ESPReSSo: Compressed Sensing Partial Subsampling

Acquisition

By reformulating the distance metric d of a vdPD with dimensions M_y and M_z, variable-density q and ESPReSSo compression factor γ as:

and embedding it inside a fast dart-throwing algorithm according to Bridson [Bridson, SIGGRAPH 2007], yields the ESPReSSo mask generation algorithm:

to derive the ESPReSSo mask Φ.

Reconstruction

The ESPReSSo compression is accounted for in the reconstruction as an additional Hermitian symmetry constraint which can be formulated as a zero-forcing imaginary operator:

or as a phase-correcting projection-onto-convex-sets (POCS) operator:

The final output image ρ is reconstructed from the subsampled k-space ν by:

which can be solved via a FOCal Underdetermined System Solver (FOCUSS) [Gorodnitsky and Rao, TSP 1997] resulting in the following reconstruction algorithm:

Download

The subsampling mask generation is implemented into a spoiled gradient echo sequence, termed CS_FLASH (Siemens, VB20P). The acquisition sequence, as well as the C++ implementation of the mask generation code and the reconstruction code can be downloaded:

Stable release:

Source codes are available at GitHub: https://github.com/thomaskuestner/CS_MoCo_LAB

Documentation can be found here: CS LAB: An MR acquisition and reconstruction system

Please cite one of the papers, if you use it in a scientific publication.

References