I am not absolutely sure that I understand your conclusion entirely, but if you are saying that there is no metric to measure the accuracy of a noise detection algorithm then you might be correct. We generally evaluate an algorithm using restoration quality (SSIM, PSNR, etc.). If you are saying noise detection algorithm requires some thresholding that is not always correct. We have several types of noises and many optimization algorithms that do not require any threshold at detection stage; some of them even do not have any separate detection step ( they may have other tunable parameters though). Other experts of RG who are working on restoration may give you more information.

I fully agree with Saumik; as I may add the following: Sometimes "thresholding procedure" may be used as a part of any suggested technique in order to achieve noise detection or image filtering "de-noise an image". In such cases, the used technique is mostly applied to solve special problem in a special domain considering a limited number of special constraints. These types of solutions are not always robust, and we can't generalize it to solve other problems.

saumik and abdellatif there are parameters for detection stage efficiency like accuracy of detection and percussion we can also Calculate it in terms of true positive and false positive etc but not generally used . the other adjustable parameters that you are referring is key and or difference etc their values are again use to compare and take decision, means the key or difference etc are acting like threshold value for respective algorithm. Again my question stands where ever threshold will be considered over detection or under detection will also exist. if you have some knowledge of such algorithms which are not using just think can you share the paper name or links so i can update my self.