# Bi-Linear Modeling of Data Manifolds for Dynamic-MRI Recovery

## TL;DR

This paper introduces a bi-linear manifold-learning framework for dynamic MRI recovery that leverages data geometry and spatio-temporal patterns without external training, showing significant improvements over existing methods.

## Contribution

It proposes a novel bi-linear modeling approach for dynamic MRI data recovery using manifold learning and sparse approximation, with a guaranteed convergence algorithm.

## Key findings

- Notable improvements over state-of-the-art methods in MRI reconstruction.
- Effective manifold-based modeling without external training.
- Successful application to real cardiac MRI data.

## Abstract

This paper puts forth a novel bi-linear modeling framework for data recovery via manifold-learning and sparse-approximation arguments and considers its application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain MR image is viewed as a point that lies onto or close to a smooth manifold, and landmark points are identified to describe the point cloud concisely. To facilitate computations, a dimensionality reduction module generates low-dimensional/compressed renditions of the landmark points. Recovery of the high-fidelity MRI data is realized by solving a non-convex minimization task for the linear decompression operator and those affine combinations of landmark points which locally approximate the latent manifold geometry. An algorithm with guaranteed convergence to stationary solutions of the non-convex minimization task is also provided. The aforementioned framework exploits the underlying spatio-temporal patterns and geometry of the acquired data without any prior training on external data or information. Extensive numerical results on simulated as well as real cardiac-cine and perfusion MRI data illustrate noteworthy improvements of the advocated machine-learning framework over state-of-the-art reconstruction techniques.