1. A color imaging apparatus comprising: a single-plate color imaging element including color filters arranged on a plurality of pixels formed by photoelectric conversion elements arranged in horizontal and vertical directions, the color filters having a color filter array where all colors are periodically arranged in each line in the horizontal and vertical directions; an image acquisition unit that acquires a mosaic image from the color imaging element; weighted average filters with predetermined filter coefficients, wherein a relationship between the colors of the pixels and the filter coefficients in a local area extracted from the mosaic image corresponding to the weighted average filters is set so that proportions of sums of the filter coefficients of each color in the lines in the horizontal and vertical directions are equal; a weighted average calculation unit that calculates weighted average values of each color based on the filter coefficients of the weighted average filters and pixel values of the pixels in the local area extracted from the mosaic image corresponding to the weighted average filters; a demosaicing processing unit that calculates a pixel value of another color at a pixel position of a target pixel of demosaicing processing at a center section of the weighted average filters and that interpolates a pixel value of the target pixel based on a color ratio or a color difference between the calculated weighted average values of the color and the another color of the target pixel to calculate the pixel value of the another color; and a control unit that repeatedly operates the weighted average calculation unit and the demosaicing processing unit while shifting the local area extracted from the mosaic image corresponding to the weighted average filters by a target pixel unit of the demosaicing processing.