Compressive sensing using extropy measures of ranked set sampling

The aim of this paper is to consider the extropy measure of uncertainty proposed by Lad, Sanfilippo and Agro for the problem of compressive sensing. For this purpose, two sampling designs, i.e., simple random sampling (SRS) and a modified version of ranked set sampling, known as maximum ranked set sampling procedure with unequal samples (MRSSU), are utilized and some uncertainty measures such as extropy, cumulative extropy and residual extropy are obtained and compared for these sampling designs. Also, some results of extropy in record ranked set sampling data are developed. Then a study on comparing the behavior of estimators of cumulative extropy in MRSSU and SRS using simulation method is obtained. As an example, two sampling methods MRSSU and SRS are utilized for compressive sensing technique and their performances are compared via signal to noise ratio (SNR), correlation coefficient of reconstructed and the original signal and cumulative extropy measure of uncertainty. The results show that the values of SNR and correlation coefficient for MRSSU are higher than those of SRS. Furthermore, it is shown that MRSSU scheme can efficiently reduce the uncertainty measure of cumulative extropy.