Using Toeplitz Matrices to obtain 2D convolution

Optimising the discrete convolution operations is important due to the fast growing interest and successful applications of deep learning to various fields and industries. In response to that, we propose an algorithm that views the 2D convolution operation between matrices as a matrix multiplication that involves a Toeplitz matrix; our algorithm is based on the mathematical result that we prove. We will present the complexity of the resulting algorithm and benchmark it against other 2D convolution algorithms in known Python computational libraries. The current implementations of our algorithm suggest a potential speed-up of convolution operation if the sparsity of the Toeplitz matrix was utilised.