Optimal Kronecker product approximation of block Toeplitz matrices (Q2706248)

The problem is to find \((n,n)\)-matrices \(A_k, B_k\) that minimize \(\|T-\sum A_k\otimes B_k\|_F\), where \(\otimes\) denotes the Kronecker product and \(T\) is a banded \((n,n)\)-block Toeplitz matrix with banded \((n,n)\)-Toeplitz blocks. It is proved that the optimal matrices are banded Toeplitz matrices, and an efficient approximative method is given. Application to an image restoration problem from the Hubble space telescope illustrates the effectiveness of the method.