Scale Recognition, Regularization Parameter Selection, and Meyer's G Norm in Total Variation Regularization

2006 ◽  
Vol 5 (1) ◽  
pp. 273-303 ◽  
Author(s):  
David M. Strong ◽  
Jean-François Aujol ◽  
Tony F. Chan
Keyword(s):  
Total Variation ◽  
Regularization Parameter ◽  
Parameter Selection ◽  
Total Variation Regularization ◽  
Regularization Parameter Selection

scholarly journals Data-Driven Regularization Parameter Selection in Dynamic MRI

2021 ◽  
Vol 7 (2) ◽  
pp. 38
Author(s):  
Matti Hanhela ◽  
Olli Gröhn ◽  
Mikko Kettunen ◽  
Kati Niinimäki ◽  
Marko Vauhkonen ◽  
...  
Keyword(s):  
Regularization Parameter ◽  
Dynamic Mri ◽  
Parameter Selection ◽  
Data Driven ◽  
Reference Image ◽  
Total Variation Regularization ◽  
Test Case ◽  
Regularization Parameters ◽  
S Curve ◽  
Regularization Parameter Selection

In dynamic MRI, sufficient temporal resolution can often only be obtained using imaging protocols which produce undersampled data for each image in the time series. This has led to the popularity of compressed sensing (CS) based reconstructions. One problem in CS approaches is determining the regularization parameters, which control the balance between data fidelity and regularization. We propose a data-driven approach for the total variation regularization parameter selection, where reconstructions yield expected sparsity levels in the regularization domains. The expected sparsity levels are obtained from the measurement data for temporal regularization and from a reference image for spatial regularization. Two formulations are proposed. Simultaneous search for a parameter pair yielding expected sparsity in both domains (S-surface), and a sequential parameter selection using the S-curve method (Sequential S-curve). The approaches are evaluated using simulated and experimental DCE-MRI. In the simulated test case, both methods produce a parameter pair and reconstruction that is close to the root mean square error (RMSE) optimal pair and reconstruction. In the experimental test case, the methods produce almost equal parameter selection, and the reconstructions are of high perceived quality. Both methods lead to a highly feasible selection of the regularization parameters in both test cases while the sequential method is computationally more efficient.

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