Comparing Measures of Sparsity

2008/11/28 by Niall P. Hurley, Hurley, Niall P., Scott Rickard +1 · 14 citations
Computer Science · Engineering · Physics and Astronomy · #FOS: Computer and information sciences #Image and Signal Denoising Methods #Information Theory (cs.IT) #Sparse and Compressive Sensing Techniques #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.0811.4706

openalex publication_date 2008/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Sparsity of representations of signals has been shown to be a key concept of fundamental importance in fields such as blind source separation, compression, sampling and signal analysis. The aim of this paper is to compare several commonlyused sparsity measures based on intuitive attributes. Intuitively, a sparse representation is one in which a small number of coefficients contain a large proportion of the energy. In this paper six properties are discussed: (Robin Hood, Scaling, Rising Tide, Cloning, Bill Gates and Babies), each of which a sparsity measure should have. The main contributions of this paper are the proofs and the associated summary table which classify commonly-used sparsity measures based on whether or not they satisfy these six propositions and the corresponding proofs. Only one of these measures satisfies all six: The Gini Index. measures based on whether or not they satisfy these six propositions and the corresponding proofs. Only one of these measures satisfies all six: The Gini Index.

Citations

• Measurement of Inequality of Incomes

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