1. An image processing apparatus that can perform time-sequential weighting addition processing on a moving image constituted by a plurality of frames, the apparatus comprising: a filter unit configured to obtain an image by performing recursive filter processing on a frame image that precedes a present target frame, which is one of the plurality of frames constituting the moving image; a coefficient acquisition unit configured to acquire a weighting coefficient for the present target frame based on a noise statistic of a differential image between an image of the present target frame and the image obtained by the filter unit; and an addition unit configured to perform addition processing on the moving image constituted by the plurality of frames based on the weighting coefficient acquired by the coefficient acquisition unit.