Bidimensional ensemble entropy: Concepts and application to emphysema lung computerized tomography scans

Bidimensional entropy algorithms provide meaningful quantitative information on image textures. These algorithms have the advantage of relying on well-known one-dimensional entropy measures dedicated to the analysis of time series. However, uni- and bidimensional algorithms require the adjustment of some parameters that influence the obtained results or even findings. To address this, ensemble entropy techniques have recently emerged as a solution for signal analysis, offering greater stability and reduced bias in data patterns during entropy estimation. However, such algorithms have not yet been extended to their two-dimensional forms.

We therefore propose six bidimensional algorithms, namely ensemble sample entropy, ensemble permutation entropy, ensemble dispersion entropy, ensemble distribution entropy, and two versions of ensemble fuzzy entropy based on different models or parameters initialization of an entropy algorithm. These new measures are first tested on synthetic images and further applied to a biomedical dataset.

The results suggest that ensemble techniques are able to detect different levels of image dynamics and their degrees of randomness. These methods lead to more stable entropy values (lower coefficients of variations) for the synthetic data. The results also show that these new measures can obtain up to 92.7% accuracy and 88.4% sensitivity when classifying patients with pulmonary emphysema through a k-nearest neighbors algorithm.

This is a further step towards the potential clinical deployment of bidimensional ensemble approaches to detect different levels of image dynamics and their successful performance on emphysema lung computerized tomography scans. These bidimensional ensemble entropy algorithms have potential to be used in various imaging applications thanks to their ability to distinguish more stable and less biased image patterns compared to their original counterparts.