Automatic determination of the regularization weighting for wavelet-based compressed sensing MRI reconstructions

To present a method that automatically, rapidly, and in a noniterative manner determines the regularization weighting for wavelet-based compressed sensing reconstructions. This method determines level-specific regularization weighting factors from the wavelet transform of the image obtained from zero-filling in k-space.

We compare reconstruction results obtained by our method, $$ , to the ones obtained by the L-curve, $$ , and the minimum NMSE, $$ . The comparisons are done using in vivo data; then, simulations are used to analyze the impact of undersampling and noise. We use NMSE, Pearson's correlation coefficient, high-frequency error norm, and structural similarity as reconstruction quality indices.

Our method, $$ , provides improved reconstructed image quality to that obtained by $$ regardless of undersampling or SNR and comparable quality to $$ at high SNR. The method determines the regularization weighting prospectively with negligible computational time.

Our main finding is an automatic, fast, noniterative, and robust procedure to determine the regularization weighting. The impact of this method is to enable prospective and tuning-free wavelet-based compressed sensing reconstructions.