  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.
