PaperlayerView exact revision on arXiv

Source-linked AI summary

Self-Supervised Noise2Noise-Enhanced Denoising for Continuous-Scan Air-Plasma THz Spectroscopy

Adam Umra, Oways Alsoloh, Oliver Nagy, Aydin Sezgin, Clara Saraceno

arXiv:2608.16454v1eess.SPcs.LG

TL;DR

Continuous-scan air-plasma THz-TDS requires averaging noisy traces, increasing measurement time. This paper trains supervised and Noise2Noise residual U-Nets, whose ensemble reaches a trace-reduction factor of approximately 5.4× at K=1.

  • Problem

    Recovering high-quality THz traces from few noisy scans remains difficult because conventional averaging requires additional measurements and supervised denoising needs heavily averaged reference targets.

  • Method

    A compact one-dimensional residual U-Net is trained using reference-supervised and Noise2Noise strategies, with the latter learning from independently acquired noisy trace pairs.

  • Results

    A 5.4× trace-reduction factor at K=1 was achieved by the ensemble, compared with 4.9× for Noise2Noise, 4.6× for the supervised baseline, and 3.2× for Wiener filtering.

  • Takeaways & Limitations

    Self-supervised learning from repeated noisy acquisitions can reduce the number of continuous-scan THz traces required for high-quality reconstruction without clean training targets.

  • Takeaways & Limitations

    The method assumes paired traces share the same waveform with approximately independent, zero-mean noise, and broader validation across samples and acquisition conditions is required.

Abstract

from arXiv · show

Terahertz time-domain spectroscopy (THz-TDS) based on air-plasma generation and balanced air-biased coherent detection offers gap-free broadband coverage, but individual continuous-scan traces are strongly affected by pulse-to-pulse fluctuations and electronic noise. Reaching a useful signal-to-noise ratio therefore requires averaging multiple traces, which directly increases measurement time. We propose a learned denoising approach that recovers high-quality THz waveforms from as few as one complete continuous delay sweep, referred to here as a single-scan trace. A compact one-dimensional residual U-Net is trained using two complementary strategies: a reference-supervised baseline that maps individual noisy traces to long-average reference waveforms, and a Noise2Noise approach that learns from pairs of independently acquired noisy traces without requiring a clean training target. Averaging the predictions of both models reduces systematic bias and yields a trace-reduction factor of approximately $5.4\times$ at $K=1$, meaning that one denoised trace achieves the reconstruction accuracy of averaging approximately five raw traces. The Noise2Noise model alone achieves $4.9\times$, outperforming both the reference-supervised baseline ($4.6\times$) and classical Wiener filtering ($3.2\times$). These results show that self-supervised learning from repeated noisy measurements can support faster continuous-scan THz-TDS without hardware modification.

I. INTRODUCTION

Air-plasma THz-TDS provides broad, gap-free coverage but typically requires many repeated scans to suppress noise, limiting acquisition speed. This work adapts Noise2Noise with a compact residual U-Net to recover high-quality traces from few scans without clean targets.

  • Motivation: Air-plasma THz-TDS enables broad, gap-free spectral coverage and broadband sensitivity without crystalline-media phonon-resonance limitations.Generation and detection occur in ambient gas rather than crystalline media.
  • Problem: Repeated averaging is needed to suppress shot-to-shot fluctuations, electronic noise, timing jitter, and baseline variations, increasing measurement time.The resulting speed limitation affects rapid feedback, repeated measurements, high-throughput screening, and measurements across many sample positions.
  • Method: Noise2Noise trains on pairs of noisy observations from repeated scans of an unchanged sample instead of requiring clean targets.The approach assumes paired traces represent the same physical state with approximately independent, zero-mean noise.
  • Contribution: A compact one-dimensional residual U-Net is evaluated through reference-supervised and Noise2Noise training, alongside raw averaging and Wiener-filter baselines.The evaluation uses a held-out acquisition and quantifies reconstruction with root-mean-square error, signal-to-noise ratio, and an effective trace-reduction factor.

II. THZ GENERATION AND DETECTION

The system combines two-color air-plasma THz generation with balanced air-biased coherent detection for continuous-scan broadband spectroscopy. Air-plasma emission avoids crystal phase-matching limits, while balanced detection preserves signed waveforms and enables shot-to-shot common-mode rejection for single-scan operation.

  • THz generation: Two-color pulses at 800 nm and 400 nm are co-focused in ambient air to generate broadband THz radiation from a plasma filament.The transient photocurrent from the temporally asymmetric driving field radiates the THz pulse.
  • THz generation: Air-plasma emission is not limited by crystal phase matching and provides continuous spectra from the sub-THz range to tens of THz.
  • THz detection: Balanced ABCD detects the THz field through a third-order interaction among the THz transient, optical probe pulse, and static bias field.The detected second-harmonic intensity contains a heterodyne cross-term proportional to the THz field.
  • THz detection: The balanced configuration encodes opposite bias-polarity components in orthogonal polarization channels measured by separate APDs, providing shot-to-shot common-mode rejection without consecutive-shot bias modulation.This detection scheme is essential for single-scan operation and preserves the signed time-domain electric-field waveform.

III. DATASET · A. Acquisitions · B. Preprocessing

The dataset comprises 500 single-scan THz waveforms from three independent continuous-scan acquisitions. Preprocessing removes offsets, corrects scan-direction and polarity effects, extracts aligned waveform windows, and defines long averages as evaluation references.

  • A. Acquisitions: 500 single-scan trace waveforms were collected across three independent acquisitions using the balanced-ABCD continuous-scan system.The first two acquisitions contain N = 200 traces each, while the third contains N = 100 traces.
  • A. Acquisitions: 1.3 µm stage steps correspond to a round-trip sampling increment of ∆t ≈8.67 fs.This increment is defined as ∆t = 2 × 1.3 µm/c.
  • B. Preprocessing: Three preprocessing operations remove per-trace DC offsets, reverse odd-indexed return-sweep traces, and multiply all traces by −1.These steps address slow electronic drift, bidirectional stage motion, and signal-polarity convention, respectively.
  • B. Preprocessing: L = 80 samples (≈ 693 fs) are extracted from every trace around the maximum absolute value in its acquisition’s long-average waveform.The extraction window is centered using the corresponding long-average waveform.
  • B. Preprocessing: The long-average ¯x is computed as the mean of all N preprocessed traces and serves as the reference ground truth for evaluation.Each acquisition has its own long-average reference.
  • B. Preprocessing: All waveform amplitudes are globally normalized by the standard deviation of the training waveforms.Normalization is applied after window extraction and reference construction.

C. Training and Validation Split · IV. NETWORK ARCHITECTURE AND TRAINING · A. One-Dimensional Residual U-Net

The study reserves two 200-trace acquisitions for training and one 100-trace acquisition for validation, while training two independently targeted residual U-Nets whose predictions are averaged at inference. The shared compact architecture processes length-80 traces through a residual encoder–decoder with skip connections and learns waveform corrections.

  • C. Training and Validation Split: 200-trace acquisitions provide training data, while the 100-trace acquisition is held out for validation and its long-average is used only for RMSE and SNR references.The validation long-average is never used during training.
  • IV. NETWORK ARCHITECTURE AND TRAINING: Two independently trained residual U-Nets process the same noisy input: one uses a long-average reference, and the other uses a different noisy trace as its target.The two models’ predictions are averaged during inference to produce the final estimate.
  • A. One-Dimensional Residual U-Net: 80-sample noisy traces enter the shared one-dimensional residual U-Net and produce denoised traces of the same length.Both learned denoisers use the same residual U-Net backbone.
  • A. One-Dimensional Residual U-Net: Three convolutional encoder blocks with stride-2 average pooling reduce the temporal dimension from 80 to 10 while expanding channels from 1→32→64→128.A 128-channel bottleneck operates at length 10, and the decoder mirrors the encoder with nearest-neighbour upsampling.
  • A. One-Dimensional Residual U-Net: Skip connections concatenate corresponding encoder feature maps before decoder blocks, restoring the decoder channel sequence 128→64→32.The supplied passage describes the decoder as mirroring the encoder structure.
  • A. One-Dimensional Residual U-Net: 467 000 approximate parameters implement Conv1d blocks with kernel size 5, same-padding, Group Normalization, GELU activation, and a global residual output connection.The residual connection makes the network learn a correction rather than the full waveform.

B. Training Variants and Objectives

The study compares reference-supervised training against Noise2Noise training for denoising continuous-scan traces. The supervised variant uses long-average targets and combined time-domain and spectral losses, whereas Noise2Noise learns from independent noisy trace pairs using only time-domain MSE.

  • Reference-supervised: Reference-supervised training pairs each noisy trace with its acquisition file’s long-average waveform as the target.Only two distinct target shapes are available, one per training file, limiting the diversity of supervised references.
  • Reference-supervised: The reference-supervised objective combines time-domain mean-squared error with an auxiliary spectral log-magnitude loss.The spectral loss normalizes one-sided DFT magnitudes by the target spectral peak, expresses them in decibels, and applies a −40 dB floor.
  • Noise2Noise: Noise2Noise training uses two independently drawn, distinct traces from the same acquisition file as input–target pairs without a long-average reference.Independent, approximately zero-mean noise makes the conditional expectation of the noisy target equal to the underlying long-average signal, yielding the same MSE fixed point as supervised training.
  • Noise2Noise: Noise2Noise uses only the time-domain loss, with λ = 0, because spectral shaping would amplify noise in its noisy target.The target remains noisy during training, motivating removal of the auxiliary spectral term.

C. Ensemble

The ensemble averages outputs from two models with complementary error characteristics: one anchored to long-average shapes and the other guided by pairwise noise structure. This averaging reduces variance from each model’s individual bias.

  • Variant (a) is anchored to the long-average shapes observed during training.
  • Variant (b) is guided solely by the pairwise noise structure.
  • Averaging both model outputs reduces the variance contribution from each model’s individual bias.

D. Optimization · V. NUMERICAL RESULTS · A. Evaluation Protocol

The denoising variants use matched optimization budgets, while evaluation compares denoised and raw traces by RMSE to a held-out long-average target and reports the equivalent raw-trace requirement.

  • D. Optimization: 2 × 10^-3 initial learning rate is decayed to zero with a cosine schedule for both variants.Both models use the Adam optimizer.
  • D. Optimization: 32 is the batch size used for training both variants.
  • D. Optimization: 400 epochs over 400 traces produce 1.6×10^5 training samples for variant (a).
  • D. Optimization: 4,000 randomly sampled intra-file pairs per epoch for 40 epochs give variant (b) the same total step count as variant (a).
  • A. Evaluation Protocol: 100 held-out traces form the test set, with their long-average x̄ serving as a reconstruction target never observed during training.
  • A. Evaluation Protocol: RMSE to x̄ is averaged over 500 random, without-replacement subsets to assess K-trace estimates formed by averaging K predictions.
  • A. Evaluation Protocol: Keq quantifies the raw traces needed to match the RMSE of K denoised traces.Keq is estimated by log-log interpolation of the raw K-sweep curve.

B. Qualitative Comparison

Qualitatively, both learned denoisers closely reproduce the held-out reference waveform while suppressing the broadband noise evident in a raw single trace. The ensemble performs best overall, with the smallest residual in both time and spectral domains.

  • Waveform and spectral comparison: Both learned denoisers and their ensemble closely reproduce the held-out reference waveform, unlike the raw single trace whose fluctuations obscure the THz pulse shape.Figure 2 compares the reference-supervised, Noise2Noise, and ensemble predictions with a representative raw trace.
  • Waveform and spectral comparison: The raw single trace raises the noise floor by approximately 20 dB across the full bandwidth, whereas denoising substantially improves the spectral appearance.
  • Waveform and spectral comparison: Noise2Noise matches or exceeds the reference-supervised baseline without observing a clean target, while the ensemble reduces error by averaging complementary model biases.
  • Residual-domain comparison: The raw single-trace residual is an order of magnitude larger than any denoised residual, and its spectral error is broadband rather than low-frequency concentrated.
  • Residual-domain comparison: The ensemble achieves the smallest residual in both the time and spectral domains.

C. Few-trace Performance

Few-trace denoising is most effective at low K, where learned methods substantially outperform raw averaging before residual bias floors limit gains. At K=1, the ensemble reaches a trace-reduction factor of approximately 5.4, while Noise2Noise alone reaches 4.9 and outperforms the reference-supervised and Wiener baselines.

  • RMSE behavior: Beyond K ≈10, raw averaging becomes competitive with or superior to denoised estimates that plateau at a fixed RMSE floor.The Wiener filter follows the same trend but has a higher bias floor than the neural methods.
  • Trace-reduction performance: At K = 1, the (a)+(b) ensemble achieves ρ ≈5.4, making one denoised trace equivalent in RMSE to roughly five raw traces.The trace-reduction advantage is strongest at low K and decays toward unity as K grows.
  • Trace-reduction performance: 4.9× is achieved by variant (b), compared with 4.6× for variant (a) and 3.2× for the Wiener filter.Variant (b), the Noise2Noise model, outperforms the reference-supervised baseline despite lacking clean training targets, while Wiener filtering still improves over raw averaging.
  • Evaluation metric: SNR gain quantifies the noise-power improvement of each denoised single trace relative to a raw single trace as 20 log10(RMSEraw/RMSEmethod).Table I reports this metric at K=1.

D. Generalization and Limitations · VI. CONCLUSION

The study demonstrates that learned denoising can reduce continuous-scan air-plasma THz measurements while identifying limits on generalization and Noise2Noise assumptions. An ensemble achieves approximately 5.4× trace reduction at K=1, with strongest gains in the few-trace regime.

  • D. Generalization and Limitations: Generalization is tested on an unseen acquisition, but not on fundamentally different samples, waveforms, or experimental configurations.Only two acquisitions are included in training, limiting represented waveform shapes and measurement conditions.
  • D. Generalization and Limitations: Noise2Noise assumes paired traces share the same underlying waveform and contain approximately independent, zero-mean noise.Violations can cause the model to learn acquisition artifacts as signal.
  • D. Generalization and Limitations: Correlated baseline drift, systematic timing errors, or sample changes between paired scans can invalidate the Noise2Noise assumptions.Such effects may be incorporated into the reconstructed waveform rather than removed.
  • D. Generalization and Limitations: For time-varying measurements, the model may suppress genuine temporal changes that resemble trace-to-trace fluctuations.This limitation follows from distinguishing temporal variation from measurement noise.
  • VI. CONCLUSION: 5.4× trace-reduction factor at K=1 is achieved by an ensemble of supervised residual U-Net and Noise2Noise-trained models.The ensemble substantially reduces the number of continuously scanned traces required for high-quality reconstruction.
  • VI. CONCLUSION: 3.2× trace-reduction factor is obtained by Wiener filtering, while the learned ensemble performs best in the few-trace regime (K ≲4).The comparison highlights the largest gains when only a few traces are available.
  • VI. CONCLUSION: Noise2Noise performs competitively without clean targets, supporting learned single-scan trace denoising from repeated noisy measurements.The conclusion emphasizes reduced measurement requirements without hardware modification.
Loading 2608.16454v1…