We build a computer program to reconstruct convex bodies using even Lp surface area measures for p ≥ 1. Firstly, we transform the minimization problem \(\cal{P}_1\) , which is equivalent to solving the even Lp Minkowski problem, into a convex optimization problem \(\cal{P}_4\) with a finite number of constraints. This transformation makes it suitable for computational resolution. Then, we prove that the approximate solutions obtained by solving the problem \(\cal{P}_4\) converge to the theoretical solution when N and k are sufficiently large. Finally, based on the convex optimization problem \(\cal{P}_4\) , we provide an algorithm for reconstructing convex bodies from even Lp surface area measures, and present several examples implemented using MATLAB.
