Photon-starved imaging through turbulence at the diffraction limit

Ground-based imaging systems struggle to achieve diffraction-limited resolution when atmospheric turbulence and photon scarcity act simultaneously. In this regime, conventional adaptive optics, speckle imaging, and blind deconvolution lack sufficient information diversity to reliably estimate either the scene or the turbulence. We present Turbulence Aware Poisson Blind Deconvolution (TAP-BD), a framework designed for robust image recovery in these extreme conditions. TAP-BD extracts more information from coded-detection through phase diversity and decodes it with a physics-informed optimization that incorporates low photon Poisson statistics. Experiments show that TAP-BD provides reliable reconstructions of both scene and turbulence using only a few tens of measurements, even under strong aberrations and photon-starved conditions where existing methods fail. This capability enables photon-efficient, turbulence resilient imaging for applications such as space situational awareness and long-range remote sensing.

💡 Research Summary

The paper “Photon-starved imaging through turbulence at the diffraction limit” addresses a critical challenge in ground-based optical imaging: achieving diffraction-limited resolution when atmospheric turbulence and photon scarcity occur simultaneously. In this extreme regime, conventional methods like adaptive optics, speckle imaging, and standard blind deconvolution fail due to insufficient information diversity for reliable estimation of either the scene or the turbulence.

The authors introduce a novel hardware-software co-design framework named Turbulence Aware Poisson Blind Deconvolution (TAP-BD). The hardware component employs a spatial light modulator (SLM) to sequentially impose a set of known phase diversity patterns onto the distorted wavefront from the target. This optical encoding step creates multiple coded intensity measurements, where each frame contains complementary information about both the object and the turbulence, thereby enriching the overall information content from a limited photon budget.

The software reconstruction pipeline consists of two main stages. First, a dedicated Plug-and-Play (PnP) Poisson denoiser is applied to the raw measurements to suppress the dominant shot noise in photon-starved conditions, stabilizing the subsequent inverse problem. Second, a physics-informed optimization algorithm performs the joint estimation. The core innovation here is the decomposition of the severely ill-posed global problem into two tractable, physically aligned sub-problems: 1) Blind Deconvolution to estimate the object intensity and an intermediate set of Point Spread Functions (PSFs), and 2) Wave Propagation (Phase Retrieval) to estimate the underlying turbulence phase from those PSFs. These sub-problems are solved iteratively within an Alternating Direction Method of Multipliers (ADMM) framework. Crucially, each sub-problem is formulated to admit efficient closed-form or proximal updates in the Fourier domain, leading to high computational efficiency with a per-iteration cost of O(N log N).

Through comprehensive simulations, the paper demonstrates TAP-BD’s superior performance. Compared to direct imaging (a baseline without phase diversity), TAP-BD consistently achieves higher Peak Signal-to-Noise Ratio (PSNR) and lower phase Root-Mean-Square Error (RMSE), closely approaching the theoretical Cramér-Rao Lower Bound (CRLB). This indicates that the algorithm effectively leverages the additional information provided by the coded hardware. In comparisons with NeuWS, a notable neural network-based benchmark, TAP-BD shows remarkable robustness and data efficiency. While NeuWS performs well with abundant measurements, its performance degrades sharply under strong turbulence with only a few tens of measurements, often producing oversmoothed or degenerate solutions. TAP-BD, constrained by its explicit physical model, delivers reliable and high-fidelity reconstructions of both the scene and the turbulence phase even in these information-starved regimes. Furthermore, TAP-BD offers a significant computational advantage, being up to 57 times faster than NeuWS in some scenarios.

In conclusion, TAP-BD presents a robust and efficient solution for photon-efficient, turbulence-resilient imaging. Its success hinges on the synergistic combination of optical information multiplexing via phase diversity and a computationally stable, physics-based inversion algorithm. This work enables new capabilities for applications such as space situational awareness and long-range remote sensing, where targets are faint and atmospheric conditions are severe.