You did not attach your image. The best way to remove noise it to use more light. Then you can use a longer integration time (fewer frames per second so it collects more light). You can also play with the gamma of the camera. Sometimes there is glare, haze, reflection of the lens or iris, etc. and the best way to get rid of those is adjust the geometry of your lighting and camera. Sometimes you have specular reflections off shiny things in your image and the best way to get rid of those is to use a polarizer in front of your light source and a polarizer at crossed angles in front of your camera. And of course another way is to simply get a better webcam. These are all ways to prevent noise from getting into your photo in the first place. It's much much better to do that than to try to remove the noise once it has gotten into your image and destroyed your pixel values.
Now I suspect you're going to say that you don't want to, or can't, do anything to prevent corruption of your image, though I hope not. You can remove noise in images with a variety of noise reduction algorithms. They range from the simple conv2(), imfilter(), and medfilt2(), to better methods like bilateral filters, KNN filters, morphological filters, mean shift filters, guidedfilter(), to the best but much more complicated filters like BM3D, K-LLD, UINTA, etc. I'd suggest you start very very simple with medfilt2() (a 2D median filter) and see how well that works.
Professor Milanfar (now at Google and The University of California, Santa Cruz https://users.soe.ucsc.edu/~milanfar/publications/, previously at Stanford University) seems to always be at the forefront of noise reduction algorithms, prolifically developing state of the art denoising algorithms.
