  For a triangulated category $\mathcal{T}$, Matsui recently introduced a
topological space $\mathrm{Spec}_\triangle(\mathcal{T})$ which we call the
triangular spectrum of $\mathcal{T}$ as an analog of the Balmer spectrum
introduced by Balmer for a tensor triangulated category. In the present paper,
we use the triangular spectrum to reconstruct a noetherian scheme $X$ from its
perfect derived category $\mathrm{D^{pf}}(X)$. As an application, we give an
alternative proof of the Bondal-Orlov-Ballard reconstruction theorem. Moreover,
we define the structure sheaf on $\mathrm{Spec}_\triangle(\mathcal{T})$ and
compare the triangular spectrum and the Balmer spectrum as ringed spaces.
