Before revision:  In this work, we provide the first algorithm using directional persistence diagrams to reconstruct simplicial complexes in arbitrary finite dimension  .
After revision:  In this work, we provide the first algorithm using directional persistence diagrams to reconstruct simplicial complexes in arbitrary finite dimension using an oracle to query for augmented persistence diagrams. In the process, we also describe a discretization of other topological transforms, including the Betti Curve Transform and Euler Characteristic Curve Transform .