# A review of decomposition methods for brain states estimation

## TL;DR

This paper reviews various methods for separating mixed brain states in fMRI data to better understand brain activity.

## Contribution

The paper offers a comprehensive survey and comparison of decomposition methods for analyzing fMRI data.

## Key findings

- Decomposition methods like classical, probabilistic, and tensor-based approaches are essential for analyzing mixed brain states in fMRI data.
- The review highlights the strengths and limitations of decomposition algorithms compared to other fMRI analysis techniques.
- These methods are broadly applicable for extracting distinct brain states from complex fMRI datasets.

## Abstract

In the rapidly advancing field of neuroscience, sophisticated imaging techniques such as functional magnetic resonance imaging (fMRI) enable detailed analysis of brain activity. Researchers increasingly seek to disentangle distinct brain states, recognizing that fMRI data typically comprise a mixture of these states. To enable independent analysis of individual brain states, numerous methodologies have been proposed, each requiring careful consideration in practical application. This review provides a comprehensive survey of decomposition methods, covering classical, probabilistic, and tensor-based approaches and their applications. Furthermore, the review discusses additional methodological considerations essential for the effective use of these techniques. By comparing decomposition algorithms with other widely used techniques in fMRI data analysis, this review highlights their methodological strengths and limitations, and further demonstrates their broad applicability for extracting brain states from fMRI data.

The online version contains supplementary material available at 10.1186/s12938-026-01542-5.