how to detect center of a blurry circle with opencv
You'll need to improve the contrast of the image first, then filter it strongly to remove the noise. since the circles are 'thick' (blurry), you can filter quite a bit without destroying the circles structure. 

I would then apply some edge detection algorithm to get a binary edge image that can be processed by the Circular Hough Transform.

I get the following edge image from your image:


Using the following MATLAB commands:

 % x is the input grayscale image. First we adaptively improve the contrast over the image
 y= adapthisteq(x);

 % next we use the Canny edge detector with a strong Gaussian lowpass filter
 ee=edge(y, 'canny', [], 5);