Automatic Coil Selection for SENSE Imaging with Large Coil Arrays

Introduction Parallel imaging using coil arrays with large number of receive elements allows improved imaging performance and increased SNR [1, 2]. However, the use of a large number of coil elements can lead to memory storage problems and to increased reconstruction times. Several techniques for data reduction were presented, realized either by linear combination of the original coil data or by discarding particular data from unimportant coils elements [3-5]. In this work, we focus on coil selection and present an efficient approach applicable to massively parallel SENSE imaging. Methods An appropriate criterion for a coil subset selection should refer to the image quality if an image is acquired with a given coil configuration. One such quality measure is the signal-to-noise-ratio (SNR). The SNR in parallel imaging is spatially variable, so local SNR optimization will lead to a different coil configuration for each pixel. A more global quality characteristic is the mean SNR. The optimal coil set can be found by performing an exhaustive search through all possible coil subsets and selecting the set with highest mean SNR, but the number of possible coil combinations makes this problem computationally challenging. The SENSE reconstruction of uniformly undersampled Cartesian data consists of solving a linear system of L equations with R variables, where L is the number of coil elements and R is the reduction factor. The reconstruction problem could be solved by means of singular value decomposition (SVD). The data a and the sensitivity S are projected from the L to an R dimensional space Pa a'= , PS S'= and the problem is solved in this lower dimensional space. The projection matrix can be given as P = U, where U comes from the SVD of the sensitivity matrix S = UΣV. The coil sensitivities in the R-dimensional space can be considered as coil sensitivities of R virtual coils [6]. If the best subset of a given coil set has to be selected, the upper SNR limit would be given by the full coil set. So, finding those coils that have the most similar projection on the R-dimensional problem space to the projection of the full coil set will result in an optimal SNR coil configuration. The i-th row vector of S’ can be written as a linear combination of the rows of S