  We consider the problem of sequential decision making on random fields
corrupted by noise. In this scenario, the decision maker observes a noisy
version of the data, yet judged with respect to the clean data. In particular,
we first consider the problem of sequentially scanning and filtering noisy
random fields. In this case, the sequential filter is given the freedom to
choose the path over which it traverses the random field (e.g., noisy image or
video sequence), thus it is natural to ask what is the best achievable
performance and how sensitive this performance is to the choice of the scan. We
formally define the problem of scanning and filtering, derive a bound on the
best achievable performance and quantify the excess loss occurring when
non-optimal scanners are used, compared to optimal scanning and filtering.
  We then discuss the problem of sequential scanning and prediction of noisy
random fields. This setting is a natural model for applications such as
restoration and coding of noisy images. We formally define the problem of
scanning and prediction of a noisy multidimensional array and relate the
optimal performance to the clean scandictability defined by Merhav and
Weissman. Moreover, bounds on the excess loss due to sub-optimal scans are
derived, and a universal prediction algorithm is suggested.
  This paper is the second part of a two-part paper. The first paper dealt with
sequential decision making on noiseless data arrays, namely, when the decision
maker is judged with respect to the same data array it observes.
