To noticeably reduce image inhomogeneity caused by Sum-of-Squares (SOS) channel combination by using geometric average of channels (GAC)

Sum-of-Squares (SOS) is a widely accepted channel combination method in multi-channel MR Imaging [1], featuring fast calculation and generally high image quality and signal-to-noise ratio (SNR). However, SOS is also sensitive to signal variation as a result of coil sensitivity of different channel and sometimes leads to spatial inhomogeneity in reconstructed images. Although certain techniques that improve the spatial inhomogeneity caused by SOS have been proposed, some of them require additional data collection which is susceptible to additional artifacts, while others involve complicated computation that is time-consuming. These limitations have prevented their wide-spread usage in most clinical settings except for certain special applications.

One of the properties of geometric average is it's insensitive to the value variation between components to be averaged [2]. Taking advantage of this property, geometric average of channels (GAC) can be used to correct for image spatial imhomogeneity caused by SOS reconstruction. The proposed method first reconstruct the same collected multi-channel data using SOS and GAC respectively, and subsequently divide the SOS image over GAC image pixel-by-pixel to have a GAC/SOS map. Then a Gaussian smooth filter is applied on the map to obtain a profile map that reflects the spatial inhomogeneity of SOS image as a result of varying coil sensitivity of different channels. Finally this map is normalized to yield proper dynamic range, and multiplied pixel-by-pixel onto the SOS image to correct for inhomogeneity. This method is straight-forward and only simple calculation is needed thus results in fast computation. It requires no additional data collection so it is free of additional artifacts associated with such data.

Figure 1 is an example of inhomogeneity correction using GAC in multi-channel MR Imaging with SOS. One healthy volunteer was imaged at 1.5T (uMR560, United Imaging Healthcare) using a combination of spine coils and body-array coils. Following localizer, a 3D stack-of-stars radial sequence covering the liver was acquired during free-breathing. The parameters are: slice thickness 3mm,flip angle 10°, frequency-selective fat saturation, TE/TR 2.2/4.9 ms, 40 slices interpolated to 80 slices, BW 345 Hz/pixel, FOV 260×260 mm², resolution 256×256, 340 radial views using golden-angle acquisition. For each channel, data is first regridded onto Cartesian coordinates [3].

Figure 1(a) is an axial slice reconstructed by GAC showing liver and kidneys. Figure 1(b) is the same slice reconstructed by SOS. Please note the substantial signal inhomogeneity on image shown as bright regions on dorsal and ventral side of the abdomen. Figure 1(c) is the normalized GAC/SOS map before filtering. Though the map is noisy, the spatial inhomogeneity has smooth variation in image space, and therefore can be denoised by a simple Guassian smooth filter. Applying the denoised map onto Figure 1(a) yields inhomogeneity-corrected SOS image as shown in Figure 1(d).

We have proposed a novel method that corrects for signal imhomogeneity on SOS reconstructed images caused by varying coil sensitivity. The proposed method is straight-forward method and requires no additional acquisition. It has the potential to be a fast and robust reconstruction method for multi-channel image data.