Quillwave: Sparse-Sensor Reconstruction of Synthetic Ripple Fields

Ada Placeholder1

1Department of Imaginary Sciences, Example University (fictional)

Research in preparation

Linear interpolation of 64 point sensors loses the wave fronts; Quillwave recovers them. A synthetic test scene.

Abstract

Quillwave reconstructs a full 256x256 ripple field from 64 point sensors. Ripple fields are procedurally generated sums of interfering circular waves: cheap to synthesise, but hard to interpolate, because the wave fronts between sensors are lost by smooth interpolation. Quillwave encodes the sensor readings into a 128-dimensional latent field code and decodes it with a coordinate-based field decoder. On RippleBench-Synthetic, a benchmark of 500 synthetic test fields generated for this work, Quillwave reaches 29.46 dB PSNR and 0.887 SSIM, 5.41 dB above radial-basis interpolation (the best baseline), which is a 71.2% lower mean squared error. It is also 1.36x faster than radial-basis interpolation at inference. All results are on synthetic fields only.

Method

Pipeline: 64 point sensors feed a sensor encoder, which produces a 128-dimensional latent field code; a field decoder takes the code and a pixel position and outputs a value and confidence, forming the 256x256 field.
Figure 1. Quillwave pipeline: the 64 point sensors, the sensor encoder, the 128-dimensional latent field code, the field decoder, and the reconstructed 256x256 field.

The input is 64 point sensors on a regular 8x8 grid. A sensor encoder maps the readings to a 128-dimensional latent field code. A coordinate-based field decoder then predicts the field value, and a confidence, at every pixel. Quillwave-Lite is the ablation without the latent code: its decoder is conditioned on the raw readings. Quillwave has 1.2M parameters and was trained on 2000 synthetic fields for 200 epochs.

Results

On RippleBench-Synthetic (500 synthetic test fields, 64 sensors, 256x256 fields, mean over 5 training runs), Quillwave improves PSNR by 5.41 dB over the best baseline, radial-basis interpolation. That is a 71.2% reduction in mean squared error, and Quillwave runs 1.36x faster than radial-basis interpolation. Linear interpolation is the fastest method. Quillwave has the highest PSNR at every sensor count tested (16, 32, 64 and 128); its margin over radial-basis interpolation is 4.14 dB at 16 sensors, 5.05 dB at 32, 5.41 dB at 64 and 5.23 dB at 128.

Table 1. Reconstruction quality on RippleBench-Synthetic (64 sensors, 256x256 fields, mean over 5 training runs). Higher PSNR and SSIM are better; lower runtime is better.

MethodPSNR (dB)SSIMRuntime (ms)
Linear interpolation21.370.6120.8
Radial-basis interpolation24.050.7016.4
Quillwave-Lite (ablation)27.820.8343.1
Quillwave (ours)29.460.8874.7
Six panels: PSNR and SSIM against number of sensors, runtime per field, an error histogram, per-scene PSNR of Quillwave against radial-basis interpolation, and the validation PSNR training curve.
Figure 2. Results on RippleBench-Synthetic. Top row: (a) PSNR and (b) SSIM against the number of sensors (16, 32, 64, 128), and (c) runtime per field. Bottom row: (d) histogram of absolute per-pixel error, (e) per-scene PSNR of Quillwave against radial-basis interpolation (points above the diagonal favour Quillwave), and (f) validation PSNR during training.

Qualitative Comparison

Four test scenes in rows. Columns: sensor map, linear interpolation, radial-basis interpolation, Quillwave and ground truth. The Quillwave column closely matches the ground truth; the interpolations are blurred.
Figure 3. Qualitative comparison on four test scenes. Columns, left to right: sensor map, linear interpolation, radial-basis interpolation, Quillwave (ours), ground truth. The wave fronts in the Quillwave column stay sharp.

Comparison Loops

Second test scene: linear interpolation of the 64 sensors, and Quillwave.
Third test scene: linear interpolation of the 64 sensors, and Quillwave.

Limitations

  • Baselines are not compute-matched. Quillwave is trained for 3.5 GPU-hours, while the interpolation baselines need no training at all.
  • Synthetic fields only. Every result is on RippleBench-Synthetic; no real sensor data was used, and behaviour on real measurements is unknown.
  • Confidence is not calibration. The per-pixel confidence map that Quillwave outputs has not been checked against observed error rates, so it should not be read as a calibrated probability.

BibTeX

@misc{placeholder2026quillwave,
  title  = {Quillwave: Sparse-Sensor Reconstruction of Synthetic Ripple Fields},
  author = {Ada Placeholder},
  year   = {2026},
  note   = {Research in preparation. Fictional entry for testing}
}