1. An image processor comprising: a high-frequency component detecting unit that detects high frequency components contained in image data by calculating a convolution for a pixel group of the image data, to output the detection result; a smoothing unit that smoothes the image data, to output the smoothed image data, wherein the smoothing unit generates the smoothed image data for each of pixels of interest in an image region of the image data from data of pixels contained in a region to be smoothed that is composed of one of the pixels of interest and pixels around the pixel of interest and wherein the number of pixels in the region to be smoothed is set smaller than that of pixels in the pixel group to be calculated; and an image data processing unit that combines the image data with the smoothed image data at a combination ratio determined from the detection result, to output the combined image data.