# Advanced Dimensionality Reduction for Imaging Mass Spectrometry of Human Eye Tissue through Low-Rank Modeling with Sparse and Dense Residuals

## TL;DR

This paper introduces new dimensionality reduction methods for imaging mass spectrometry data of human eye tissue, improving data compression and analysis.

## Contribution

The paper proposes low-rank models with sparse and dense residuals for better IMS data compression and signal preservation.

## Key findings

- PCP and SPCP outperform PCA in dimensionality reduction and data compression for IMS.
- The methods reduce signal overestimation while preserving spatially sparse features in eye tissue data.
- Results are demonstrated on MALDI Q-TOF IMS measurements of human cornea and retina.

## Abstract

Imaging mass spectrometry (IMS) yields high-dimensional
and large
data sets commonly exceeding 100,000 pixels, each reporting a mass
spectrum of 200,000 intensity values or more. Reducing the dimensionality
and size of IMS data is often necessary to enable downstream analysis,
and matrix-factorization-based approaches are often used for this
purpose. However, the model underlying most of these techniques, decomposing
measurements into the sum of a low-rank term (presumed signal) and
a small entry-wise residual term (presumed noise), is often not optimal
for IMS. For example, while spatially or spectrally sparse signals
are common in IMS data, they can heavily distort the low-rank approximation.
Therefore, we propose capturing the IMS data structure using low-rank
models that, in addition to a dense residual, allow for sparse variation
to be captured separately. We implement two such methods, principal
component pursuit (PCP) and stable principal component pursuit (SPCP),
apply them to IMS data, and compare them to a classical factorization
method, principal component analysis (PCA). We investigate their dimensionality
and noise reduction performance on MALDI Q-TOF IMS measurements of
human cornea and retina tissue since the human eye is a complex organ
with lots of small, tightly packed tissue substructures that are spatially
sparse. Our results suggest that if parameters are set adequately,
PCP and SPCP enable stronger dimensionality reduction and higher compression
of IMS data compared to PCA, while concurrently reducing signal overestimation.