Null Space Imaging: A Novel Gradient Encoding Strategy for Highly Efficient Parallel Imaging

Leo Tam¹, Jason Peter Stockmann¹, Robert Todd Constable, ¹²

Null Space Imaging (NSI) defines nonlinear encoding gradients to complement the spatial localization abilities of a parallel receiver array. To complement coil sensitivities, gradients should encode where coil sensitivities poorly distinguish signal. The singular value decomposition analyzes coil sensitivities to generate a complete basis set of vectors spanning the null space of sensitivities. By interpreting the orthogonal vectors in the null space as a complementary gradient set, NSI enables highly accelerated (R=16) parallel imaging as demonstrated by simulated spin echo experiments. NSI suggest complementary gradient design is a powerful concept for parallel imaging requiring only a limited set of receivers.