1. An image processing apparatus comprising: a reduced image generation unit configured to generate a reduced image of an input image; a noise reduction unit configured to generate a first pre-noise reduction image obtained by reducing an impulse noise of the input image, and to generate a second pre-noise reduction image obtained by reducing the impulse noise of the reduced image; a smoothing unit configured to calculate a first smoothed value obtained by smoothing signal levels of a plurality of pixels including a processing target pixel in a local area of the input image, and to calculate a second smoothed value obtained by smoothing signal levels of a plurality of pixels including the processing target pixel in a local area of the reduced image; a feature amount calculation unit configured to calculate a first feature amount representing an edge degree of the processing target pixel using the first pre-noise reduction image, and to calculate a second feature amount representing an edge degree of the processing target pixel using the first pre-noise reduction image or the second pre-noise reduction image; an addition unit configured to weighted-add a signal level of the processing target pixel of the input image and the first smoothed value at a ratio corresponding to the first feature amount in order to output the weighted addition result as a signal level after noise reduction processing of the input image, and to weighted-adds a signal level of the processing target pixel of the reduced image and the second smoothed value at a ratio corresponding to the second feature amount in order to output the weighted addition result as a signal level after noise reduction processing of the reduced image; and a selection unit configured to select and output one of the signal level after noise reduction processing of the input image and the signal level after noise reduction processing of the reduced image according to a variance value of signal levels of the input image or a variance of signal levels of the first pre-noise reduction image of the input image, wherein the addition unit performs the weighted addition such that as a pixel has a feature amount that represents a higher edge degree, a ratio of the smoothed value decreases.