Photo Noise Reducer Pro is a free-for-personal-use app which does exactly what its name suggests: optimise images to reduce any noise.
Tapping either "Light" or "Medium" applies a preset smoothing level, or you can choose "Custom" and use a slider to select whatever intensity you need.
A "Smooth" slider is available to clear away any remaining issues.
Zoom in on an important area with a pinch gesture, and you're able to quickly switch between the original and denoised images to see how they compare.
The app works with images in your gallery, but you can also use the Camera function to take a picture and denoise it right away.
- Minor bug fixes
It's not exactly feature-packed, but Photo Noise Reducer Pro worked well for us, is reasonably configurable, and has no ads or other hassles to get in your way.