MAP signal estimation in noisy sequences of morphologically smooth images

In a recent paper [1], it has been demonstrated that morphological openings and closings can be viewed as Maximum a posteriori (MAP) estimators of morphologically smooth signals in signal-independent i.i.d. noise. In this correspondence, we extend these results to the M-fold independent observation case, and show that the aforementioned estimators are strongly consistent. We also demonstrate the validity of a thresholding conjecture [2] by simulation, and use it to evaluate estimator performance. Taken together, these results can help determine the least upper bound, M̄, on M, which guarantees virtually error-free reconstruction of morphologically smooth images.