I've been wanting to analyze WMAP data statistically for a while now in order to evaluate the non-Gaussianity of various portions of the WMAP data. Mathematica natively supports FITS files, which are apparently the standard in astronomy. So I have set about working with FITS files from the WMAP mission. It's a lot harder than I expected; the files are massive collections of data points and they are somewhat clumsy to work with. Here is my first several hours of effort on day one:
As you can see, this is not ideal. I had to scale down the notebook on a huge screen to show even the first twenty rows of data from each table (there are tens of thousands of rows and at least 2.5 million data points in each FITS file). Getting from here to generating meaningful statistics and images is going to be pretty rough.
I spoke with one of the creators of HEALPix, Dr. Kristof Gorsky at JPL, and there is some interest in a Mathematica port of HEALPix. Looking at the code, it looks possible but will be a lot of effort. I am wondering if anyone shares my interest in this or if this is going to be a solo project (lol). Thanks.
The easiest (but far from the nicest) solution is to access MATLAB though Mathematica using MATLink.
Otherwise, I think Rohit's suggestion of interfacing with the existing C/C++ libraries using LibraryLink is the way to go. My LTemplate package should make this task easier, and the implementation more compact. It's by no means a small task though, even with LTemplate.
I am very keen to have a Mathematica version of HEALPix. I have written some code, but only a very minor subset of what is in HEALPix.
There is a Matlab version (mealpix) at Penn State. I have looked at it and it could be used as a guide. My impression is that a full working version would take a large investment of time, but would be valuable. Perhaps someone could persuade Wolfram to take it on.
Rather than porting HEALPix to WL, maybe you can use LibraryLink to link to the HEALPix libraries.