Using TotalVariationFilter on dataset with missing data

Question

TotalVariationFilter does not work on a dataset with missing data. Does anybody has a good idea to make it work?

I don't know if first splitting the dataset into parts with no missing data, applying the filter on each part and then gathering them is a good idea?

Thanks for your help?

Answer 1

This is a workaround in some cases. Imagine data:

data = {1, 3, 3, Missing[], 4, 3, 2};

TotalVariationFilter would not work:

TotalVariationFilter[data]

TotalVariationFilter::arg1: Expecting an image or a non-empty real numeric array instead of {1,3,3,Missing[],4,3,2}.

Try the trick:

repairMissing[data_, n_] :=TimeSeries[data, MissingDataMethod -> 
{"Interpolation", InterpolationOrder -> n}]["Values"]

Now this will work:

Grid[{repairMissing[data, 1],
  TotalVariationFilter[repairMissing[data, 1]]}]

Alternatively you could work just simply in TimeSeries format:

{ListLinePlot[data, PlotTheme -> "Business"],
 ListLinePlot[
  TotalVariationFilter[
   TimeSeries[data, 
    MissingDataMethod -> {"Interpolation", InterpolationOrder -> 1}]],
   PlotTheme -> "Business"]}