Thermography time evolution
I've had this post up with no takers so I will just put what I have found so far.

The algorithm that has resulted in the least noise for my application that I have tried is:

Let $X =[x1,x2,....,xn]$ be a sample of a function over discrete time intervals where x is a real number and represents the output of a particular pixel at $\delta t*i$ where $0&lt;i&lt;n$ .

Find a linear function $f$ that best approximates the data in the form (I tried polynomials of varying degrees but a linear function performed the best):

$f(x) = m *x + b$

Evaluate the function at ${t }= {{n*\delta t} \over{2}}$

So $f({{n*\delta t} \over{2}}) \approx Median $ 

My motivation was to find the median but it may be a somewhat bold assertion.  I wanted the median value of each pixel but the chances of picking a pixel due to noise was too great.  Plus because of the physical constraints I know that the data is either decreasing or increasing over the intervals with respect to the phase of data collection.

I do this for both hot and cold images to form the image using the notation above $I=\bar{H} - \bar{C}$.