Interpolation based on stationary and adaptive AR(1) modeling

In this paper, we describe a minimal mean square error (MMSE) optimal interpolation filter for discrete random signals. We explicitly derive the interpolation filter for a first-order autoregressive process (AR(1)), and show that the filter depends only on the two adjacent points. The result is extended by developing an algorithm called local AR approximation (LARA), where a random signal is locally estimated as an AR(1) process. Experimental evaluation illustrates that LARA interpolation yields a lower mean square error than other common interpolation techniques, including linear, spline and local polynomial approximation (LPA).