L1k-t ESPIRiT: Accelerating Dynamic MRI Using Efficient Auto-Calibrated Parallel Imaging and Compressed Sensing Reconstruction

Background Iterative self-consistent parallel imaging (PI) reconstruction (SPIRiT) [1, Lustig M, MRM 64:457-71,2010] has been extended for dynamic imaging by exploiting temporal correlations in k-t space (k-t SPIRiT) [2,Santelli C, MRM 72:1233-45, 2014]. Using eigendecomposition of a modified SPIRiT operator, computationally optimized reconstruction formally translates into auto-calibrated SENSE (ESPIRiT) [3, Uecker, MRM 71:990-1001, 2014]. In this work, this principle is applied to a k-t SPIRiT operator resulting in SENSE-like reconstruction of a coilcombined x-f space object. The method is tested on dynamic cardiac short-axis view data and compared to standard L1-regularized k-t SPIRiT. Methods L1 k-t SPIRiT reconstructs a multi-coil x-f image series r by solving the optimization problem (1) (Figure 1a). For each x-f voxel, the PI-operator G reduces to a matrix-vector multiplication resulting into a computational complexity of O(NcxNc) (Nc: No. of coils). Following [3], eigenvectors and eigenvalues of G assemble the matrix Sx,f (composed of stacked diagonal matrices) directly transforming an x-f object into its multi-coil sensitivity-weighted representation. Thereby, the PI matrix G in (1) can be replaced by Sx,f in the modified data-consistency term in (2) (Figure 1a). Solving (2), termed as L1 k-t ESPIRiT, then results in a computationally optimized equivalent of (1) with an O(Nc) PI