Combustion chamber imaging

I need to use Matlab to implement a numerical method that will calculate flight times of waves emitted across a chamber containing a user specified temperature distribution. I then need to use these flight times and the knowledge that the waves (sound) increase proportionally with temperature, to reconstruct an image of that temperature field. Assuming the chamber is cylindrical, I am looking at a 2-d circular slice of the chamber at any point, for which I have an integral involving the temperature distribution T(r), and a radial coordiante r along a line y=constant, where y=constant, represents the path of the wave across the circle from a source to a receiver. The integral, with limits y and 1, returns a time of flight in seconds from source to receiver. Given that the centre of the circle is at the origin on a set of axes, I assume that I need to initially instruct matlab to run the integral for a variety of lines y=constant, but doing this and trying to understand how to then go from flight times to a temperature reconstruction is confusing me! I have access to the PDE Toolbox but haven't used it thoroughly before, also Image toolboxes.

[Image Analyst]

Do you already have your 2D cross sectional temperature image? Do you have that cross sectional image at different time points already?

[Daniel]

No, I'm struggling to produce the cross sectional images for the distributions, I don't know the best way to approach this I'm afraid