A descriptive review to sparsity measures

Compressive sensing is a recent data sampling technique with a variety of advantages over the classical Shannon–Nyquist based technique. The main theoretical approach to compressive sensing is based on the informative value of data according to sparsity where the higher sparsity indicates the higher information content. Therefore, while data samples are linearly mixed and sensed by a much smaller number of sensors and result in compressively sensed data of much less volume, the sparsity maximization is a strong approach to retrieving the original higher volume data from the compressed one. The sparsity analysis is the main approach to the idea of compressive sensing, and an efficient measure of sparsity has a key role in this regard. Although k-sparsity is the sparsity measure in use by compressive sensing techniques, it being well established in the theoretical analysis of compressive sensing, there are a variety of sparsity measures. This chapter reviews the sparsity measures from the k-sparsity already in use to be compared with other more complicated sparsity measures.