Journal
IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING
Volume 6, Issue -, Pages 1309-1319Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCI.2020.3019111
Keywords
Convergence; Image reconstruction; Minimization; Magnetic resonance imaging; Optimization; Transforms; Continuation scheme; proximal algorithm; regularization parameter; scale factor; sparse reconstruction
Funding
- Science & Engineering Research Board (SERB) [CRG/2019/002060]
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For compressed sensing magnetic resonance imaging (CS-MRI) that utilize sparse representations, the regularization parameter establishes a trade-off between sparsity and data fidelity. While convergence to the desired solution is slow for mean squared error (MSE) optimal constant regularization, continuation using decreasing parameter values enables faster convergence. To derive an explicit rule for continuation, we propose an intermediate step optimization that involves maximization of the l(2)-norm of the gradient descent update. This is achieved by inclusion of an extra prior to the CS-MRI cost function. The solution is obtained using an alternating minimization approach in which the first sub-problem deals with the sparse regularization using the previously computed parameter value, and the second sub-problem aims at estimation of the parameter value to be used in the succeeding iteration. The solution to the second sub-problem is computed using standard root finding methods. Irrespective of the initial choice of the regularization parameter, we show that application of this continuation based proximal approach enables faster convergence to the desired solution.
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