BioMed Research International / 2019 / Article / Alg 1

Research Article

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.

: 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