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Compressive sensing involves 3 main processes: signal sparse representation, linear encoding or measurement collection, and nonlinear decoding or sparse recovery. In the measurement process, a measurement matrix is used to sample only the components that best represent the signal. The choice of the measurement matrix has an important impact on the accuracy and the processing time of the sparse recovery process. Hence, the design of accurate measurement matrices is of vital importance in compressive sensing. Over the last decade, a number of measurement matrices have been proposed. Therefore, a detailed review of these measurement matrices and a comparison of their performances are strongly needed. This paper explains the foundation of compressive sensing and highlights the process of measurement by reviewing the existing measurement matrices. It provides a 3‐level classification and …