A two-dimensional recursive model for bilinear systems with applications to image reconstruction

A recursive model is obtained for two-dimensional shift-variant bilinear systems whose double impulse response is representable by a kth order degenerate sequence. The bilinear system may be quarter-plane or weakly causal. This formulation makes use of the structure of the matrix input-output characterization of the system to arrive at a recursive model. The model is based on a three-point recurrence formula, similar to that of the state-space model for n-dimensional linear shift-variant systems. A recursive algorithm is developed to reconstruct bilinearly degraded images. The advantage of the present model over the direct input-output characterization of bilinear systems is clearly established. The formulation proposed is evaluated using data obtained from real images. >