Extract trajectory from recurrence plot

Question

Let's say I have a time series in a vector $v$, and I compute its recurrence(-like) plot $R(i,j)=\left \| v(i)-v(j) \right \|$.

Is there any standard way of extracting $v$ knowing only $R(i,j)$ ??

See wikipedia page https://en.wikipedia.org/wiki/Recurrence_plot for examples of what I mean. In the main figure there are four examples of 1D signals converted to recurrence plot.

Many thanks!

Answer 1

It isn’t possible to recover v from its recurrence plot. The recurrence plot doesn’t retain enough information about v, because two vectors can have the same recurrence plot.