1. A noise reduction device that applies noise reduction processing to a pixel value of a notice pixel of a color image by using pixel values of pixels including the notice pixel of a neighboring region, the noise reduction device comprising: a processing device including at least one processor and a memory, the processing device being configured to implement, a representative-value vector calculation unit configured to extract from the neighboring region the pixels of a similarity region having a degree of similarity, greater than or equal to a threshold, to the notice pixel in a predetermined color space and calculates a representative-value vector of the pixels of the similarity region; a difference projection unit configured to project a difference vector between a notice-pixel vector of the notice pixel and the representative-value vector in a specific direction of the color space; and a pixel-value correction unit configured to replace the pixel value of the notice pixel with an element of a vector obtained by adding the difference vector projected in the specific direction to the representative-value vector.