Comparing Measures of Sparsity

作者：Niall Hurley, Scott Rickard · 发表于：IEEE Transactions on Information Theory · 年份：2009 · DOI：10.1109/tit.2009.2027527 · 被引用次数：777 · 研究领域：Sparse and Compressive Sensing Techniques、Image and Signal Denoising Methods、Blind Source Separation Techniques

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 commonly-used 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. Only two of these measures satisfy all six: the pq-mean with p les 1, q > 1 and the Gini index.