1. A resolution estimating device which estimates a resolution of an original image of an input image, the original image being an image before a scaling-up process, the device comprising: a proximity-degree acquiring circuit that sets an estimated proximity degree of each target pixel in such a manner that, as a pixel position of the target pixel is assumed to be closer to a pixel position at which a pixel in the original image is disposed when the original image is scaled up, the estimated proximity degree is set larger; an accumulation circuit that accumulates the estimated proximity degrees of the target pixels in a second direction orthogonal to a first direction on the image, and that obtains a one-dimensional data sequence of the accumulated estimated-proximity-degree values; a frequency transform circuit that performs a frequency transform on the one-dimensional data sequence of the accumulated estimated-proximity-degree values obtained by the accumulation circuit, and that obtains a one-dimensional frequency-component data sequence which is a one-dimensional data sequence for frequency regions; a spectrum analyzing circuit that detects periodicity in the first direction on an image of the estimated proximity degrees on the basis of the one-dimensional frequency-component data sequence obtained by the frequency transform circuit, and that estimates the resolution of the original image of the input image on the basis of the detected periodicity, the original image being the image before the scaling-up process; and an image processing circuit that adjusts a scaling-up factor according to the resolution of the original image and processes the input image with respect to the scaling-up factor to generate an output image.