Simultaneous unwrapping and low pass filtering of continuous phase maps based on autoregressive phase model and wrapped Kalman filtering

•Gaussian Markov random field phase model allows noise robust phase unwrapping.•Spatial phase variation can be effectively modelled as autoregressive(AR) process.•The wrapped Kalman filter accurately estimates AR coefficients using wrapped phase.•Reliable phase unwrapping is observed with under-sampled wrapped phases. We propose a simultaneous noise filtering and phase unwrapping algorithm. Spatial evolution of phase is modeled as an autoregressive Gaussian Markov random field. Accordingly, phase value at a pixel is related to phase values at surrounding pixels in a probabilistic manner. The problem of estimation of these probabilities is formulated as state space analysis using the wrapped Kalman filter. Simulation and experimental results demonstrate the practical applicability of the proposed phase unwrapping algorithm.