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QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstruction
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Proposes QN-Mixer, a second-order unrolled network for sparse-view CT that combines a latent BFGS update (inverse Hessian on downsampled gradients) with a learned Incept-Mixer regularizer, outperforming first-order unrolling and post-processing baselines on AAPM and DeepLesion.
Problem
Sparse-view CT reconstruction is ill-posed; post-processing and first-order unrolling networks struggle with ultra-sparse views, long-range dependencies, slow convergence, and high computational cost.
Approach
Unroll a quasi-Newton (BFGS) optimizer whose inverse Hessian is maintained in a learned latent space of encoded gradients (memory-efficient latent BFGS), with a non-local Incept-Mixer (inception + MLP-Mixer) as the learned gradient of the regularizer.
Key results
- On AAPM with no noise at nv=32, QN-Mixer reaches 39.51 dB PSNR / 96.11% SSIM versus 38.71 / 95.42 for RegFormer.
- On DeepLesion, QN-Mixer outperforms RegFormer by an average of +2.23 dB PSNR and +1.02% SSIM across nv=32/64/128.
- QN-Mixer uses 14 unrolling iterations versus 30 for LEARN and 18 for RegFormer, with 7.83 GB memory vs 10.19 GB for RegFormer.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use QN-Mixer instead of RegFormer | Sparse-view CT reconstruction · DeepLesion, 32, 64, and 128 views | PSNR (dB): 37.38 -> 39.39; 41.70 -> 43.75; 46.10 -> 48.62 | Helped |
| use QN-Mixer instead of RegFormer | Sparse-view CT reconstruction · DeepLesion, 32, 64, and 128 views | SSIM (%): 93.89 -> 95.67; 96.78 -> 97.73; 98.39 -> 98.64 | Helped |
| use QN-Mixer instead of RegFormer | Sparse-view CT reconstruction · AAPM, 32 views, no noise | PSNR (dB): 38.71 -> 39.51 | Helped |
| use QN-Mixer instead of RegFormer | Sparse-view CT reconstruction · AAPM, 32 views, low noise (N1) | PSNR (dB): 37.21 -> 37.50 | Helped |
| use QN-Mixer instead of RegFormer | Sparse-view CT reconstruction · AAPM, 32 views, high noise (N2) | PSNR (dB): 35.93 -> 35.91 | Hurt |
| increase the inverse Hessian approximation size (ablation) | QN-Mixer · AAPM, 32 views, no noise | PSNR (dB): 35.69 -> 38.11 -> 39.37 -> 39.51 | Helped |
| use Incept-Mixer instead of Inception as the regularizer (ablation) | QN-Mixer · AAPM, 32 views, no noise | PSNR (dB): 31.65 -> 39.51 | Helped |
| use Incept-Mixer instead of U-Net as the regularizer (ablation) | QN-Mixer · AAPM, 32 views, no noise | PSNR (dB): 34.29 -> 39.51 | Helped |
| use Incept-Mixer instead of MLP-Mixer as the regularizer (ablation) | QN-Mixer · AAPM, 32 views, no noise | PSNR (dB): 36.89 -> 39.51 | Helped |
| use FBP instead of A† for the pseudo-inverse (ablation) | QN-Mixer · AAPM, 32 views, no noise | PSNR (dB): 38.94 -> 39.51 | Helped |
| use latent BFGS instead of first-order optimization (ablation) | Incept-Mixer reconstruction framework · AAPM, 32 views, no noise | PSNR (dB): 37.45 -> 39.51 | Helped |
Surprising findings
- Under high noise, QN-Mixer is nearly on par with or slightly below RegFormer at some view counts, which the authors attribute to compressed latent gradient information.
- Replacing the pseudo-inverse A† with FBP gave a slightly better result (39.51 vs 38.94 dB), contrary to the interpretability motivation.
Limitations
- Memory requirements of quasi-Newton methods; the latent projection is needed to keep the Hessian approximation tractable (642x642 max in experiments).
- Degraded advantage under high noise due to compressed gradient information.
- Applicability to other inverse problems may be limited with larger Hessian sizes.
Experimental setup
Datasets: AAPM 2016 NIH-AAPM-Mayo Clinic Low-Dose CT Grand Challenge DeepLesion
Benchmarks: AAPM DeepLesion
Metrics: PSNR SSIM
Baselines: FBPConvNet DuDoTrans Learned PD LEARN RegFormer
Builds on: LEARN Learned Primal-Dual MLP-Mixer Inception BFGS RegFormer
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