off-resonance ($$$\Delta f_0$$$) map [1]. Three-dimensional $$$\Delta f_0$$$ maps can be acquired quickly, but imperfections may arise from dynamic processes (e.g. scanner heating) or patient motion (mis-alignment or nonlinear field map distortion). We propose a modified autofocusing technique [2-5] to refine the measured $$$\Delta f_0$$$ map and remove residual off-resonance blurring in spiral images.

Autofocusing works by minimizing some blurring metric voxel-by-voxel through a range of off-resonance frequencies. The cost function here is the sum of the magnitude of the imaginary channel over a small window $$$V$$$, i.e. $$$\underset{V(x,y,z)}{\int}{|Im(I(\Delta f)|^{\alpha}dV}$$$ where $$$I(\Delta f)$$$ is the conjugate-phase reconstruction with relative center frequency $$$\Delta f$$$. This assumes the true image is entirely real, with local phase introduced by off-resonance blurring.

Our approach operates on water images after joint separation and deblurring using a measured $$$\Delta f_0$$$ map. This eliminates issues from fat signal and reduces the $$$\Delta f$$$ search space to avoid local minima. Additional quadratic weighting on the cost function reinforces the influence of the measured $$$\Delta f_0$$$ map.

All scans were performed on a Philips Ingenia 3T scanner using a 15 channel head coil. To assess the ability to correct for minor motion between field map and image acquisition, 3D gradient echo images of a healthy volunteer were acquired with a distributed spiral trajectory [6], voxel size 0.9 x 0.9 x 2.0 mm³, ADC time 9.9 ms, 70 slices, scan time 1:42. A second volume was acquired after the volunteer moved slightly; extrinsic XYZ rotations estimated using rigid registration with FLIRT [7] were 2.9°, 1.4°, and 2.3°.

To evaluate the robustness of the algorithm, autofocusing was also applied to six existing 2D SE spiral datasets. These data had 3 TEs such that they could be separated and deblurred without a previously acquired field map, eliminating issues from motion or system heating.

Water images after the first-pass deblurring were zero-padded by 20% and low-pass filtered by a 10% Hann window to evaluate the slowly-varying phase, which was then subtracted from the zero-padded images. The autofocusing window was 11 x 11 x 5 pixels on the zero-padded matrix. The autofocusing process searched a residual off-resonance range between -100 to +100 Hz in 31 steps (6.5 Hz increments).

Figure 1 shows a representative slice of the dataset with motion between initial $$$\Delta f_0$$$ map and image data collection before and after autofocusing. Figure 2 shows the corresponding magnitude imaginary channel after high-pass filtering (i.e. the autofocusing cost metric); a reduction in magnitude and contrast is seen as a result of autofocusing. Figure 3 shows the measured $$$\Delta f_0$$$ map, and the $$$\Delta f_0$$$ map with residual off-resonance added as measured with autofocusing. Results from the SE datasets (Figure 4) show minor improvements, with no apparent reduction in image quality where first-pass deblurring was accurate.

Autofocused images can be calculated in two ways: 1) by choosing the pixel value from the conjugate-phase reconstruction that minimized the cost metric, or 2) by adding the residual field map values from autofocusing to the initial field map, then processing the original images again through joint water-fat separation and deblurring. The first method (used in Figures 1 and 4) may suffer artifacts from discretized off-resonance frequencies and non-locally-uniform fields, particularly when large (>10 Hz) increments are used. The second method can mitigate these errors by smoothing the residual field map, but suffers additional reconstruction time and reduced effectiveness in areas where the field map is changing rapidly.

Autofocusing, in conjunction with our current water-fat separation and deblurring, improves image quality, particularly in the case of minor motion between $$$\Delta f_0$$$ map and image data collection, while robustly maintaining image quality where the initial $$$\Delta f_0$$$ map is correct. We expect to see improvement (and potentially corrected fat-water swaps) in other cases where the initial $$$\Delta f_0$$$ map is incorrect, including as a result of of scanner heating or pooled contrast agent.