2-D interpolation, matrix factorization and applications to signal processing

A method for solving a class of 2-D interpolation problems is presented. The method is not restricted to uniform interpolation points and has the attractive features of recursive computability and permanence of the solution. By combining two different approaches to the problem, the authors obtained the LU decomposition of the interpolation matrix without having to check the nonsingularity of submatrices. This decomposition gives the computational advantage of reducing the original problem to the solution of two triangular systems. The method can be used for the design of 1-D and 2-D FIR (finite-impulse response) filters.<>