Images shot at the baseline ISO 100 are noise free.
There are no problems with ISO 200 either.
At ISO 400 there is a minor softening of detail, but overall quality is still very good.
At ISO 800 the softening of detail is more pronounced, but noise is still well controlled.
At ISO 1600 is quite soft and shadow detail has been compromised, but there is little sign of colour noise.
The sea-change occurs at ISO 3200, where the image begins to fall apart.
ISO 6400 is really only for emergencies only.
The following full-size examples show what the J1 is capable of in a real-world situation at higher ISO settings. Click on the images to enlarge.