Noise quality in images is affected by the nature and amplification of sensor signal. This signal is determined by the characteristics of the sensor, particularly the type and construction, such as the pixel pitch (how large the pixels are, not how many) - the smaller the pixel pitch the lesser sensitive the sensor becomes to light, and the lesser the sensitivity the greater the required amplification becomes in environments with less available light. This signal amplification occurs at high ISO values.
Phone sensors have pixel pitches that are small. Even the Lumia 1020 with a huge 41-megapixel sensor has a pixel pitch of just 1.12micrometers (if I remember correctly) which makes it perform terribly at "high" ISO values. For example, no matter how people praise the L1020, the photos at ISO 6400 are simply unacceptable.
You may try shooting at lower ISO values, starting from ISO 100 going up to ISO 400 and so on, and determine which ISO value has acceptable noise performance for you. At ISO 100, you would have the least amount of noise but since the sensor would also be least sensitive that also means you will need longer exposure times (slower shutter speeds) - if you don't have a tripod or very stable hands your photos will all be blurry at this setup. Hence, there is a tradeoff: low ISO, long exposure time - least noise, risk of blurring; high ISO, short exposure time - increased noise, reduced risk of blurring.
Find the balance between ISO value and exposure time (shutter speed) which would give you acceptable noise without blurred images (manually adjust the ISO while leaving exposure time (shutter speed) at auto).
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