Adaptive information-maximization encoding for ghost imaging--A general Bayesian framework under experimental physical constraints
Jianshuo Sun, Chenyu Hu, Zynwang Bo, Zhentao Liu, Mengyu Chen, Longkun Du, Weitao Liu, Shensheng Han
TL;DR
This work addresses how to design information-theoretically optimal encoding for ghost imaging when the scene prior is unknown. It introduces Adaptive Information-Maximization Encoding (AIME), a closed-loop framework that uses Bayesian posterior tracking with a linear forward model $\mathbf{z}=\beta\mathbf{H}\mathbf{x}+\mathbf{n}$ to select the next illumination pattern by maximizing an information criterion, such as mutual information ${\rm I}(z_k,\mathbf{x}|\mathbf{Z}_{k-1})=\frac{1}{2}\log\left(\frac{\beta^2 \mathbf{h}_k^T \hat{\mathbf{P}}_{k-1}\mathbf{h}_k + R_k}{R_k}\right)$ or a CRB-based objective ${\mathcal{L}}_{\rm CRB} = \frac{\mathbf{h}_k^T \hat{\mathbf{P}}_{k-1}^2 \mathbf{h}_k}{\mathbf{h}_k^T \hat{\mathbf{P}}_{k-1} \mathbf{h}_k + R_k/\beta^2}$. Under a total-energy constraint, the optimal encoding reduces to a point-like adaptive scan, while under amplitude constraints it becomes a numerically solvable, coarse-to-fine pattern that concentrates information where the posterior uncertainty is highest. Experimental results show that AIME outperforms fixed point-to-point imaging across sampling ratios and SNRs, with higher PSNR/SSIM and greater information accumulation (mutual and Fisher information) in the measurements, particularly in low-SNR regimes. The framework is general and extensible to nonlinear forward models and higher-dimensional sensing, and it provides a principled link between information-theoretic limits and practical, hardware-constrained computational imaging.
Abstract
Ghost imaging (GI) has demonstrated diverse imaging capabilities enabled by its encoding-decoding-based computational imaging mechanism. Accordingly, information-theoretic studies have emerged as a promising avenue for probing the fundamental performance bounds of of GI and related computational imaging paradigms. However, the design of information-theoretically optimal encoding strategies remains largely unexplored, primarily due to the intractability of the prior probability density function (PDF) of an unknown scene. Here, by leveraging the ability of recursively estimating the PDF of the object to be imaged via Bayesian filtering, we propose to establish an adaptive information-maximization encoding (AIME) design framework. Based on the adaptively estimated posterior PDF from previously acquired measurements, the expected information gain of subsequent detections is evaluated and maximized to design the corresponding encoding patterns in a closed-loop manner. Within this framework, the theoretical form of the information-optimal encoding under representative physical constraints is analytically derived. Corresponding experimental results show that, GI systems employing information-optimal encoding achieve markedly improved imaging performance compared with conventional fixed point-to-point imaging without relying on additional heuristic regularization schemes, particularly in low signal-to-noise ratio regimes. Moreover, the proposed strategy consistently enables significantly enhanced information acquisition capability compared with existing encoding strategies, leading to substantially improved imaging quality. These results establish a principled information-theoretic foundation for optimal encoding design in computational imaging paradigms,provided that the forward model can be accurately characterized.