I higly recommend this article, if you can get your hands on it: https://www.sciencedirect.com/science/article/pii/S0306261915016311

It presents, among other things, how to implement a measurement matrix for compressive sensing in a hardware system. Disclaimer: this article is a bit difficult to decypher, as are all articles in compressive sensing.

If your measurement matrix size is MxN then use randn(M,N); where i have assumed measurement matrix is normally distributed. u can also use random binary matrix .

Use a Random Gaussian Matrix and orthogonalize it's rows such that

(\phi) * (\phi)T= I . If you are using python you can implement it by importing numpy and giving the following command

np.random.normal (Mean, Standard Deviation, (M,N)). Where N being the dimension after you vectorize the original image matrix.