Novel Structured Low-rank algorithm to recover spatially smooth exponential image time series
This work addresses the challenge of efficient image reconstruction in medical or scientific imaging, though it appears incremental as it builds on existing low-rank and exponential modeling techniques.
The authors tackled the problem of recovering spatially smooth exponential image time series from under-sampled Fourier measurements by proposing a structured low-rank matrix completion algorithm, resulting in significant improvement over state-of-the-art methods in parameter mapping.
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 under-sampled 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.