[Python] Improving speed and robustnes for opencv HoughCircles for only single circle

There are many threads on how to detect multiple circles via OpenCV's HoughCircles function, and I understand that this is a complex task with no single good answer. However, maybe someone can give some hints for parameters for the specific problem of only finding a single circle. I also want to only get an answer when the algorithm is sure enough, so no 'maybe', please. The data sometimes has a background of 100-150 (out of 255) with the signal peaking all the way to >200 for most of the time. Does the function handle offsets well or would it be worth to spend some time to remove the background?

My current code:

im8blur = cv2.blur(im8, (n, n))


or

im8blur = cv2.GaussianBlur(im8, (n,n), cv2.BORDER_DEFAULT)


with n in the range of 3-10 for the first case or >30 for the second case.

Then, with these parameters, the results are best, but it takes >20 minutes for 140 images...

detected_circles = cv2.HoughCircles(im8blur,
cv2.HOUGH_GRADIENT, 1,
minDist = 2000,
param1 = 14,
param2 = 4,
minRadius = 400,
maxRadius = 600)


My circles are all around 520px in radius, but setting the minRadius to 500 or setting the maxRadius to -1 yielded worse results.

For my 1400x1400 pictures, I picked a 2000 minDist to ensure only one circle to be found.

However, I still get mixed results. Only when it is super clear, I get a good fit, but most of the time a circle is places somewhere.

For the case of only one circle, there must be a better solution...?

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