# Novel Structured Low-rank algorithm to recover spatially smooth exponential image time series

## TL;DR

This paper introduces a structured low-rank matrix completion algorithm that leverages spatial smoothness and exponential structure to accurately recover image time series from under-sampled Fourier data, improving over existing methods.

## Contribution

The novel algorithm combines spatial smoothness and exponential structure in a low-rank framework for improved image time series recovery from limited data.

## Key findings

- Significant improvement over state-of-the-art methods.
- Effective recovery of exponential parameters from under-sampled data.
- Demonstrated in parameter mapping applications.

## 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 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.