RECONSTRUCTION PROBLEMS OF CONVEX BODIES FROM EVEN ${L_p}$ SURFACE AREA MEASURES

doi:10.1007/s10473-025-0110-1

Abstract

Abstract: We build a computer program to reconstruct convex bodies using even $L_p$ surface area measures for $p\geq 1.$ Firstly, we transform the minimization problem $\mathcal{P}_1$, which is equivalent to solving the even $L_p$ Minkowski problem, into a convex optimization problem $\mathcal{P}_4$ 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 $\mathcal{P}_4$ converge to the theoretical solution when $N$ and $k$ are sufficiently large. Finally, based on the convex optimization problem $\mathcal{P}_4$, we provide an algorithm for reconstructing convex bodies from even $L_p$ surface area measures, and present several examples implemented using MATLAB.

Key words: reconstruction problem, even $L_p$ surface area measures, spherical harmonic

CLC Number:

52A40

Juewei Hu, Gangsong Leng. RECONSTRUCTION PROBLEMS OF CONVEX BODIES FROM EVEN $ {L_p}$ SURFACE AREA MEASURES[J].Acta mathematica scientia,Series B, 2025, 45(1): 126-142.

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References

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RECONSTRUCTION PROBLEMS OF CONVEX BODIES FROM EVEN $ {L_p}$ SURFACE AREA MEASURES

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