1. A recursive noise reduction device for reducing noise in a present image represented by a present image signal, comprising: a memory unit to store a previous image having a correlation with the present image and represented by a previous image signal; a calculating unit to recursively calculate a sum of a coefficient K times the present image signal and (1-K) times the previous image signal, the value of K being in the range from 0 to 1; and a movement detection unit to detect movement in the present image, and in response, generating a movement detection signal; said calculating unit continuously decreasing the value of K corresponding to a number of times said calculating unit calculates the sum, and changing the value of K based upon the movement detection signal.