An Optimization Method for Measurement Matrix Based on Eigenvalue Decomposition

Measurement matrix is a very important part in compressive sensing. In order to decrease the mutual coherence between the measurement matrix and sparse transformed matrix and improve the quality of reconstruction, a Gram matrix was constructed based on the product of the measurement matrix and sparse transformed matrix. Then a new global mutual coherent coefficient was defined based on offdiagonal elements of the Gram matrix. After deriving the relationship between the global mutual coherent coefficient and the eigenvalues of the Gram matrix, we proposed an optimization model, which could minimize the global mutual coherent coefficient of the given matrices by adjusting the eigenvalues above zero to the average value of the sum of these eigenvalues without changing the sum. The speed of optimizing matrix is fast and the PSNR of the picture is improved with the optimized measurement matrix from the experimental results. These showed that our proposed method had some advantages in terms of reconstruction effect and optimization speed.