On a Direct Approach for the Solution of Linear Space-Invariant 2-D Differential Convolution Models

Abstract

2-D differential convolution operators in a rectangular discrete domain are modelled as linear differential matrix equations of the form Х(t) = Σ A_jX(t)B_i + F(t), where the coefficient matrices A_i ∈ IR(MxM),B_i ∈ IR(NxN) and F(t) ∈ IR(MxN) is a piecewise continuous function matrix of t. Under some periodicity assumptions an analytical solution method is presented making use of the 2-D discrete Fourier transform (DFT). For most general problems an iterative computational method founded in the Peano-Baker series is proposed.