  In this work, we propose an improved approach to reconstruct the
three-dimensional intergalactic medium from observed Lyman-$\alpha$ forest
absorption features. We present our new method, the Optimized Reconstruction
with Constraints on Absorption (ORCA), which outperforms the current baseline
Wiener Filter (WF) when tested on mock Lyman Alpha forest data generated from
hydrodynamical simulations. We find that both reconstructed flux errors and
cosmic web classification improve substantially with ORCA, equivalent to
30-40\% additional sight-lines with the standard WF. We use this method to
identify and classify extremal objects, i.e. voids and (proto)-clusters, and
find improved reconstruction across all summary statistics explored. We apply
ORCA to existing Lyman Alpha forest data from the COSMOS Lyman Alpha Mapping
and Tomography Observations (CLAMATO) Survey and compare it to the WF
reconstruction.
