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