Local Rényi entropy-based Gini index for measuring and optimizing sparse time-frequency distributions

Abstract

This paper introduces a novel localized Gini index (GI) designed for the assessment and optimization of time-frequency distributions (TFDs). This approach employs the localized Rényi entropy (LRE) to quantify the local number of signal components, providing a unique perspective on interpreting time and frequency slice segments while considering the presence of auto-terms or cross-terms. The results demonstrate the effectiveness of the proposed LRE-based GI in overcoming the limitations of conventional concentration and sparsity measures, particularly in scenarios with varying component numbers and missing essential components that may arise during TFD reconstruction using the compressive sensing method. Furthermore, it proves as an efficient objective function in meta-heuristic optimization, ensuring the preservation of auto-terms and a significant enhancement in overall TFD quality. The performance of the proposed LRE-based GI is demonstrated on noisy synthetic and real-life signals.