There are several ways we can try to improve the
result seen in the left panel of Figure 5.
We can think of smoothing the paths through the
score matrix. We can also make some reasonable
*a priori* assumptions.
We can add to our similarity matrix.
We might put large weights in the matrix by saying
that
time 0 should be the same in the PP and PS section or
by visually matching a single reflector.
These approaches improve our result, but still lead
to something less than ideal.

A better solution is to return to a more generic
form of dynamic programming.
We can improve our 1-D estimates by remembering
that what we are really doing is estimating a ratio. This ratio has to be a continuous function of time, as a result
it is not reasonable to have large gaps in our trace alignment.
First, if we consider the traces to be samples in a PP gather,
we can assume that the our alignment function will be single
valued. As a result, we can make our series of decisions one
PP time element at a time. Changing our decision definition
takes away the nice feature of the NW algorithm that we only
have to consider three states at each decision. On the other hand, we can
limit ourselves to considering the subset of states that correspond
to a reasonable path. We know that each PP sample
must correspond to the previous PP sample +*x*, where *x* is a very
small number. As a result, we again need to only consider two to
four states at each decision.
The right panel of Figure 5 shows the result of applying this
dynamic programming concept, along with the constraints
discussed above, to the Alba alignment problem.
Note how the solution is better than the result
shown in the left panel of Figure 5, but
still could be improved.

5/23/2004