THz-SSDD: Self-Supervised Denoising & Deblurring

• The paper introduces THz-SSDD, a deep network that combines self-supervised learning and PCA-based spectral subspace selection to address frequency-dependent blur and noise in THz-TDS imaging.
• It employs a cascaded U-Net architecture with dedicated denoising and deblurring subnetworks, integrating PSF awareness and instance normalization to preserve spatial details.
• Experimental results show enhanced PSNR and reduced spectral error across materials, demonstrating its potential in accurate defect detection and imaging restoration.

The Terahertz Self-Supervised Denoising and Deblurring Network (THz-SSDD) is a deep neural network framework designed to address the intertwined challenges of frequency-dependent blur and noise in terahertz time-domain spectroscopy (THz-TDS) imaging. It leverages a principled self-supervised training paradigm and principal component analysis (PCA)–based spectral subspace selection to restore amplitude images degraded by diffraction-limited system optics and frequency-dependent noise, without requiring access to ground-truth clean data (Zhu et al., 17 Jan 2026).

1. Frequency-Dependent Degradation in THz Systems

Terahertz imaging systems, particularly those relying on THz-TDS, present coupled degradations that fundamentally limit defect characterization and material identification. The primary sources are:

• Low-frequency blurring: The THz beam exhibits a wavelength-dependent Gaussian point-spread function (PSF), broadening at lower frequencies so that boundaries (e.g., defects or inclusions) appear diffused and spatially unresolved.
• High-frequency noise: Noise intensifies with frequency due to a combination of antenna-induced electromagnetic fluctuations, Poisson (photon-counting) statistics, and electronic/thermal detector noise, empirically described by $\sigma^2(f) = \sigma_0^2 + \beta f^p$.

Classical approaches, such as Wiener filtering, wavelet denoising, and Richardson–Lucy deblurring, act either in the noise or blur regime, often exacerbating artifacts by amplifying noise during deblurring or oversmoothing edges during denoising. The boundary between blur- and noise-dominated frequencies is itself sample-dependent and generally unknown, precluding manual or heuristic solutions with predictable outcomes (Zhu et al., 17 Jan 2026).

2. Network Architecture

THz-SSDD employs a two-stage, cascaded U-Net architecture:

• Denoising subnetwork (net D): A U-Net variant processes spectrally decomposed images, targeting additive noise, and incorporates instance normalization after each convolutional block.
• Deblurring/deconvolution subnetwork (net C): Receives the denoised representation and the system PSF kernel $h_f$ as input, performing learned deconvolution.
• Dataflow: $\text{Input} \to$ [U-Net Denoiser] $$\to \text{denoised } \hat{y} \to [\text{Concatenate with } h_f] \to$$ [U-Net Deblurrer] $\to$ Output $\tilde{y}$.

Each U-Net contains four encoder/decoder levels with $3\times3$ convolutions and LeakyReLU activations. Skip connections are retained to preserve spatial granularity and contextual detail. The deburring subnetwork is explicitly convolution-aware, utilizing explicit PSF knowledge for frequency-adaptive inversion (Zhu et al., 17 Jan 2026).

3. Self-Supervised Learning via Recorrupted-to-Recorrupted (R2R) Strategy

Direct supervised learning with clean targets is infeasible given the absence of artifact-free amplitude THz data. THz-SSDD implements a Recorrupted-to-Recorrupted (R2R) scheme:

• Recorruption process: For a noisy THz observation $y$, two additional noisy versions are synthetically generated:
  • $\tilde{x} = y + D^T n_1$
  • $\tilde{y} = y - D^{-1} n_2$
  • where $n_1, n_2 \sim \mathcal{N}(0, \Sigma_y)$; $\Sigma_y$ captures estimated local variance from $y$.
• Loss function: The network (composed as $f = \text{net C} \circ \text{net D}$) is trained to minimize

$$L(\theta) = \mathbb{E}_{y, n_1, n_2} \left[ \| D(f_D(f_C(\tilde{x}))) - \tilde{x} \|_2^2 + \lambda_1 \| \downarrow((f_C(f_D(y)) * h_f) - \tilde{y}) \|_2^2 + \lambda_2 \|\nabla^2 f_C(f_D(y))\|_1 \right]$$

where $\nabla^2$ is a Laplacian regularizer penalizing high-frequency artifacts, and $\downarrow(\cdot)$ models detector down-sampling.

The key property is invariance of signal statistics under repeated corruption, enabling the network to disambiguate noise from blur without supervised reference (Zhu et al., 17 Jan 2026).

4. PCA-Based Spectral Decomposition and Subspace Reconstruction

Restoration fidelity in THz imaging is constrained by the information content distributed across hundreds of spectral bands. THz-SSDD integrates PCA as follows:

• Spectral cube reshaping: The amplitude cube $X \in \mathbb{R}^{H \times W \times B}$ is reshaped to $Y_{2D} \in \mathbb{R}^{B \times N}$, with $N = HW$.
• Covariance computation: $C = \frac{1}{N-1} \overline{X} \,\overline{X}^T$, $\overline{X}$ mean-centered along frequency.
• Eigendecomposition: Principal vectors $v_i$, eigenvalues $\lambda_i$ ($i=1..B$).
• Subspace selection: The $r$ principal components capturing 95–99% variance are retained, forming projector $E \in \mathbb{R}^{B\times r}$.
• Component-wise restoration: Each principal-component image is denoised and deblurred using the THz-SSDD network.
• Spectral cube reconstruction: $\tilde{X}_{2D} = E\,\tilde{Z} + \mu\,1^T$, then reshaped back to $\mathbb{R}^{H \times W \times B}$.

This strategy ensures computational resources are focused on informative spectral modes while minimizing effort wasted on high-order, noise-dominated components (Zhu et al., 17 Jan 2026).

5. Training Protocol and Experimental Datasets

• Calibration/training: Single unlabeled GFRP laminate plate (80x80x300, 0.1–2 THz) is used under reflection mode; contains six blind holes.
• Test conditions: Unseen sample types (e.g., pyrolyzed spruce woods, HDPE dog-bone specimens under plastic deformation, flax/basalt hybrid laminates post-impact) and measurement modes (reflection/transmission).
• Hyperparameters:
  • Batch size: 16 (principal-component images)
  • Epochs: 200
  • Initial learning rate: $1\times10^{-3}$, halved every 50 epochs
  • Optimizer: Adam ($\beta_1=0.9$, $\beta_2=0.999$)
  • R2R noise matched to empirical calibration (fit for $\sigma_0$, $\beta$, $p$)
• Preprocessing: FFT to amplitude spectra, PCA decomposition; no further augmentation (Zhu et al., 17 Jan 2026).

6. Quantitative and Qualitative Performance

Metric	Result (Representative)
Peak Signal-to-Noise Ratio (PSNR)	GFRP: increased from ~23.5 dB (input) to ~27.1 dB (post-THz-SSDD)
Relative Spectral Error (RSE)	HDPE, composites: $\approx 0.3–0.5$ (i.e., <50% deviation)
HDPE at 1.93 THz	PSNR increased 18 dB $\to$ 26 dB
Qualitative defects (flax/basalt PP, 0.57 THz, 30 J impact)	Impact signatures become visible post-processing

Qualitative results indicate substantial suppression of high-frequency (Gaussian) noise and recovery of sharp edges at defect boundaries, with consistent detail recovery in previously blurred and noisy regimes (Zhu et al., 17 Jan 2026).

7. Limitations and Prospects

• Advantages:
  • Unified denoising/deblurring without separation of spectral regimes or manual tuning.
  • Requires only a small, unlabeled calibration set; no ground-truth need.
  • PCA-enabled subspace focus enhances generalization to new modalities and materials.
  • Physical fidelity preserved as established by RSE analysis.
• Limitations:
  • RSE as high as 0.5 implies moderate spectral distortion, which may limit quantitative spectroscopic analysis.
  • The heuristic nature of principal component retention (targeting 95–99% variance) may necessitate empirical tuning.
  • Some artifact amplification observed at mid-range frequencies in highly absorbing materials.
• Potential extensions:
  • Replacement of classical PCA with autoencoder-based subspace selection for adaptivity.
  • Incorporation of complex-valued networks to leverage full phase/amplitude information inherent in THz-TDS.
  • Application to hyperspectral or 3D tomographic regimes, including nondestructive evaluation of aerospace composites or pharmaceutical layers.
  • Few-shot self-supervised fine-tuning on novel samples (Zhu et al., 17 Jan 2026).

THz-SSDD defines a data-efficient, physically aware restoration pipeline for THz imaging, generalizable across materials and measurement conditions, representing a significant technical advance in the domain of self-supervised restoration for spectral imaging systems.