The complex geometry of the Lyman-alpha ($\mathrm{Ly}\alpha$) forest data has motivated the use of various two-point statistics as alternatives to the three-dimensional power spectrum ($P_{3\mathrm{D}}$), which carries cosmological information in Fourier space. On large scales, the three-dimensional correlation function (${\xi }_{3\mathrm{D}}$) has provided robust measurements of the baryon acoustic oscillation scale at 150 Mpc. On smaller scales, the one-dimensional power spectrum, $P_{1\mathrm{D}}(k_{\parallel })$, has been the primary tool for extracting information. At the same time, the cross spectrum, $P_{\times }(\theta ,k_{\parallel })$, has been introduced to incorporate angular information without the complications caused by survey window functions. We propose an analytical forward-modeling framework to reconstruct $P_{3\mathrm{D}}$ from all these observables, based on the mathematical relation between them and $P_{3\mathrm{D}}$. We demonstrate the performance of our method using a hypothetical mock data vector representative of future Dark Energy Spectroscopic Instrument measurements. We show that the monopole of $P_{3\mathrm{D}}$ can be reconstructed in $25k$ bins between $0.07{\mathrm{Mpc}}^{-1}$ and $1.8{\mathrm{Mpc}}^{-1}$, achieving an average precision of ${\sigma }_P/P=13\%$ across the bins. Our method can serve as an intermediary for consistency checks, though it is not intended to replace direct $P_{3\mathrm{D}}$ estimation.

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• Large scale structure of the Universe
• Numerical techniques