Untrained Position-Encoded Multilayer Perceptron Network for Structured Illumination Microscopy Reconstruction.

Structured Illumination Microscopy (SIM) enables super-resolution imaging by encoding high-frequency spatial information through patterned light. While traditional Fourier-based reconstruction methods are prone to artifacts under suboptimal conditions, recent deep learning approaches often require large training datasets and lack adaptability across different imaging setups. In this work, we present Position Encoded Multi-Layer Perceptron (PEM) network that leverages implicit neural representations (INRs) and SIM forward-model-driven modeling to reconstruct super-resolved images without any training data. PEM-SIM represents each spatial coordinate as a combination of sinusoidal functions across multiple frequencies, enabling rich encoding of fine spatial detail. A forward model grounded in SIM image formation principles is then used to iteratively optimize reconstructions by minimizing the structural similarity loss between the generated images and the acquired SIM data. We demonstrate that PEM-SIM reconstructs both 2D and 3D SIM images with fewer input frames than conventional methods and successfully predicts missing axial planes in 3D stacks. The method shows robustness across varying signal-to-noise ratios and performs comparably to standard algorithms on both synthetic and experimental datasets. By eliminating the dependency on large datasets and enabling flexible, high-resolution reconstructions, PEM-SIM offers a data-efficient alternative for super-resolution imaging in microscopy.