Robust non-local regularization framework for motion compensated dynamic imaging without explicit motion estimation

We introduce an regularized reconstruction scheme to recover dynamic imaging datasets with significant inter frame motion from undersampled Fourier data. The proposed nonlocal regularization penalty is an unweighted sum of distances between image patch pairs in the 3-D dataset. We use robust distance metrics to compute the distance between image patches; these metrics encourage the smoothing between similar patches, while discouraging the averaging of dissimilar patches. Hence, this algorithm is capable of exploiting the similarities between patch pairs in adjacent frames even when they are well separated due to motion, eventhough it does not perform explicit motion estimation. Unlike current non-local regularization schemes, the proposed penalty does not need good initial guesses to estimate the weights. Hence, this approach is readily applicable to accelerated dynamic imaging problems, where good initial guesses are challenging to obtain. The validation of the proposed scheme on numerical phantoms and dynamic MRI datasets demonstrate the superior performance of the proposed scheme over current dynamic imaging schemes.