Compressive sensing cardiac cine MRI using invertible non-linear transform

Since compressive sensing (CS) is robust to noise and does not require any special hardware, CS-based methods are advantageous to other ones for increasing MRI speed. Monotonic re-ordering (sorting) of the desired signal can increase its sparsity and consequently CS reconstruction efficiency. To use this, it is essential to estimate re-ordering operator which usually has been done by parallel imaging methods. These methods need regular sampling patterns which may not be optimum for CS reconstruction. We replaced the re-ordering operator by an invertible non-linear transform. The advantages of this approach are greater reconstruction speed, no need for preliminary reconstruction and estimation of the re-ordering operator and possibility of having an arbitrary sampling pattern. We successfully applied our approach to speed up cardiac cine MRI by factor of 2. This reduced the mean reconstruction error from 5.65% for standard CS to 5.41% and reconstruction time from 66.3 for CS plus re-ordering operator to 5.1 seconds.