[rer0tsaz]

I agree that the staircasing effect is definitely the biggest drawback of Total Variation. In the "Smoothed" picture the noise is removed but the results are blocky.

The first way to deal with it is to take into account higher powers of the differences, e.g. using a linear combination p-norms or a Huber function.

The second way is to take into account second order differences. This promotes piecewise affine instead of piecewise constant functions. You can go further and look at third order differences, but the improvement is minimal.

Other than being more complex, the biggest downside is that all of these methods have some new parameter(s) to tune.

[tansey]

> Other than being more complex, the biggest downside is that all of these methods have some new parameter(s) to tune.

They're so fast to run though, that just doing warm-starts and a huge solution path (or grid in the case of additional penalties) with a BIC selection criteria is a pretty decent way to auto-tune the parameters.