A Novel Complex-Valued Gaussian Measurement Matrix for Image Compressed Sensing

The measurement matrix used influences the performance of image reconstruction in compressed sensing. To enhance the performance of image reconstruction in compressed sensing, two different Gaussian random matrices were orthogonalized via Gram–Schmidt orthogonalization, respectively. Then, one was used as the real part and the other as the imaginary part to construct a complex-valued Gaussian matrix. Furthermore, we sparsified the proposed measurement matrix to reduce the storage space and computation. The experimental results show that the complex-valued Gaussian matrix after orthogonalization has better image reconstruction performance, and the peak signal-to-noise ratio and structural similarity under different compression ratios are better than the real-valued measurement matrix. Moreover, the sparse measurement matrix can effectively reduce the amount of calculation.