1. A pixel interpolation circuit for interpolating a missing pixel in an image, comprising: a plurality of mean preserving interpolation calculation circuits for determining values of candidate interpolation data DI for the missing pixel such that a mean value of a plurality of pixels constituting an inclusive group of pixels including the missing pixel is equal to a mean value of a plurality of pixels constituting a non-inclusive group of pixels not including the missing pixel but being disposed near the missing pixel and having the same number of pixels as the inclusive group of pixels, each mean preserving interpolation calculation circuit also selecting one of the plurality of pixels disposed near the missing pixel as a test pixel T, and determining a value of test interpolation data TD for the test pixel such that a mean value of a plurality of pixels equal in number to the inclusive group and including the test pixel is equal to a mean value of a plurality of pixels equal in number to the non-inclusive group of pixels and not including the test pixel but being disposed near the test pixel; a left-right mean interpolation calculation circuit for determining a mean value of pixels disposed on the left and right of the missing pixel as interpolation candidate data D 0 and determining a mean value of pixels on the left and right of each said test pixel as test interpolation data TD 0 ; wherein mutually differing numbers of pixels k 1 -kn in said inclusive group of pixels and said non-inclusive group of pixels are set in the mean preserving interpolation calculation circuits, which determine a plurality of interpolation candidate data DI 1 -Din and test interpolation data TD 1 -TDn; further comprising a marking circuit for calculating a difference between actual image data of the test pixels and each of the plurality of test interpolation data TD 0 -TDn calculated by the left-right interpolation calculation circuit and the mean preserving interpolation calculation circuits as marking data M 0 -Mn; and an output circuit for outputting the interpolation candidate data calculated by the circuit having minimum marking data, among the left-right mean interpolation calculation circuit and the mean preserving interpolation calculation circuits, as interpolation data IP for the missing pixel.