1. An image processing apparatus comprising: circuitry configured to: hold a pixel value input thereto; calculate a basic pixel value from pixel values of a plurality of pixels which are neighboring pixels preceding and succeeding a pixel of interest having the pixel value held and which have the same color as the pixel of interest; calculate a different color pixel difference which is a difference between pixel values of neighboring pixels having a color different from the color of the pixel of interest; calculate a same color pixel difference which is a difference between pixel values of neighboring pixels having the same color as the pixel of interest; combine the basic pixel value, the different color pixel difference, and the same color pixel difference to calculate an estimated pixel value of the pixel of interest; and correct the pixel value of the pixel of interest to the estimated value.