If you plan to use this technique frequently you may want to create a few Patterns with different Add Noise-values, so you can use them as Pattern Layers and don’t have to create a new Layer, fill it with 50% gray, etc. each time.
Sorry this isn't personal work so I don't have a before picture. But the solution that c.pfaffenbichler seems to be what I'm looking for. Looks like it can be done with hue/saturation and noise effects? Thank you!