Spectral-Routed Mixture of Experts for High-Fidelity Complex-Field Measurement in Single-Frame Lens-Free On-Chip Microscopy

Single-frame lens-free on-chip microscopy (LFOM) offers a compact and cost-effective solution for biomedical diagnostics and micro/nanoscale inspection, but suffers from severe twin-image artifacts and frequency-dependent degradation due to numerical aperture (NA) limitations. Existing reconstruction methods often neglect the heterogeneous frequency sensitivity of LFOM and fail to explicitly suppress artifacts, leading to suboptimal complex-field measurement quality. To address these challenges, we propose a spectral-expert measurement network (SEMNet) that introduces frequency-aware modeling into single-frame LFOM reconstruction. Specifically, SEMNet transforms captured holograms into polar Fourier space, partitions them into directional subbands, and adaptively routes each subband via a soft top- k gating mechanism to lightweight expert networks specialized for low-frequency (LF), mid-frequency (MF), and high-frequency (HF) restoration. A physics-consistent loss jointly enforces complex-field fidelity, Fresnel-likelihood consistency, twin-image suppression, and spectral load balancing, thereby aligning the reconstruction objective with physical imaging principles. Extensive experiments on 404 high-resolution hologram–complex field pairs from seven types of biological tissues demonstrate that SEMNet improves peak signal-to-noise ratio by up to 1.7 dB over strong single-frame baselines, with statistically significant gains in structural similarity indices (p\lt 0.001). SEMNet restores HF textures while suppressing NA-boundary artifacts. It delivers 47.1 frames/s end-to-end inference with 100\times fewer parameters than a representative CNN baseline and 5\times fewer MACs than a representative Transformer baseline, highlighting a frequency-structured, physics-aligned design for efficient LFOM.