[SciPy-User] Difference in quality from different interpolation orders

[David Baddeley]

I think it's a really interesting, but also really hard question, and one which 
is going to depend a lot what you're going to use it for.

I suspect that one should nominally do the interpolation by fitting smoothing 
(rather than standard) splines, or use some other type of regularisation 
whenever the data is noisy. At what point this extra work becomes worthwhile, 
however, is moot. A quick google search turned up a several papers on 
interpolation of noisy data, with e.g. Tikhonov regularisation, but the maths 
seems to get pretty torrid pretty quickly. 

My gut instinct is that if you want the most accurate interpolation possible you 
should start with a form/order of interpolation that gives reasonable accuracy 
on noiseless data, and then add some form of smoothness constraint to deal with 
the noise, should you get an unacceptable level of artefacts, rather than 
decreasing the order of interpolation. Of course this comes with a not 
insignificant computational cost and a lot of the time 'good enough' is going to 
be OK.

David


----- Original Message ----
From: Zachary Pincus <zachary.pincus at yale.edu>
To: SciPy Users List <scipy-user at scipy.org>
Sent: Fri, 17 June, 2011 12:52:08 PM
Subject: Re: [SciPy-User] Difference in quality from different interpolation 
orders

> I'd have to disagree with Zach on the making up data count. If you've got 
>microscopy images, you know that the original data is band limited, and can in 
>theory reconstruct it perfectly from your samples (assuming you've satisfied 
>Nyquist).

Right indeed -- thanks for pointing that out! (Modulo, as you mention elsewhere, 
sensor noise...) Is there a good procedure, in a non-theoretical context, to 
determine which order of interpolation is appropriate for the data and noise 
level you have at hand? Or is visual inspection to make sure there's not too 
much ringing from shot noise etc. really the right way to go? I'm curious.

Zach
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