Novel structured low-rank algorithm to recover spatially smooth exponential image time series

Abstract

We propose a structured low rank matrix completion algorithm to recover a time series of images consisting of linear combination of exponential parameters at every pixel, from undersampled Fourier measurements. The spatial smoothness of these parameters is exploited along with the exponential structure of the time series at every pixel, to derive an annihilation relation in the k - t domain. This annihilation relation translates into a structured low rank matrix formed from the k - t samples. We demonstrate the algorithm in the parameter mapping setting and show significant improvement over state of the art methods.