1. An imaging device comprising: an image sensor that includes an array of pixels that respectively correspond to a plurality of colors; an imaging control section that performs a control process that acquires a captured image while mechanically sequentially shifting a position of an object image on the image sensor by a shift amount that is smaller than a pixel pitch of the image sensor; an image conversion section that calculates luminance values and color difference values based on pixel values of the acquired captured image that respectively correspond to the plurality of colors, and outputs a luminance image formed by the calculated luminance values and a color difference image formed by the calculated color difference values; an estimation calculation section that calculates an estimated luminance value of each pixel of a high-resolution image having a resolution higher than a resolution obtained by the pixel pitch of the image sensor based on the luminance image, and calculates an estimated color difference value of each pixel of the high-resolution image based on the color difference image; and a pixel value conversion section that converts the estimated luminance value and the estimated color difference value into RGB pixel values of each pixel of the high-resolution image, wherein a range that includes a plurality of pixels of the high-resolution image is set to be an addition unit, a pixel value that corresponds to a first addition unit is set to be a first pixel value, a pixel value that corresponds to a second addition unit is set to be a second pixel value, and the first addition unit and the second addition unit overlap each other, wherein the luminance image or the color difference image is input to the estimation calculation section as an input image, wherein the first pixel value and the second pixel value are pixel values obtained by pixel values of the input image, or obtained by interpolation based on the input image, and wherein the estimation calculation section calculates a difference value between the first pixel value and the second pixel value, and calculates the estimated luminance value or the estimated color difference value as an estimated pixel value based on the difference value.