🚀 go-pugleaf

I'm looking for some feedback on a problem that I am working on.  It
is basically an interpolation problem in which I would like to use
image reconstruction techniques (or anything similar that is relatively
fast and non-interactive, e.g., thin plate splines). The catch is
that I do not have ground truth or an underlying model.

I have data (a soil property) on a non-uniform grid for an area of a
few hectares.  In one direction, the samples are spaced approx. 5-8
meters apart, but in the other, they are spaced approx 20-30
centimeters apart.  [I'm using a sensor and a slow-moving vehicle to
make these measurements. Since the vehicle does not/cannot always travel
in straight lines, I do not have a regular grid.] As far as I know, 
no one has ever sampled soil properties this densely.

Since I have no ground truth, my approach to testing different
interpolation methods is to find some (spatial?) model of the soil
property so that I can
 1. create a pseudo-realistic example surface,
 2. resample (simulating my current sampling process),
 3. use whatever interpolation techniques to reconstruct surfaces,
 4. then compare the errors.

If my example surfaces are the best that I can create, then the "best"
technique should be the one that I use for my real data.

My first thought regarding a model was to find published semivariogram
constants/models for this soil property (hence pseudo-realistic) and
use kriging to create my example surface.  How does this sound?

Since the sampling is so dense, I bawk a little at using the
semivariogram/kriging approach as my underlying model, but this is the
only way that I can think of to use realistic surfaces
in my testing (I assume that there are a few published reports of
semivariogram fitting for the variable that I am interested in).

Why not just use kriging as my interpolation method? Well, I need
something that can be fully automated.  Many folks more knowledgeable
than myself have insisted that semivariogram fitting simply
cannot be automated.

So, does my approach sound good or bad? Could it be improved upon?

FOR THE IMAGE PROCESSING FOLKS:

Does anyone have any references that present an overview of image
reconstruction from irregular sampling? The only ones that I have
found make an assumption of band-limited images. I suppose what I'm
looking for are methods which do not make very strict assumptions like
this.

To be clear, the space that I'm sampling from is not actually
rectangular, but I am hoping that if I pad with zeros or
extend my boundaries, an image reconstruction technique may work (I
hope that there will be no significant edge effects).  

Pixels are real-valued and are from the spatial domain.

Image reconstruction is an area in which I have practically no
experience, so I would be most grateful for any pointers. Email and I
will summarize (to s.i.p if necessary). If anyone wants the refs that
I mentioned above, I have temporarily put them up for anonymous ftp from
pasture.ecn.purdue.edu:/pub/mccauley/misc/recons.irr-samples.band-limited.

Can anyone suggest a better approach to this problem (or make comments
on what I have outlined)?

My apologies for this being sort of lengthy, but I'm afraid that 
bandwidth would be wasted if I did not make myself clear the first
time. This is for my PhD research and I haven't gotten to know too
many people locally that I could bounce these ideas off of (hence
I turn to USENET, which has been very helpful in the past).

Constructive flames appreciated (as long as you teach me something :-)
Thank you,
--
Darrell McCauley                      Dept of Ag Engineering, Purdue Univ
internet: mccauley@ecn.purdue.edu     West Lafayette, Indiana 47907-1146, USA
bitnet: mccauley%ecn@purccvm          UUCP: pur-ee!mccauley

P.S. If any local professors are reading this and find it somewhat
     interesting, get in touch. I'm still looking for one more 
     committee member :-)