Recently, a theory on local polynomial approximations for
phase-unwrapping algorithms, considering a state space analysis, has
been proposed in Appl. Opt. 56, 29
(2017)APOPAI0003-693510.1364/AO.56.000029. Although this work
is a suitable methodology to deal with relatively low signal to noise
ratios observed in the wrapped phase, the methodology has been
developed only for local-polynomial phase models of order 1. The
resultant proposal is an interesting Kalman filter approach for
estimating the coefficient or state vectors of these local plane
models. Thus, motivated by this approach and simple Bayesian theory,
and considering our previous research on local polynomial models up to
the third order [Appl. Opt. 58, 436
(2019)APOPAI0003-693510.1364/AO.58.000436], we propose an
equivalent methodology based on a simple maximum a posteriori estimation, but considering a different state
space: difference vectors of coefficients for the current high-order
polynomial models. Specific estimations of the covariance matrices for
difference vectors, as well as noise covariance matrices involved with
the correct estimation of coefficient vectors, are proposed and
reconstructions with synthetic and real data are provided.