1. A noise-reduction processing device comprising: an edge-strength calculation part that calculates, for each pixel of an input image, an edge strength indicating an edge amount at a pixel of interest on the basis of the pixel of interest and surrounding pixels that surround the pixel of interest; a first direction-discrimination part that discriminates an edge direction at the pixel of interest and that outputs a first direction-discrimination result; a first filter-processing part that subjects the pixel of interest to smoothing processing along a direction that is based on the first direction-discrimination result and that outputs a first filter-processing result; a second filter-processing part that subjects the pixel of interest to smoothing processing producing a lower low-pass effect than that of the first filter-processing part and that outputs a second filter-processing result; and a synthesizing part that synthesizes, according to the edge strength calculated by the edge-strength calculation part, the first filter-processing result and the second filter-processing result, with the ratio of the first filter-processing result increased as the edge strength becomes higher and the ratio of the second filter-processing result increased as the edge strength becomes lower.