Recurrent Sinusoidal INRs for Efficient High-Fidelity Representation

Researchers Hyunmin Cho, Jaejun Yoo, and Kyong Hwan Jin at Korea University and UNIST propose Harmonic-Siren, a recurrent implicit neural representation that reuses one bias-free sinusoidal block across multiple unrolled steps instead of adding independently parameterized layers. Their harmonic line-spectrum analysis, derived through the Jacobi–Anger expansion, shows that sinusoidal transformations generate integer combinations of learned coordinate frequencies, enabling iterative enrichment of high-frequency content. At optimization step 500, increasing recurrent unrolling from one feed-forward pass to 5 steps raises PSNR from 39.724 dB to 63.378 dB with the parameter count fixed at 593.7K. The model also combines bipolar Gray-coded supervision with cosine alignment, allowing exact quantized reconstruction: on Set5, it reaches 58.16 dB and 0.9997 SSIM after only 100 iterations using 609K parameters. On Kodak24, it reaches 42.84 dB in 6.52 seconds and 59.12 dB in 22.45 seconds, substantially faster than feed-forward baselines. Ablations show that recurrence, rather than binarized supervision alone, supplies the main fidelity gain, improving Kodak24 PSNR from 42.15 dB to 64.19 dB before exact coding reduces bit error to zero. The decoder also transfers to super-resolution, NeRF on LLFF, and signed-distance-function reconstruction, although gains weaken under severe parameter constraints.