The detection and analysis of Martian auroras provide critical insights into the planet's atmosphere and magnetosphere. This study presents the first application of an entropy-based method for detecting and analysing nightside martian aurorae, using data from the Emirates Mars Mission's Hope Probe. This novel approach quantifies the complexity of pixel intensity distributions to identify and characterise auroral structures on the martian atmosphere. Compared to traditional techniques, the entropy-based method showed superior sensitivity, effectively detecting subtle aurorae and distinguishing between discrete and diffuse aurorae. This research marks a significant advancement in Martian aurora studies, offering new insights into Mars' atmospheric and magnetospheric dynamics, establishing a methodological framework for future planetary research and highlighting the potential of computational methods in advancing our understanding of planetary phenomena.