New sparsity measure based on energy distribution

Abstract

Sparsity has long been a theoretical and practical signal property in applied mathematics and is utilized as a crucial concept in signal/image processing applications such as compression, source separation, sampling theory, signal recovery, and feature extraction. However, many previously proposed sparsity measures are often application-dependent, in this article, we present a new sparsity measure that is appropriate for all applications. This sparsity measure is called the counter of the sparsity of the components based on energy distribution (CSCE). It is proved mathematically that the CSCE satisfies six criteria that are necessary for the measurement of sparsity. Then, sparsity measures are evaluated using statistical analysis. Accordingly, new statistic metrics named resolution and robustness of sparsity measures are presented for statistical analysis. Finally, we analyze diverse synthetic statistical data and various signals and images for a comprehensive evaluation. The metrics and extensive experimental results have demonstrated the major effectiveness and adequacy of our proposed approach compared with the most common methods in the sparsity measure.