I was struggling with the same problem for some time and finally found a very easy solution. Save the date.
x = Column indicator of the matrix
y = Raw indicator of the matrix
v = Look up table matrix
xq, yq = Point where interpolation takes place
vq1 = interp1(x,v',xq,'linear','extrap') % This calculation gives an array which are the interpolated values (wrt xq) of every raw. PS : Don't forget to take the transpose of v matrix.
vq = interp1(y,vq1,yq,'linear','extrap') % This part interpolates the new calculated vq1 for the value yq and gives the final result
Since it is possible to extrapolate by adding ///,'linear','extrap'/// in this method, your task of extrapolating 2d maps will be accomplished. Good by NaNs.