Model-based Compressed Sensing Reconstruction for MR Parameter Mapping

Introduction:Compressed Sensing [1-4] suggests that compressible signals can be reconstructed from far less samplesthan required by the Nyquist-Shannon sampling theorem. Signal recovery is achieved by Basis Pursuit (BP) [2] or greedyalgorithms like Orthogonal Matching Pursuit (OMP) [4]. The latter has weaker performance guarantees, but it is oftenfaster and is thus an attractive alternative to BP. Most commonly, orthonormal bases are applied as a sparsifyingtransform. However, allowing the signal to be sparse with respect to an overcomplete dictionary adds a lot of flexibilitywith regard to the choice of the transform and could improve the transform sparsity.MR parameter mapping measurements of relaxation times T1 and T2, diffusion coefficients, etc. require the acquisition ofmultiple images of the same anatomy at varying parameters, which is associated with long acquisition times. These dataare described by a model with only few parameters, which could be used to design a model-based overcomplete dictionaryfor CS reconstruction. In this work we demonstrate this approach for the acceleration of T1 mapping data acquisition.