ESPReSSo: Compressed Sensing Partial Subsampling
ESPReSSo (Compressed Sensing Partial Subsampling) is a Cartesian subsampling scheme which incorporates the idea of Partial Fourier acquisition and variable-density Poisson Disc (vdPD) subsampling by redistributing the sampling space onto a smaller region aiming to increase k-space sampling density for a given acceleration factor (as illustrated in the Figures below). Especially the normally sparse sampled high-frequency components benefit from this sampling redistribution, leading to an improved edge delineation which is useful in applications benefitting from sharp image boundaries, such as motion correction.
variable-density Poisson Disc subsampling mask
ESPReSSo subsampling mask
Acquisition
By reformulating the distance metric d of a vdPD with dimensions My and Mz, 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.