Motion during data acquisition causes data inconsistency which typically leads to ghosting artifacts. If there is sufficient redundancy in the data set, image quality can be improved by identifying and rejecting corrupted data based on self-consistency¹. If such an approach is based on SENSE, coil sensitivity maps (CSM) need to be known. Here, we present a method which does not need prior information about CSM but estimates CSM, image and corrupted data simultaneously.

Data acquisition: We performed phantom and volunteer experiments on a 3T MR scanner to demonstrate the new technique using a 13-channel head coil and a multi-slice T₂w fast spin-echo sequence for routine brain imaging (TE=100 ms, 0.6x0.6x3 mm³ resolution). The temporal order of the acquisition was modified to separate interleafs which are close in k-space as much as possible in time. Volunteers were instructed to perform small incidental movements during the scan (swallowing, coughing, etc.)

Reconstruction algorithm: First step is to reconstruct images for each receive channel. These images are used to calculate an initial estimate of the relative coil sensitivities. In this step, we enforce spatial smoothness of the resulting CSM by applying regularization. The width of the smoothing kernel is matched empirically to a typical length scale for the used multi-channel coil. This smoothing step is important because it suppresses propagation of noise and artifacts from the single-channel images to the CSM estimate. Second step is an iterative SENSE reconstruction to reject corrupted data and to remove their influence from the reconstructed image. As an optional step inside the iteration loop, the relative coil sensitivities are recalculated based on the current image and the current set of non-rejected data each time an interleaf is rejected.

Figure 1 shows two examples of a reconstruction from data sets with motion. Images a) show standard reconstructions without data rejection displaying typical motion related ghosting artifacts. Fig. 1b shows the images after applying auto-calibrated iterative SENSE with data rejection but without updating the CSM (this is an image-space analogue to the k-space method COCOA²). This image is already much improved but for the case of the phantom some artifacts remain because errors from the initial image carry over to the initial CSM. Updating the CSM inside the iteration loop improves the reconstructed image even further (Fig.1c). For the volunteer image, the initial CSM estimate was already of good quality, so images b) and c) are equivalent.This algorithm combines features of data rejection schemes with joint-SENSE^3,4 where CSM and image are updated iteratively. Driving force for both update processes is minimizing data inconsistency. The distribution of inconsistent data controls which action is taken: Inconsistencies which are located in a connected region in image space lead to an update of the CSM. Inconsistencies which are connected with respect to data acquisition time (i.e. profiles in k-space belonging to the same interleaf) lead to data rejection.An iterative reconstruction enforcing self-consistency can improve image quality substantially. Two sources of inconsistency are addressed here: information about coil sensitivities and motion. The presented method can be applied to data from many MRI sequences.