A Non-Hermitian Biorthogonal Encoding Paradigm for Physical-Layer Secure Computational Imaging

Abstract

The conventional paradigm of computational imaging, rooted in Hermitian systems, is fundamentally constrained by rigid orthogonal basis transformations, which bottleneck the balance between reconstruction fidelity, computational load, and physical-layer security. In this work, we propose a generalized secure computational imaging framework based on non-Hermitian biorthogonal symmetry breaking. By mapping spatial information into a biorthogonal operator space, we establish an asymmetric sensing architecture governed by distinct left-basis $\langleϕ_{m}\vert{}$ and right-basis $\vert{}ψ_{n}\rangle$ modes, satisfying the biorthogonality relation $\langleϕ_{m}\vert{}ψ_{n}\rangle = δ_{mn}$. Within this manifold, precise tuning of the non-Hermitian parameter $γ$ establishes a physical-layer cryptographic gate, where high-fidelity retrieval is exclusively enabled by matching the dual basis; any parameter mismatch triggers deterministic inter-modal crosstalk that effectively neutralizes unauthorized access. Notably, this architecture intrinsically supports direct, iteration-free image retrieval across a wide range of sampling ratios, significantly reducing the computational overhead compared to conventional iterative reconstruction. We validate this framework on a single-pixel imaging platform, demonstrating a fundamental paradigm shift: by embedding security directly into the measurement physics, we transform image retrieval from a software-dependent task into a parameter-sensitive physical decryption process that ensures architecture-intrinsic confidentiality.