Deep learning has transformed computational imaging, but traditional pixel-based representations limit their ability to capture continuous, multiscale details of objects. Here we introduce a novel Local Conditional Neural Fields (LCNF) framework, leveraging a continuous implicit neural representation to address this limitation. LCNF enables flexible object representation and facilitates the reconstruction of multiscale information. We demonstrate the capabilities of LCNF in solving the highly ill-posed inverse problem in Fourier ptychographic microscopy (FPM) with multiplexed measurements, achieving robust, scalable, and generalizable large-scale phase retrieval. Unlike traditional neural fields frameworks, LCNF incorporates a local conditional representation that promotes model generalization, learning multiscale information, and efficient processing of large-scale imaging data. By combining an encoder and a decoder conditioned on a learned latent vector, LCNF achieves versatile continuous-domain super-resolution image reconstruction. We demonstrate accurate reconstruction of wide field-of-view, high-resolution phase images using only a few multiplexed measurements. LCNF robustly captures the continuous object priors and eliminates various phase artifacts, even when it is trained on imperfect datasets. The framework exhibits strong generalization, reconstructing diverse objects even with limited training data. Furthermore, LCNF can be trained on a physics simulator using natural images and successfully applied to experimental measurements on biological samples. Our results highlight the potential of LCNF for solving large-scale inverse problems in computational imaging, with broad applicability in various deep-learning-based techniques.

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