1. A video signal processing apparatus, comprising: an enhancement gain generating section configured to obtain an enhancement gain for each pixel based on a luminance signal forming part of an input video signal and a predetermined enhancement gain; and an enhancing section configured to perform a process of enhancing the luminance signal forming part of the input video signal based on the enhancement gain for each pixel obtained by the enhancement gain generating section, wherein the enhancement gain generating section includes a mean deviation calculating portion configured to obtain a mean deviation of luminance values of a plurality of pixels included in a predetermined region centered at a pixel of interest that is the pixel for which the enhancement gain is to be obtained, a weighting coefficient generating portion configured to generate a weighting coefficient for the pixel of interest according to the value of the mean deviation calculated by the mean deviation calculating portion, and a multiplication portion that multiplies the predetermined enhancement gain by the weighting coefficient generated by the weighting coefficient generating portion to obtain the enhancement gain for the pixel of interest.