Hi,
 
I was recently plowing through the docs of the quantreg package by Roger
Koenker and came across the total variation penalty approach to
1-dimensional spline fitting. I googled around a bit and have found some
papers originated in the image processing community, but (apart from
Roger's papers) no paper that would discuss its statistical aspects.
 
I have a couple of questions in this regard:
* Is it more natural to consider the total variation penalty in the
context of quantile regression than in the context of OLS? 
* Could someone please point to a good overview paper on the subject?
Ideally something that compares merits of different penalty functions.
 
Threre seems to be an ongoing effort to generalize this approach to 2d,
but at this time I am more interested in 1-d smoothing.
 
Thanks,
Vadim

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