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DEALing with Image Reconstruction: Deep Attentive Least Squares
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Proposes DEAL, an iteratively attentive quadratic (Tikhonov-style) reconstruction method whose learned filters and spatial attention masks are refined over iterations, trained for denoising and applied universally to inverse problems.
Problem
Image reconstruction for inverse problems (denoising, super-resolution, MRI, deblurring) with regularizers that are either complex deep networks or PnP denoisers, which are computationally heavy and lack interpretability and convergence guarantees.
Approach
Replace the LASSO-type attentive refinement of spatially adaptive field-of-experts regularizers with quadratic potentials, so each update is a linear system solved by conjugate gradient; learn filters and a shallow CNN attention mask end-to-end via unrolled deep-equilibrium-style training on denoising, yielding a convergent, interpretable fixed-point reconstruction operator.
Key results
- On BSD68 gray denoising at sigma=25, DEAL reaches 29.16 dB vs 29.18 for Prox-DRUNet and 29.48 for DRUNet, with about 30x fewer parameters than DRUNet.
- On 8-fold multi-coil MRI (PD), DEAL reaches 36.21 dB, the best among compared methods, above Prox-DRUNet's 35.82 dB.
- Color super-resolution at s=2 with lowest noise (2.55) gives DEAL 27.99 dB, outperforming DPIR's 27.79 dB and Prox-DRUNet's 27.88 dB.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DEAL instead of spatially adaptive baselines WCRR, SARR, and SAFI | Image denoising · BSD68 and CBSD68 | PSNR | Helped |
| Use DEAL instead of DRUNet | Image denoising · BSD68 and CBSD68 across the reported noise levels | PSNR | Hurt |
| Use DEAL instead of competing super-resolution methods | Color super-resolution · CBSD68, s=2 and s=3 | PSNR | Mixed |
| Use DEAL instead of the strongest listed baseline | MRI reconstruction · 4-fold single-coil PD and 8-fold multi-coil PD | PSNR | Helped |
| Use DEAL instead of Prox-DRUNet | MRI reconstruction · 4-fold single-coil PDFS | PSNR: 34.92 vs 35.05 | Hurt |
| Use DEAL instead of SAFI | MRI reconstruction · 8-fold multi-coil PDFS | PSNR: 35.32 vs 35.36 | Hurt |
| Use DEAL instead of DPIR | Grayscale deblurring · Set3, reported blur kernels and noise levels | PSNR | Hurt |
| Reduce the DEAL filter count from 128 to 64 (ablation) | DEAL grayscale denoiser · Denoising, σ=25 | PSNR: around 0.1 | Hurt |
| Reduce the DEAL filter count from 128 to 32 (ablation) | DEAL grayscale denoiser · Denoising, σ=25 | PSNR: around 0.15 | Hurt |
| Increase the Multi-Conv filter size beyond 9×9 (ablation) | DEAL · Denoising | PSNR | No clear effect |
| Remove the spline constraints (ablation) | DEAL mask-generation nonlinearities · Image reconstruction | performance | No clear effect |
Surprising findings
- Additional outer iterations do not degrade performance, unlike many PnP methods such as DPIR.
- Reconstruction converges to the same result (in about 10 steps) regardless of initialization in the super-resolution task.
Limitations
- Trained only on denoising; other inverse problems rely on universality without task-specific training.
- Designed only for an l2 data-fidelity term; extensions to other fidelities are left open.
- Does not beat DRUNet-based approaches on denoising; performance on some super-resolution settings is comparable rather than superior.
Experimental setup
Datasets: BSD68 CBSD68 Set3 Set12 fastMRI knee
Benchmarks: BSD68 CBSD68 Set3 deblurring CBSD68 super-resolution fastMRI knee MRI
Metrics: PSNR SSIM
Baselines: BM3D WCRR SARR SAFI DnCNN DRUNet Prox-DRUNet DPIR IRCNN TV PnP-DnCNN EPLL
Builds on: fields-of-experts WCRR SAFI Prox-DRUNet deep equilibrium models
Closest papers by meaning
- End-to-end reconstruction meets data-driven regularization for inverse problems (NeurIPS 2021 · similarity 0.87)
- Normalize Filters! Classical Wisdom for Deep Vision (NeurIPS 2025 · similarity 0.85)
- LMD: Faster Image Reconstruction with Latent Masking Diffusion (AAAI 2024 · similarity 0.85)
- A Restoration Network as an Implicit Prior (ICLR 2024 · similarity 0.85)
- Stochastic Deep Restoration Priors for Imaging Inverse Problems (ICML 2025 · similarity 0.85)
- Image Reconstruction Via Autoencoding Sequential Deep Image Prior (NeurIPS 2024 · similarity 0.85)
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