RLS-GRAPPA: RECONSTRUCTING PARALLEL MRI DATA WITH ADAPTIVE FILTERS W. Scott Hoge 1 , Fernando Gallego 2 , Zhikui Xiao 3 , Dana H. Brooks 4 (1) Dept. of Radiology, Brigham and Women’s Hospital, 75 Francis St., Boston, MA (2) Universitat Polit` ecnica de Catalunya, Barcelona, Spain, (3) Tsinghua University, Beijing, China, (4) ECE Dept., Northeastern University, 360 Huntington Ave., Boston, MA ABSTRACT GRAPPA is one of the predominant methods used to recon- struct accelerated parallel MRI data. In has been shown previously that spatially varying the GRAPPA reconstruc- tion coefficients can be advantageous. A significant problem with these approaches, however, is an increase in computa- tion time due to an increase in the number of linear system solves needed. Here, we leverage the fact that these systems vary slowly over the coordinate space and employ recursive adaptive filters in place of explicit system solves. This ap- proach produces high quality spatially variant GRAPPA re- constructions with a computation time comparable to stan- dard GRAPPA. Index Terms— Magnetic resonance imaging, Parallel MRI, GRAPPA, RLS 1. INTRODUCTION Parallel MR imaging (pMRI) employs multiple receiver coils to acquire data. These coils contribute an inherent spatial do- main encoding that complements traditional Fourier encod- ing. This enables one to subsample during image acquisition, allowing one to reduce image acquisition time, improve spa- tial and/or temporal resolution, or some combination of both. A good review of pMRI can be found in [1]. GRAPPA [2] is one of the most widely used parallel MR re- construction algorithms in clinical use today. The technique is based on finding correlations in the acquired data, which orig- inate from the multi-coil view of the imaged plane. GRAPPA is often referred to as an auto-calibrated k-space technique, as the reconstruction parameters can be derived directly from the acquired data in certain scenarios, and the processing typically takes place completely in the Fourier domain—in contrast to SENSE [3] and similar methods, which require explicit estimates of the acquisition coil sensitivities. Be- cause explicit coil sensitivity estimates are not required in GRAPPA, the technique remains robust in many situations where SENSE can fail, e.g. [4]. Support for this research provided in part by NIH U41 RR019703-01A2 (Jolesz, PI) To improve the performance of GRAPPA, many extensions have been proposed including processing in the image- and/or hybrid- (both k- and x- space) domains to reduce computation time [5] and the use of coordinate dependent reconstruction parameters to improve image quality [6, 7, 8]. It was shown in [9] that an alternative to using a 2D k-space (k x ,k y ) recon- struction kernel is to use instead a 1D kernel in hybrid-space, (x, k y ). It was further shown in [5] that employing the re- construction parameters in the hybrid-space is more efficient computationally. Similarly, it was shown in [6] and [7] that varying the re- construction parameters across the coordinate space produces higher quality reconstructions. For example, in KIPA [6] one employs a set of reference data fully sampled at the Nyquist rate to calculate reconstruction coefficients for a number of different locations in k-space. These coefficients are then used in subsequent accelerated acquisitions. The authors claim high acceleration rates, although the method is cur- rently limited to scenarios where the reference data closely matches the accelerated data. Varying the reconstruction parameters substantially in- creases the computational load, however, as the number of system solves needed to identify those parameters necessar- ily increases. Previous approaches to mitigate this included computing the reconstruction coefficients at only a few loca- tions and then interpolating between them, as in SV-GRAPPA [7]. However, the linear system associated with finding these coefficients changes in a structured way, from point-to-point along data coordinate space. Specifically, points at the trailing edge of the contribution window are removed, while points at the leading edge are added. All points in between remain. This scenario mirrors the data flow that drove develop- ment of adaptive filtering algorithms. We demonstrate be- low that through the use of adaptive filters, one can dramati- cally reduce the computational load in SV-GRAPPA, while si- multaneously capitalizing on efficiencies provided by hybrid- domain calculations. Furthermore, the approach may provide a mechanism to achieve a self-referenced version of KIPA. In Proc of 2008 IEEE International Symposium on Biomedical Imaging (ISBI 2008). Paris, France. May 2008, pp. 1537-1540.