TriINR: Unsupervised Atmospheric Turbulence Mitigation with Triple Implicit Neural Representations

Yuka Ogino; Rikuto Otsuka; Yuho Shoji; Takuya Ogawa; Takahiro Toizumi; Atsushi Ito

cs.CVOct 16, 2026

TriINR: Unsupervised Atmospheric Turbulence Mitigation with Triple Implicit Neural Representations

Authors: Yuka Ogino, Rikuto Otsuka, Yuho Shoji, Takuya Ogawa, Takahiro Toizumi, Atsushi Ito

Organizations: NEC Corporation, Japan

Abstract

Atmospheric turbulence degrades image quality in long-range imaging. The degradation is generally modeled with two spatio-temporally varying components, tilt and blur. Recent unsupervised turbulence mitigation methods have demonstrated the effectiveness of representing a sharp image as an implicit neural representation (INR). However, their tilt and blur representations remain frame-dependent, and the number of optimization parameters grows with the number of input frames. To address this limitation, we propose TriINR, an unsupervised turbulence mitigation method that recovers a sharp image from multiple degraded frames. TriINR represents the sharp image, tilt, and blur as three implicit neural representations. By modeling tilt and blur as spatio-temporal INRs, TriINR achieves frame-count-independent degradation representation and memory-efficient optimization. We further incorporate physical and statistical properties of atmospheric turbulence as constraints on the INRs to improve restoration accuracy. Experiments on synthesized turbulence data with three degradation strengths show that TriINR restores images more robustly across varying turbulence strengths than prior TM methods and achieves the highest accuracy among the evaluated unsupervised methods. Our method also demonstrates robustness on real long-range scenes containing additional non-ideal motion.

Figures & tables

Figure 1: Overview of TriINR. TriINR reformulates the sharp image and the degradations (tilt and blur) as three continuous implicit neural representations and jointly optimizes them from multiple turbulence-degraded observations. The tilt and the blur are each modeled as a single spatio-temporal neural field shared across all frames, yielding a frame-count-independent representation.

	NeRT [ 10 ]	TMFS [ 24 ]	TriINR (ours)
Tilt represented as INR	✓	$\times$	✓
Blur represented as INR	$\times$	✓	✓
Image represented as INR	✓	✓	✓
Parameter count scaling	$O(N)$	$O(HWN)$	$\boldsymbol{O(1)}$
#Params ( $H{=}W{=}256$ , $N{=}20$ )	$\sim 3.8$ M	$\sim 200$ M	$\sim\mathbf{0.4M}$
Tilt details	Frame-dependent INRs	Frame-dependent tensors	Frame-independent INR

Table 1: Parameter and representation comparison of unsupervised INR-based turbulence mitigation methods. Unlike prior methods, whose parameter count grows with the frame count and image size, TriINR keeps a constant parameter count. PE denotes positional encoding, and GF denotes Gaussian Fourier features [ 23 ] .

Panel of Figure 2 — Figure 2: Overview of the TriINR optimization framework. (a) Loss evaluation process in the second optimization stage. The triple INRs are jointly optimized through the atmospheric turbulence forward model. To improve scalability, only sampled observation coordinates and their local blur supports are evaluated at each optimization step. In the first stage, we optimize only the components shown in gray area. (b) Architecture of the three INRs. The Tilt INR and the Blur INR model the atmospheric degradation as spatio-temporal continuous fields shared across all input frames.

			Supervised				Unsupervised
			TMT [ 29 ]		DATUM [ 27 ]		CLEAR [ 1 ]		NeRT [ 10 ]		TriINR (ours)
Dataset	#images	image size	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM
Weak turb. on LandUse	2100	256 $\times$ 256	22.49	0.636	23.89	0.683	23.03	0.647	24.59	0.664	25.64	0.707
Middle turb. on LandUse	2100	256 $\times$ 256	26.23	0.783	27.34	0.817	24.03	0.711	24.06	0.643	25.74	0.725
Strong turb. on LandUse	2100	256 $\times$ 256	25.26	0.723	26.39	0.777	23.24	0.644	22.97	0.570	24.41	0.652
turb_syn_static [ 29 ]	1518	512 $\times$ 512	27.97	0.849	27.52	0.849	24.76	0.758	OOM	OOM	25.98	0.757

Table 2: Quantitative comparison on four benchmarks. We report PSNR and SSIM (higher is better) averaged over all scenes in each dataset. Bold : best among all methods. Underlined : best among unsupervised methods. NeRT on turb_syn_static runs out of memory (OOM) at

512{\times}512

resolution.

Panel of Figure 3 — Figure 3: Qualitative comparison on our LandUse-based synthetic dataset under three turbulence strengths (Weak / Middle / Strong; top to bottom), each restored from 20 input frames. Under Weak turbulence, supervised methods produce over-sharpening artifacts, whereas TriINR recovers the image faithfully. Across all three strengths, our method yields robust restoration.

	Base INR	Tilt INR	Blur INR
Input	$(x,y)$	$(x,y,t)$	$(x,y,t)$
PE type	Hashgrid	GF	GF
PE params	$L{=}14$ , $F{=}2$ ,	$M{=}64$	$M{=}256$
	hash table size $2^{14}$ ,	$\sigma{=}1.0$	$\sigma{=}4.0$
	base resolution 16
MLP width	64	128	128

Table 3: Network architecture of the three INRs in TriINR.

L

denotes hashgrid levels,

F

hashgrid feature channels per level, and

M

Gaussian Fourier (GF) mapping size.

Panel of Figure 4 — Figure 4: Qualitative comparison on OTIS Pattern 4 and Pattern 14, each restored from 20 input frames. TriINR recovers the pattern with the highest fidelity among all compared methods.

Panel of Figure 5 — Figure 5: Qualitative comparison of the ablation study on our synthetic dataset under Middle turbulence. Our full model with tilt zero temporal mean (ZM) constraint and hashgrid PE (third column) recovers a sharp image with faithful texture and geometry.

Level	$L$ [m]	$A$ [m]	$D/r_{0}$
Weak	$\mathcal{U}(100,400)$	$\mathcal{U}(0.001,0.005)$	$\{0.5,\,1.0,\,1.5\}$
Middle	$\mathcal{U}(400,800)$	$\mathcal{U}(0.04,0.1)$	$\{1.0,\,1.5,\,2.0\}$
Strong	$\mathcal{U}(800,1500)$	$\mathcal{U}(0.1,0.2)$	$\{1.5,\,2.0,\,3.0\}$

Table 4: Turbulence parameters used to synthesize on LandUse dataset [ 26 ] . For each scene, propagation distance

L

and aperture

A

are sampled uniformly, and

D/r_{0}

is drawn from a discrete set. The setting follows TMFS [ 24 ] .

Panel of Figure 6 — Figure 6: Qualitative comparison on a real-world turbulence-degraded scene in the real-world RLR-AT dataset [ 25 ] . The images are cropped for display; full-sized results are shown in the supplementary material.

Tilt ZM	Blur ZM	Hashgrid PE	PSNR $\uparrow$	SSIM $\uparrow$
✓	✓	-	23.94	0.605
-	-	✓	23.94	0.643
✓	✓	✓	25.54	0.715
✓	-	✓	25.74	0.725

Table 5: Ablation study on our LandUse-based synthetic dataset under Middle turbulence. Best values in bold. Our full model (last row) uses tilt zero-mean (ZM) without blur zero-mean, with hashgrid positional encoding for the image INR.

$N$	5	10	20	40	80
PSNR $\uparrow$	24.83	25.55	25.77	25.50	25.14
SSIM $\uparrow$	0.690	0.722	0.725	0.709	0.688

Table 6: Effect of the input frame count

N

on our LandUse-based synthetic dataset under Middle turbulence. PSNR and SSIM are averaged over 105 scenes (5 initial scenes per class

\times

21 classes). Best value in each row is in bold .

Panel of Figure 7 — Figure 7: Results of the two-stage optimization on a synthesized image from LandUse dataset. Top row: the ground-truth sharp image (left) and one synthesized input frame (right). Bottom row: the Image INR output after stage 1 (left) and after stage 2 (right).

	NeRT [ 10 ]	TMFS [ 24 ]	TriINR (ours)
Tilt	Frame-dependent INRs	Frame-dependent tensors	Frame-independent INR
representation	Grid deformer [ 13 ] , one CNN / frame	Noise map + correlation	PE (GF) + MLP, $(x,y,t)$ input
	( $1{\times}1$ conv, 256ch, $\times 4$ )	$(2{\times}2W{\times}2H+2)$ / frame	MLP width ${=}128\times 4$
Blur	Frame-dependent tensors	Frame- & resolution-dependent tensors	Frame-independent INR
representation	Zernike vector map	Noise map + correlation parameters	PE (GF) + MLP, $(x,y,t)$ input
	$16{\times}16{\times}36$ / frame	$(19{\times}2{\times}2W{\times}2H+19)$ / frame	MLP width ${=}128\times 4$

Table 7: Parameter and representation comparison of unsupervised INR-based turbulence mitigation methods. Unlike prior methods, whose parameter count grows with the frame count and image size, TriINR keeps a constant parameter count. PE denotes positional encoding, and GF denotes Gaussian Fourier features [ 23 ] .

Panel of Figure 8 — Figure 8: Additional qualitative comparison on our LandUse-based synthetic dataset under three turbulence strengths (Weak / Middle / Strong; top to bottom), each restored from 20 input frames.

Panel of Figure 9 — Figure 9: Qualitative comparison on the OTIS dataset [ 7 ] , each restored from 20 input frames.

Panel of Figure 10 — Figure 10: Additional qualitative comparison on OTIS patterns [ 7 ] , each restored from 20 input frames.

Panel of Figure 11 — Figure 11: FHD comparison results of RLR-AT [ 25 ]

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Atmospheric Turbulence Mitigation Image Restoration Image Deblurring Gaussian Splatting

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Atmospheric turbulence causes significant image degradation due to pixel displacement (tilt) and blur, particularly in long-range imaging applications. In this paper, we propose a novel framework for atmospheric turbulence mitigation, GSTurb, which integrates optical flow-guided tilt correction and Gaussian splatting for modeling non-isoplanatic blur. The framework employs Gaussian parameters to represent tilt and blur, and optimizes them across multiple frames to enhance restoration. Experimental results on the ATSyn-static dataset demonstrate the effectiveness of our method, achieving a peak PSNR of 27.67 dB and SSIM of 0.8735. Compared to the state-of-the-art method, GSTurb improves PSNR by 1.3 dB (a 4.5% increase) and SSIM by 0.048 (a 5.8% increase). Additionally, on real datasets, including the TSRWGAN Real-World and CLEAR datasets, GSTurb outperforms existing methods, showing significant improvements in both qualitative and quantitative performance. These results highlight that combining optical flow-guided tilt correction with Gaussian splatting effectively enhances image restoration under both synthetic and real-world turbulence conditions. The code for this method will be available at https://github.com/DuhlLiamz/3DGS_turbulence/tree/main.

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