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 decomposition unit configured to generate decomposed image data of a plurality of different frequency bands; a filter unit configured to obtain an image by performing recursive filter processing on a preceding frame that precedes a present target frame of the decomposed image data, which is one of the plurality of frames of the decomposed image data constituting the moving image; a coefficient acquisition unit configured to acquire a weighting coefficient for the present target frame of the decomposed image data based on a noise statistic of a differential image data between an image of the present target frame of the decomposed image data and the image of the preceding frame of the decomposed image data obtained by the filter unit in different frequency bands; and a reconstruction unit configured to reconstruct image data of a plurality of different frequency bands, wherein the filter unit adds the present target frame of the decomposed image data with the weighting coefficient acquired by the coefficient acquisition unit to the preceding frame of the decomposed image data.