FFAI: Flow Matching with Feedback Training and Adaptive Initialization for CT Reconstruction

Jigang Duan; Heran Wang; Genwei Ma; Xing Zhao

cs.CVOct 29, 2026

FFAI: Flow Matching with Feedback Training and Adaptive Initialization for CT Reconstruction

Authors: Jigang Duan, Heran Wang, Genwei Ma, Xing Zhao

Organizations: School of Mathematical Sciences, Capital Normal University, Beijing 100048, China · National Center for Applied Mathematics Beijing, Capital Normal University, and the Academy for Multidisciplinary Studies, Capital Normal University, Beijing 100048, China

Abstract

Although low-dose, sparse-view, and limited-angle CT involve distinct degradation mechanisms, all three pose reconstruction challenges due to limited measurement information and can therefore be addressed within a unified framework. In iterative image restoration with flow matching, prediction errors may cause inference states to deviate from the prescribed training path, while a fixed initialization may be unsuitable for inputs with varying degradation severity. We propose a unified conditional flow matching method that conditions on the initial reconstruction and combines feedback-aware training with degradation-adaptive initialization. During training, a teacher network simulates inference updates to generate shifted states, from which a student network learns to recover high-quality reference images, improving its ability to handle prediction errors. During inference, the starting time is selected based on the noise level or extent of missing projection data, and the noise added to the initial state is adjusted accordingly to adapt the starting point to the input. Experiments on public benchmark datasets show that the proposed method achieves better quantitative results than the compared methods across all three reconstruction tasks, effectively suppressing noise and artifacts while preserving anatomical structures and details.

Figures & tables

Fig. 1: Motivation and key mechanisms of FFAI. (A) The three CT tasks share a unified training procedure, with parameters learned separately for each task. (B) Feedback-based error correction: shifted states generated by teacher-simulated inference are incorporated into training, with high-quality reference images supervising restoration to improve the network’s ability to handle prediction errors. (C) Degradation adaptation: the starting time and initial state are jointly determined by the input degradation severity to accommodate different restoration needs.

Fig. 2: Unified training framework for the three tasks. Each task uses the initial reconstruction as a condition and shares the same flow matching and feedback training mechanisms, while network parameters are learned independently. After training, the student model for each task is retained for inference.

Fig. 3: Feedback-aware FM training. The standard branch learns the target velocity at the prescribed path state $\bm{x}_{t_{R}}$ . In the feedback branch, the EMA teacher performs a single update from $\bm{x}_{t_{L}}$ to generate a stop-gradient feedback state $\widetilde{\bm{x}}_{t_{R}}$ , and the student’s endpoint prediction is supervised by the reference image. $t_{L}$ and $t_{R}$ are the nearest inference nodes on either side of the randomly sampled time $t$ .

Fig. 4: Degradation-adaptive inference. The starting time $\tau_{\omega}$ is selected from the degradation descriptor $\bm{q}_{\omega}$ , and the corresponding initial state is constructed. Conditioned on the fixed image $\bm{c}_{\omega}$ , the task-specific student network performs Euler updates along a decreasing time grid to obtain the final reconstruction.

Metric	FBP	Noise2Noise	MTD-GAN	FoundDiff	TAMP	FORCE	FFAI
PSNR (dB) $\uparrow$	40.99 $\pm$ 0.08	41.79 $\pm$ 0.23	46.03 $\pm$ 0.08	45.51 $\pm$ 0.06	42.45 $\pm$ 1.13	40.81 $\pm$ 0.33	48.30 $\pm$ 0.05
SSIM (%) $\uparrow$	93.70 $\pm$ 0.14	95.50 $\pm$ 0.10	97.81 $\pm$ 0.05	97.87 $\pm$ 0.53	96.43 $\pm$ 1.39	96.04 $\pm$ 0.47	97.96 $\pm$ 0.39

TABLE I: Quantitative results for quarter-dose CT reconstruction (mean

\pm

standard deviation). SSIM is reported as a percentage. Bold and underlined values indicate the best and second-best means, respectively.

Fig. 5: Quarter-dose CT reconstructions obtained with different methods. Representative pelvic, thoracic, and abdominal slices are shown from top to bottom. In each group, the upper row shows CT images, and the lower row shows difference maps relative to the full-dose reference. Reference denotes the full-dose reference image, LDCT denotes the quarter-dose input image, and Proposed denotes FFAI. The display window is $[-260,340]$ HU, and the color scale for the difference maps spans $[-100,100]$ .

Method	$60^{\circ}$		$90^{\circ}$
Method	PSNR (dB) $\uparrow$	SSIM (%) $\uparrow$	PSNR (dB) $\uparrow$	SSIM (%) $\uparrow$
FBP	17.28 $\pm$ 1.97	53.55 $\pm$ 3.06	19.62 $\pm$ 1.89	64.09 $\pm$ 4.05
IRON	31.57 $\pm$ 1.70	90.36 $\pm$ 3.26	35.61 $\pm$ 3.65	94.60 $\pm$ 2.66
ProCT	34.98 $\pm$ 1.59	92.56 $\pm$ 2.00	38.83 $\pm$ 1.90	95.67 $\pm$ 1.52
TLIR	20.33 $\pm$ 1.14	54.57 $\pm$ 12.04	25.23 $\pm$ 3.02	46.09 $\pm$ 3.59
TAMP	20.79 $\pm$ 1.75	60.87 $\pm$ 3.33	24.57 $\pm$ 3.01	77.62 $\pm$ 2.53

TABLE II: Quantitative results for

60^{\circ}

and

90^{\circ}

limited-angle CT reconstruction (mean

\pm

standard deviation). SSIM is reported as a percentage. Bold and underlined values indicate the best and second-best means, respectively, for each angular range.

Fig. 6: Reconstructions obtained with different methods under the $60^{\circ}$ limited-angle setting. The upper and lower groups show representative thoracic and abdominal slices, respectively. In each group, the upper row shows CT images, and the lower row shows difference maps relative to the reference. Reference denotes the full-dose reference image, and Proposed denotes FFAI. The display window is $[-260,340]$ HU, and the color scale for the difference maps spans $[-200,200]$ .

Fig. 7: Reconstructions obtained with different methods under the $90^{\circ}$ limited-angle setting. The upper and lower groups show representative thoracic and abdominal slices, respectively. In each group, the upper row shows CT images, and the lower row shows difference maps relative to the reference. Reference denotes the full-dose reference image, and Proposed denotes FFAI. The display window is $[-260,340]$ HU, and the color scale for the difference maps spans $[-200,200]$ .

Method	40 views		80 views
Method	PSNR (dB) $\uparrow$	SSIM (%) $\uparrow$	PSNR (dB) $\uparrow$	SSIM (%) $\uparrow$
FBP	26.65 $\pm$ 1.07	48.52 $\pm$ 2.82	32.25 $\pm$ 0.79	73.07 $\pm$ 1.62
LipCT	37.29 $\pm$ 0.56	87.27 $\pm$ 0.97	39.25 $\pm$ 0.21	90.72 $\pm$ 0.86
MetaInv	35.56 $\pm$ 1.76	84.50 $\pm$ 2.34	37.08 $\pm$ 1.14	88.08 $\pm$ 0.97
DPS	32.33 $\pm$ 0.40	74.75 $\pm$ 1.14	32.42 $\pm$ 0.43	75.04 $\pm$ 0.96
TAMP	30.25 $\pm$ 0.65	80.55 $\pm$ 1.07	36.00 $\pm$ 0.49	89.11 $\pm$ 0.95

TABLE III: Quantitative results for sparse-view CT reconstruction with

40

and

80

views (mean

\pm

standard deviation). SSIM is reported as a percentage. Bold and underlined values indicate the best and second-best means, respectively, for each view setting.

Fig. 8: CT reconstructions obtained with different methods under the $40$ -view sparse-sampling setting. The upper and lower groups show representative thoracic and abdominal slices, respectively. In each group, the upper row shows CT images, and the lower row shows difference maps relative to the reference. Reference denotes the full-dose reference image, and Proposed denotes FFAI. The display window is $[-260,340]$ HU, and the color scale for the difference maps spans $[-200,200]$ .

Fig. 9: CT reconstructions obtained with different methods under the $80$ -view sparse-sampling setting. The upper and lower groups show representative thoracic and abdominal slices, respectively. In each group, the upper row shows CT images, and the lower row shows difference maps relative to the reference. Reference denotes the full-dose reference image, and Proposed denotes FFAI. The display window is $[-260,340]$ HU, and the color scale for the difference maps spans $[-200,200]$ .

Fig. 10: CT reconstructions obtained with different ablation variants. From top to bottom, the three groups correspond to quarter-dose, $60^{\circ}$ limited-angle, and $40$ -view sparse-view experiments. In each group, the upper row shows the reconstructions and the lower row shows their differences from the reference images. W/o FAT and W/o AS denote the variants without feedback-aware training and with a fixed starting point, respectively. Proposed denotes the full FFAI model. The color scale for the difference maps is $[-200,200]$ .

Variant	FAT	AS	LDCT (25%)		LACT ( $60^{\circ}$ )		SVCT (40 views)
Variant	FAT	AS	PSNR (dB) $\uparrow$	SSIM (%) $\uparrow$	PSNR (dB) $\uparrow$	SSIM (%) $\uparrow$	PSNR (dB) $\uparrow$	SSIM (%) $\uparrow$
W/o FAT	$\times$	$\checkmark$	41.44 $\pm$ 1.60	93.91 $\pm$ 2.17	28.97 $\pm$ 1.80	74.35 $\pm$ 2.98	34.87 $\pm$ 0.68	79.88 $\pm$ 1.20
W/o AS	$\checkmark$	$\times$	30.71 $\pm$ 1.77	81.85 $\pm$ 2.20	32.69 $\pm$ 0.94	82.44 $\pm$ 1.39	35.42 $\pm$ 0.63	81.12 $\pm$ 1.01
FFAI	$\checkmark$	$\checkmark$	48.30 $\pm$ 0.05	97.96 $\pm$ 0.39	38.94 $\pm$ 1.79	94.28 $\pm$ 2.07	39.08 $\pm$ 0.31	90.55 $\pm$ 1.18

TABLE IV: Ablation results for quarter-dose,

60^{\circ}

limited-angle, and

40

-view sparse-view CT reconstruction (mean

\pm

standard deviation). FAT and AS denote feedback-aware training and an adaptive starting point, respectively.

\checkmark

and

\times

indicate whether each component is enabled or removed; removing AS corresponds to using a fixed starting point. SSIM is reported as a percentage, and boldface indicates the best mean values.

Fig. 11: Quantitative comparison of cross-dataset generalizability. Low-dose CT (LDCT) uses

25\%

of routine dose, sparse-view CT (SVCT) uses 80 projection views, and limited-angle CT (LACT) uses a

90^{\circ}

angular range. Circles and squares indicate PSNR (dB) and SSIM (

\%

), respectively. Proposed denotes the proposed method.

Computed Tomography

Computed tomography uses X-ray measurements from multiple angles to reconstruct cross-sectional and volumetric images for diagnosis and scientific imaging.

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Generative models, particularly Diffusion Models (DM), have shown strong potential for Computed Tomography (CT) reconstruction serving as expressive priors for solving ill-posed inverse problems. However, diffusion-based reconstruction relies on Stochastic Differential Equations (SDEs) for forward diffusion and reverse denoising, where such stochasticity can interfere with repeated data consistency corrections in CT reconstruction. Since CT reconstruction is often time-critical in clinical and interventional scenarios, improving reconstruction efficiency is essential. In contrast, Flow Matching (FM) models sampling as a deterministic Ordinary Differential Equation (ODE), yielding smooth trajectories without stochastic noise injection. This deterministic formulation is naturally compatible with repeated data consistency operations. Furthermore, we observe that FM-predicted velocity fields exhibit strong correlations across adjacent steps. Motivated by this, we propose an FM-based CT reconstruction framework (FMCT) and an efficient variant (EFMCT) that reuses previously predicted velocity fields over consecutive steps to substantially reduce the number of Neural network Function Evaluations (NFEs), thereby improving inference efficiency. We provide theoretical analysis showing that the error introduced by velocity reuse is bounded when combined with data consistency operations. Extensive experiments demonstrate that FMCT/EFMCT achieve competitive reconstruction quality while significantly improving computational efficiency compared with diffusion-based methods. The codebase is open-sourced at https://github.com/EFMCT/EFMCT.

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