You clearly know what you're about but you haven't mentioned using thresholding, in particular have you tried applying a global threshold using Otsu to calculate the right level, then finding contours and selecting the largest ?
[Edit to clarify]
Global threshold obviously won't work due to the visible graident across the image.
I had a quick play with this and find that if you break the image into 6 chunks (2 rows of 3 columns equal sized) , then perform thresholding using Otsu on each one and then reassemble, it does a pretty god job at cleaning up the image.
There are still some minor artifacts on the upper right portion of the star.
It occurs to me that since the object has straight line boundaries, you might want to consider a Hough transform to extract these edges, intersect them to locate vertices and use the result as your object contour.
