Reduction of Motion Artifacts in the Recovery of Undersampled DCE MR Images Using Data Binning and L+S Decomposition

Algorithm 1

Proposed hybrid L+S (HL+S) reconstruction algorithm for DCE MRI.

Inputs

: Multi coil radially sampled k-space data

: Multicoil encoding operator

: Sparsifying transform

: Singular-value thresholding parameter

: Sparsity thresholding parameter

Phase 1: Respiratory signal extraction

Step 1. Find projection profiles using 1D Fourier transform along z-axis (slice dimension).

Step 2. Perform PCA for the matrix given in equation (2).

Step 3. Select the principle component to represent breathing signal with highest peak in the range

respiratory signal frequency

Phase 2: Data Binning

Step 4. Division of among contrast phases to generate sub respiratory signals etc. as

shown in Figure 1(a)

Step 5. Sort for smooth transitions

Step 6. Divide sorted in different respiratory states and assign equal number of spokes to each state as

shown in Figure 1(b) to generate data  .

Phase 3: Recovery of motion free DCE MR images

Initialization  ,

Iteration  (Repeat until not converged)

Increment   by 1

Step 7. Singular value soft thresholding

Compute using equation (7)

Step 8. Shrinkage in sparsifying domain

Compute using given in equation (6)

Step 9. Data consistency

Output

  and