Measurement-Adapted Eigentask Representations for Photon-Limited Optical Readout

End-to-end co-optimization of optical front-ends (e.g. metasurfaces) and neural network back-ends has been widely applied to imaging tasks, yet a formalism characterizing when and why such systems outperform conventional lens-based imaging is largely lacking. This paper focuses on object classification, a central imaging task, and asks when end-to-end optimization of a phase mask for incoherent imaging improves performance over a conventional focusing lens. We find that these gains arise primarily under constrained detector readout and are limited under full detector readout. In the latter setting, we prove that no incoherent phase mask exceeds the ideal-channel mutual information between detector measurements and class labels; a conventional focusing lens approaches this ceiling, and joint optimization yields no empirical gain. When detector readout is constrained -- by coarse spatial sampling or a limited number of measurements -- optimized optics can substantially improve classification by increasing class separability in the detector measurements. These gains are largest under low detector noise and shrink as noise grows, because the optics shape the signal before it reaches the detector but cannot remove noise added afterward. The advantage also depends on the spectral structure of the task: co-design helps most when class-discriminative content is concentrated at lower spatial frequencies than within-class variation. We develop a theoretical framework formalizing these distinctions and test its predictions on synthetic data and standard benchmarks (MNIST, FashionMNIST, SVHN).

We present ENLIGHT, a fast and training free framework for low-light image enhancement based on direct optimization of a perceptual objective. Unlike deep learning approaches that require large scale training data and supervision, ENLIGHT operates in a zero-shot manner by optimizing image quality at inference time. The method employs a two stage global to local optimization strategy. In the first stage, ENLIGHT performs global illumination adjustment to improve visibility while maintaining structural consistency and avoiding excessive noise enhancement. In the second stage, a shadow aware refinement selectively improves low-intensity regions through masked local optimization, enhancing visibility without overexposure. To balance quality and efficiency, we introduce two modes: Fast, which uses a multi-objective formulation combining entropy, gradient preservation, and noise regularization, and Ultrafast, which reduces computational cost via a lightweight approximation of the same objective. The framework is optimizer agnostic and supports both evolutionary and lightweight local search methods. Experiments on BAID, Backlit300, LIME, MEF, NPE, and DICM demonstrate that ENLIGHT achieves competitive perceptual quality (MUSIQ, NIQE, BRISQUE) with significantly lower inference time. Qualitative results further show improved contrast, preserved structural details, and controlled noise amplification, making ENLIGHT a practical and interpretable alternative to learning based methods.

Deep vision models degrade sharply in low-data regimes, particularly in medical imaging where labeled samples are scarce. We show this arises not merely from overfitting but from a geometric failure: finite-sample noise corrupts the embedding covariance, collapsing the eigengap and limiting the number of recoverable signal-bearing modes. We develop a spectral theory of finite-sample representation learning that quantifies the recoverable dimension K(N), the number of eigenmodes that can be stably estimated from N samples. Using perturbation theory and concentration bounds, we show that only modes with eigenvalues above the noise floor $\|\hatΣ - Σ\|_{\mathrm{op}} \sim \sqrt{D/N}$ are reliable, yielding a truncated Mahalanobis energy that governs classification performance. Under a power-law spectral model, this energy can be approximated by a truncated Riemann zeta function, linking eigenvalue decay to data efficiency and AUC. Within this framework, multimodal learning acts as spectral stabilization: vision-language models impose low-rank constraints that suppress noise-dominated directions and preserve the eigengap, increasing K(N) under data scarcity. Across MNIST and multi-disease neuroimaging, we show that multimodal training maintains more stable modes and improves class separation, even when unimodal models achieve comparable few-shot accuracy. These results identify spectral collapse as a fundamental bottleneck in low-data learning. We use truncated Mahalanobis energy and K(N) to diagnose encoder quality, and introduce zeta-based spectral filtering as a principled approach to improve data efficiency.