It is known that the set of digital parabola segments and the set of their least squares parabola fit are in one-to-one correspondence |8|. This enables constant space representation of a digital parabola segment. One of them is a representation of the form $(x_1, n, \alpha, \beta, \gamma)$ where $x_1$ and $n$ are the x-coordinate of the left endpoint and the number of digital points of the segment, respectively, while $\alpha$, $\beta$ and $\gamma$ are the coefficients of the least squares parabola fit $Y=\alpha X^2+\beta X+\gamma$ for the given parabola segment. This paper gives an $O(n \log^2 n)$ algorithm for recovering a given digital parabola segment from its proposed code.