Remove outliers from a noisy curve

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Allow me to present some images so that I may explain my problem. The images on the left contain a smooth curve surrounded by noise. enter image description here

Is there any approach that would help in eliminating the noise and retrieving the original curve. Please note, this can be any smooth curve (the image on the right) and equation is not known. No prior knowledge of the curve equation is available.

Thanks,

Sau