1. A pixel interpolation apparatus, comprising: a weighting interpolation section configured to calculate a pixel value for a missing pixel, as an interpolated pixel value, by a weighting interpolation method using, as reference pixels, pixels located in a neighborhood of the missing pixel in an input image including the missing pixel, and configured to generate a primarily interpolated image signal in which the interpolated pixel value is inserted in a position, in the input image, corresponding to the missing pixel; a frequency decomposition section configured to decompose the primarily interpolated image signal generated by the weighting interpolation section into a plurality of frequency components of a plurality of frequency regions; a halftone dot extraction section configured to calculate a halftone dot degree indicating a degree of probability that a vicinity of the missing dot is located in a halftone dot region, by using a higher frequency component of the plurality of frequency components obtained by the frequency decomposition section; a correction value calculation section configured to calculate a correction value for the interpolated pixel value, by using a low frequency component of the plurality of frequency components; and a correction section configured to correct, according to the halftone dot degree, the interpolated pixel value for the missing pixel of the primarily interpolated image signal so as to generate a corrected image signal, and configured to output the corrected image signal as a result of interpolation.