Finding Optimal Regularization Parameter for Undersampled Reconstruction using Bayesian Optimization

We present a Bayesian optimization approach to find the optimal regularization parameters for undersampled MRI reconstructions such as Compressed Sensing (CS). Bayesian optimization can find optimal points for expensive to evaluate functions by efficient sampling the next points to try by maximizing the expected improvement. Additionally, the use of pruning can speed up optimization by stopping early unpromising trials. We demonstrate the effectiveness of this optimization technique by finding optimal parameters for undersampled MRI using Total Variation and CS-Wavelet regularization. The parameters found with the proposed approach are comparable to does found by grid search but requiring shorter computational times.