Identifying Relevant Eigenimages - a Random Matrix Approach

TL;DR

This paper introduces a novel method using random matrix theory and statistical tests to distinguish relevant eigenmodes from noise in high-dimensional data, improving dimensionality reduction techniques.

Contribution

The paper presents a new approach combining random matrix theory with goodness-of-fit testing to identify significant eigenimages, validated through simulations and real MRI data.

Findings

Effective differentiation of relevant eigenmodes from noise.

Validated method with numerical simulations.

Applied successfully to real-time MRI images.

Abstract

Dimensional reduction of high dimensional data can be achieved by keeping only the relevant eigenmodes after principal component analysis. However, differentiating relevant eigenmodes from the random noise eigenmodes is problematic. A new method based on the random matrix theory and a statistical goodness-of-fit test is proposed in this paper. It is validated by numerical simulations and applied to real-time magnetic resonance cardiac cine images.