Performance Evaluation of Measurement Matrices in Compressed Sensing

This paper presents a performance comparison of various measurement matrices used in compressed sensing along with its reconstruction techniques. A measurement matrix is used to represent the significant parts of the original signal during the measurement process. The design of an optimal measurement matrix is a major challenge in the compressed sensing reconstruction process. Also its selection has a major influence on accuracy and processing time for image reconstruction. Although, in the last few decades, several measurement matrices have been explored and utilized. However, further characteristics exploration, as well as performance comparison, can provide options for a better solution. This paper presents the theory of compressive sensing along with reconstruction techniques using various modified measurement matrices and their impact on overall performance. This paper compare the performance of measurement matrices belonging to four different types using five evaluation parameters such as the recovery error, image quality through PSNR value, the structural similarity index, and mean structural similarity index of the image. Also the theoretical comparative results are validated with simulation results. It has been observed that the modified Toeplitz, and Hadamard matrices show better performance than the other measurement matrices.