Sampling and recovery of MRI data using low rank tensor models

Area of Science:

• Medical Imaging
• Data Science
• Applied Mathematics

Background:

• Dynamic Magnetic Resonance Imaging (MRI) requires significant data acquisition.
• Limited sampling in k-t space presents challenges for reconstructing high-quality dynamic MRI data.
• Existing compressed sensing (CS) methods rely on transform-domain sparsity (e.g., wavelets, total variation).

Purpose of the Study:

• To investigate the effectiveness of low-rank tensor factorization models for dynamic MRI data recovery from limited k-t space sampling.
• To assess the compressibility of 3D temporal (2D space + time) MRI data using tensor factorization.
• To compare tensor factorization approaches against CS-based methods for reconstructing undersampled temporal MRI data.

Main Methods:

• Employed several tensor factorization techniques for dimensionality reduction and data recovery.
• Applied these algebraic, data-adaptive methods to 3D temporal MRI data.
• Restricted sampling to be uniformly random along a single k-space direction, mimicking traditional MRI acquisition.

Main Results:

• Tensor factorization demonstrated significant dimensionality reduction (compressibility) for dynamic MRI data.
• These methods showed promise in recovering temporal MRI data acquired with limited, uniformly random sampling in one k-space direction.
• The data-adaptive nature of tensor factorization offers an alternative to transform-domain sparsity exploited by CS methods.

Conclusions:

• Low-rank tensor factorization is a viable and promising approach for dynamic MRI reconstruction from limited k-t space samples.
• This algebraic technique provides a data-adaptive alternative to conventional CS methods.
• Further research into tensor factorization holds potential for improving MRI data acquisition efficiency.