Ensuring the authenticity and ownership of digital images is increasingly challenging as modern editing tools enable highly realistic forgeries. Existing image protection systems mainly rely on digital watermarking, which is susceptible to sophisticated digital attacks. To address this limitation, we propose a hybrid optical-digital framework that incorporates physical authentication cues during image formation and preserves them through a learned reconstruction process. At the optical level, a phase mask in the camera aperture produces a Null-space Optical Watermark (NOWA) that lies in the Null Space of the imaging operator and therefore remains invisible in the captured image. Then, a Null-Space Network (NSN) performs measurement-consistent reconstruction that delivers high-quality protected images while preserving the NOWA signature. The proposed design enables tamper localization by projecting the image onto the camera's null space and detecting pixel-level inconsistencies. Our design preserves perceptual quality, resists common degradations such as compression, and establishes a structural security asymmetry: without access to the optical or NSN parameters, adversaries cannot forge the NOWA signature. Experiments with simulations and a prototype camera demonstrate competitive performance in terms of image quality preservation, and tamper localization accuracy compared to state-of-the-art digital watermarking and learning-based authentication methods.

翻译：确保数字图像的真实性与所有权正变得日益困难，因为现代编辑工具能够实现高度逼真的伪造。现有的图像保护系统主要依赖于数字水印技术，而这类技术易受复杂数字攻击的影响。为应对这一局限，我们提出了一种混合光学-数字框架，该框架在图像形成过程中引入物理认证线索，并通过学习式重建过程将其保留。在光学层面，相机孔径中的相位掩模产生一种位于成像算子零空间的零空间光学水印，因此在捕获的图像中保持不可见。随后，一个零空间网络执行测量一致的重建，在保持NOWA签名的同时提供高质量的保护图像。所提出的设计通过将图像投影至相机的零空间并检测像素级不一致性，实现了篡改定位。我们的设计在保持感知质量的同时，能够抵抗压缩等常见退化，并建立了一种结构性安全不对称性：若无法获取光学或NSN参数，攻击者将无法伪造NOWA签名。通过仿真与原型相机的实验表明，相较于最先进的数字水印及基于学习的认证方法，本方法在图像质量保持与篡改定位准确性方面均展现出竞争优势。