SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Table C: Comparison results with prior methods on DIV2K-MC. We report the PSNR(↑)/SSIM(↑) values of different methods.
Methods	BlurNoise	BlurJPEG	NoiseJPEG	BlurNoiseJPEG	Mean
SwinIR [15]	20.91/0.311	26.83/0.748	23.86/0.523	22.77/0.450	23.59/0.508
IPT [5]	21.28/0.327	26.83/0.748	24.15/0.535	22.96/0.459	23.81/0.517
HAT [6]	23.41/0.399	28.86/0.788	25.69/0.572	24.42/0.502	25.59/0.565
DAN [12]	24.14/0.438	28.95/0.791	26.20/0.593	24.82/0.519	26.03/0.585
DCLS-SR [18]	23.84/0.420	28.93/0.790	26.37/0.599	24.92/0.523	26.02/0.583
ZSSR [20]	24.95/0.493	29.02/0.793	26.68/0.617	25.24/0.542	26.47/0.611
KernelGAN [1]+ZSSR	23.08/0.424	28.32/0.786	21.90/0.474	22.76/0.443	24.02/0.532
MZSR [7]	18.73/0.213	24.90/0.667	20.37/0.398	20.62/0.354	21.16/0.408
DualSR [8]	25.59/0.561	28.24/0.787	23.78/0.586	24.62/0.541	25.56/0.619
DDNM [24]	22.62/0.389	26.82/0.746	25.11/0.582	23.81/0.504	24.59/0.555
EDSR [16]	24.02/0.430	28.93/0.790	26.08/0.587	24.73/0.514	25.94/0.580
TTA-C	24.29/0.446	28.93/0.790	26.35/0.598	24.91/0.522	26.12/0.589
SRTTA (ours)	26.93/0.709	28.93/0.798	29.13/0.784	27.12/0.728	28.02/0.755
SRTTA-lifelong (ours)	27.67/0.749	29.02/0.793	29.70/0.810	27.52/0.747	28.48/0.775
E.3 More Results of Ablation Studies
Effect of each component. In this part, we investigate the effect of each component and provide more ablation studies. As shown in Table D, the baseline without the degradation classifier, generates the second-order degraded images with random degradation types, achieving a limited performance in terms of both PSNR and SSIM. The baseline without the adaptation consistency loss  $\mathcal{L}_a$  results in the model collapse due to the lack of the consistency constraint. Without the self-supervised adaptation loss  $\mathcal{L}_s$ , the TTA performance of the adapted model drops significantly. These experimental results demonstrate the effectiveness of each component of our framework.
Table D: We report the PSNR/SSIM results of ablation studies of different components for  $2\times \mathrm{SR}$
Methods	GaussianBlur	DefocusBlur	GlassBlur	GaussianNoise	PossionNoise	ImpulseNoise	SpeckleNoise	JPEG	Mean
PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM
SRTTA (ours)	31.07/0.869	25.86/0.674	29.01/0.815	29.66/0.762	26.69/0.637	16.15/0.284	32.33/0.873	31.30/0.857	27.76/0.721
- w/o classifier C(·)	29.43/0.812	25.51/0.675	27.51/0.756	22.05/0.546	25.64/0.571	15.66/0.260	31.50/0.836	31.19/0.855	26.06/0.664
- w/o Ls	30.65/0.854	25.87/0.680	28.43/0.795	28.04/0.644	24.83/0.534	15.96/0.274	31.96/0.847	31.47/0.862	27.15/0.686
- w/o Ls	12.29/0.254	5.67/0.397	5.65/0.403	12.87/0.477	10.29/0.072	11.48/0.213	11.67/0.218	11.99/0.477	10.24/0.314
Effect of the hyperparameter  $\alpha$  in Eqn. (6). In this part, we investigate the effect of the weight of adaptation consistency loss  $\alpha$ . As shown in Table E, the adapted model with  $\alpha = 1$  achieves the best TTA performance. Thus, we set the  $\alpha = 1$  by default for our SRTTA during adaptation.
Table E: We report the PSNR/SSIM results of ablation studies of  $\alpha$  for  $2\times$  SR.
α	GaussianBlur	DefocusBlur	GlassBlur	GaussianNoise	PossionNoise	ImpulseNoise	SpeckleNoise	JPEG	Mean	Set5
PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM
0	12.29/0.254	5.67/0.397	5.65/0.403	12.87/0.477	10.29/0.072	11.48/0.213	11.67/0.218	11.99/0.477	10.24/0.314	11.42/0.421
0.1	11.11/0.318	8.02/0.043	5.65/0.403	22.78/0.683	5.65/0.403	12.50/0.484	15.03/0.542	30.95/0.850	13.96/0.466	37.66/0.959
0.5	10.47/0.134	10.46/0.313	23.69/0.708	29.21/0.797	27.80/0.717	16.30/0.290	32.10/0.871	30.98/0.850	22.63/0.585	37.75/0.959
1	31.07/0.869	25.86/0.674	29.01/0.815	29.66/0.762	26.69/0.637	16.15/0.284	32.33/0.873	31.30/0.857	27.76/0.721	34.59/0.924
2	30.86/0.862	25.91/0.678	28.71/0.804	29.04/0.710	25.89/0.591	16.06/0.279	32.23/0.865	31.45/0.861	27.52/0.706	35.41/0.933
5	30.74/0.857	25.91/0.680	28.53/0.798	28.47/0.670	25.29/0.558	16.00/0.276	32.08/0.855	31.48/0.862	27.31/0.695	35.89/0.939
Effect of the hyperparameter  $\rho$  in Eqn. (9). In this part, we analyze the effect of the hyperparameter  $\rho$ , which decides the ratio of parameters to freeze, for the test-time adaptation. In Table F, when  $\rho = 0.50$ , our SRTTA achieves the best TTA performance on the DIV2K-C dataset on average in the lifelong setting. Meanwhile, we also investigate the effect of the adaptive parameter preservation (APP) strategy in the parameter-reset setting. As shown in Table F, our APP strategy (with  $\rho = 0.50$ )
merely has little impact on the TTA in the parameter-reset setting. These results demonstrate the effectiveness of the APP strategy in test-time adaptation for image super-resolution.
Table F: We report the PSNR/SSIM results of ablation studies of  $\rho$  for  $2\times \mathrm{SR}$  in the parameter-reset and lifelong setting, our model is SRTTA and SRTTA-lifelong.
Setting	0	0.1	0.2	0.3	0.5	0.7	0.9	1
SRTTA	27.74/0.729	27.79/0.730	27.82/0.729	27.82/0.727	27.76/0.721	27.55/0.709	27.08/0.682	26.21/0.645
SRTTA-lifelong	27.46/0.726	27.60/0.727	27.66/0.728	27.72/0.728	27.73/0.728	27.73/0.725	27.50/0.706	26.21/0.645
Comparison with other anti-forgetting methods. In this part, we compare our adaptive parameter preservation (APP) strategy with two baseline methods to demonstrate the effectiveness of our strategy in preserving the learned knowledge of pre-trained SR models. Stochastic Restoration (STO) [21] randomly selects a different set of parameters (with a ratio of  $1\%$ ) and restores them back to the parameters of the pre-trained models. Random Selection (RS) selects a fixed set of parameters before adaption and freezes them not to update. As shown in Table G, our APP strategy achieves the best TTA results on the DIV2K-C dataset. Meanwhile, with the same ratio of selected parameters, our APP strategy consistently outperforms the Random Selection baseline for the anti-forgetting. These results demonstrate that our adaptive selection is able to select the important parameters and preserve the knowledge of the pre-trained model.
Table G: We report the PSNR/SSIM results of ablation studies of adaptive parameter preservation (APP) strategy for  $2 \times \mathrm{SR}$  in the lifelong setting.
Dataset	STO [21]	RS with different ρ	APP with different ρ (ours)
0.3	0.5	0.7	0.3	0.5	0.7
DIV2K-C (with degradation shift)	27.17/0.687	27.52/0.727	27.62/0.728	27.68/0.726	27.72/0.728	27.73/0.728	27.73/0.725
Set5 (w/o degradation shift)	35.57/0.938	33.95/0.913	34.02/0.914	34.24/0.918	34.11/0.916	34.23/0.917	34.38/0.920
E.4 Effectiveness on a New Unknown Domain
In this part, we further evaluate our SRTTA on a new unknown domain with the degradation of processed camera sensor noise [3, 26], which is not used in the training phase of the SR model or that of the degradation classifier. We report the PSNR(↑) and SSIM(↑) values of different methods on 100 images with random processed camera sensor noise. In Table H, our SRTTA method is also able to improve the model performance on this unknown degradation. These experimental results further demonstrate the generalization capability of our SRTTA model to unknown degradation types.
E.5 Comparison with Patch-Recurrence Reconstruction Loss
In this part, we investigate the effect of our second-order reconstruction loss. We compare our loss with the loss of existing zero-shot methods [20, 7, 1]. Based on the assumption of patch recurrence across scales [9, 29], these methods downsample the test image to obtain an image with a lower resolution and reconstruct the test image from the downsampled image. For simplicity, we call this patch-recurrence loss. For a fair comparison, we further downsample the second-order degraded images that are obtained using our second-order degradation scheme and reconstruct the test image with the patch-recurrence loss. As shown in Table I, our SRTTA with our second-order reconstruction loss consistently outperforms the baseline with the patch-recurrence loss. These results demonstrate the effectiveness of our second-order reconstruction loss.
Table H: Results of different methods on the unknown domain with the degradation of processed camera sensor noise.
Methods	PSNR	SSIM
SwinIR [15]	19.45	0.496
IPT [5]	19.51	0.500
HAT [6]	21.52	0.596
DDNM [24]	19.63	0.518
DAN [12]	21.53	0.598
DCLS-SR [18]	21.57	0.605
DualSR [8]	21.14	0.586
MZSR [7]	20.40	0.438
ZSSR [20]	21.57	0.621
KernelGAN [1]+ZSSR	20.60	0.543
EDSR [16]	21.56	0.601
SRTTA (ours)	21.81	0.647
E.6 Effect of the Feature-level Reconstruction
In this part, we investigate the effect of different reconstruction levels. In our second-order reconstruction, we use the feature-level reconstruction to adapt the pre-trained model as in Eqn. (6). We
Table I: We report the PSNR/SSIM results of ablation studies of the patch-recurrence reconstruction loss for  $2 \times \mathrm{SR}$  in parameter-reset and lifelong settings.
methods	Setting	GaussianBlur	DefocusBlur	GlassBlur	GaussianNoise	PossionNoise	ImpulseNoise	SpeckleNoise	JPEG	Mean
PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM
Patch-recurrence loss	parameter-reset	29.87/0.828	25.51/0.674	27.67/0.767	28.55/0.680	26.41/0.605	19.72/0.407	31.71/0.842	31.02/0.853	27.56/0.707
Patch-recurrence loss	lifelong	29.87/0.828	25.51/0.674	27.67/0.767	28.52/0.678	26.40/0.604	20.48/0.430	31.76/0.846	31.01/0.853	27.65/0.710
SRTTA(ours)	parameter-reset	31.07/0.869	25.80/0.674	29.01/0.815	29.66/0.762	26.69/0.637	16.15/0.284	32.33/0.873	31.30/0.857	27.76/0.721
SRTTA(ours)	lifelong	31.07/0.869	25.83/0.674	29.18/0.819	29.48/0.797	27.10/0.073	16.27/0.273	31.71/0.864	31.22/0.853	27.73/0.728
Table J: We report the PSNR/SSIM results of ablation studies of feature-level and image-level reconstruction for  $2 \times \mathrm{SR}$  in the lifelong setting.
Reconstruct-level	Scale	GaussianBlur	DefocusBlur	GlassBlur	GaussianNoise	PossionNoise	ImpulseNoise	SpeckleNoise	JPEG	Mean
PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM
EDSR [16]	2	30.28/0.837	25.52/0.673	27.82/0.773	25.87/0.536	22.96/0.449	15.87/0.269	30.52/0.778	30.83/0.847	26.21/0.645
Image-level	2	31.21/0.871	25.73/0.671	29.16/0.817	29.56/0.796	26.74/0.654	16.24/0.263	32.47/0.884	31.44/0.860	27.82/0.727
Feature-level	2	31.07/0.869	25.83/0.674	29.18/0.819	29.48/0.797	27.10/0.673	16.27/0.273	31.71/0.864	31.22/0.853	27.73/0.728
EDSR [16]	4	28.31/0.780	25.81/0.692	27.40/0.751	23.49/0.479	22.10/0.443	15.28/0.283	26.80/0.676	27.34/0.734	24.57/0.605
Image-level	4	28.61/0.790	26.23/0.697	28.13/0.773	26.46/0.685	25.28/0.623	15.72/0.297	28.02/0.751	27.74/0.746	25.77/0.670
Feature-level	4	28.78/0.795	26.31/0.703	28.16/0.776	26.28/0.691	25.46/0.643	15.62/0.294	27.77/0.755	27.61/0.740	25.75/0.675
compare a baseline with an image-level reconstruction, which means we reconstruct the output of the SR model instead of the feature in the middle layer. As shown in Table J, when reconstructing at the image level, the adapted model achieves a comparable performance for both  $2 \times \mathrm{SR}$  and  $4 \times \mathrm{SR}$ . Thus, both reconstruction levels are optional, we use the feature-level reconstruction by default.
Table K: We report the PSNR/SSIM results of ablation studies of adapted iterations for  $2 \times$  SR in the parameter-reset setting.
Iterations	GaussianBlur	DefocusBlur	GlassBlur	GaussianNoise	PossionNoise	ImpulseNoise	SpeckleNoise	JPEG	Mean	GPU Time
PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	seconds/image
1	30.49/0.844	25.59/0.675	28.08/0.782	27.05/0.592	24.34/0.507	15.98/0.279	31.32/0.810	31.09/0.853	26.74/0.668	0.60
2	30.72/0.854	25.82/0.679	28.62/0.800	27.76/0.630	24.99/0.538	16.02/0.280	31.76/0.830	31.23/0.856	27.12/0.683	1.41
5	30.64/0.861	25.80/0.677	28.88/0.811	28.90/0.702	26.10/0.600	15.98/0.278	32.19/0.861	31.37/0.859	27.48/0.706	2.73
10	31.07/0.869	25.86/0.674	29.01/0.815	29.66/0.762	26.69/0.637	16.15/0.284	32.33/0.873	31.30/0.857	27.76/0.721	5.38
20	31.15/0.870	25.80/0.675	29.32/0.824	29.24/0.772	26.05/0.601	16.08/0.276	32.14/0.865	31.31/0.856	27.64/0.717	10.82
50	30.71/0.856	25.64/0.674	29.28/0.821	29.12/0.743	25.40/0.569	16.02/0.265	31.54/0.838	28.46/0.846	27.02/0.701	25.64
E.7 Effect of Adaptation Iterations for Each Image
In this part, we investigate the effect of different adaptation iterations for each image. As shown in Table K, we compare the TTA performance of SRTTA with a different number of iterations  $S$  for each image. When the number of iterations  $S$  is small, the adapted SR model is not able to learn how to remove the degradation for these images well. When the number of iterations  $S$  is too large, the performance improvement of SRTTA diminishes and the adaptation cost will be greatly increased. Thus, we set  $S$  to 10 for a better efficiency-accuracy trade-off.
E.8 The Statistics of the Degradation Types of Real-world Images
In this part, we count the statistics of the degradation types of real-world images and report the results in Table L. We use our degradation classifier to identify the degradation types of real-world images from five datasets, including RealSR [4], DRealSR [25], DPED [13], OST300 [23] and ADE20K [28]. Experimental results in Table L show that the degradation type of blur happens the most among these real-world datasets.
E.9 Further Analysis of the Domain Shift Issue
In this part, we investigate the effect of the domain shift issues for pre-trained SR models, which are trained on specific domains with different degradation types. We use the EDSR baseline model as the model for analysis. In total, we separately train four EDSR baseline models on clean, blur, noise and JPEG domains, respectively. The corresponding four models are named EDSR, EDSR-B, EDSR-N and EDSR-J, respectively. We evaluate these four models on clean images and the test images with Gaussian Blur, Gaussian Noise or JPEG degradations in Figure B and Figure C.
As shown in Figure B and Figure C, when domain shift occurs, the pre-trained EDSR models, which are trained on domains different from the test domains, cannot remove the degradation from test
Table L: The count of the predicted degradation types of the real-world images from the five datasets. Note that some images can contain more than one degradation type simultaneously.
Dataset (# Images)	Clean	Blur	Noise	JPEG
RealSR (912)	48	860	1	149
DRealSR (35148)	1378	33770	0	1
DPED (187)	103	33	21	64
OST300 (300)	52	23	14	221
ADE20K (27574)	0	3452	2424	27573
Total (64121)	1581	38138	2460	28008
(a) Visualization results under clean domain.
(b) Visualization results under Gaussian Blur.
(c) Visualization results under Gaussian Noise.
Figure B: Visualization of the domain shift issue under different domains for  $2 \times \mathrm{SR}$ .
(d) Visualization results under JPEG.
images and generate unsatisfactory HR images with artifacts. For example, EDSR-B models cannot remove the noise and JPEG degradation, the EDSR-N and EDSR-J are also unable to remove the blur degradation. Instead, after test-time adaptation, our SRTTA is capable of handling the test images with unknown degradations and generating HR images with fewer artifacts. For example, our SRTTA is able to generate sharper HR images than EDSR-N and EDSR-J under Gaussian Blur domains. Indeed, our SRTTA models may be unable to completely remove the degradation compared with the upper-bound models, such as EDSR-B under Gaussian Blur. Thus, these drawbacks are required to be further addressed in future works.
F Visualization Results
F.1 Visualization Results on the DIV2K-C Images
In this part, we show more visualization comparison results of different SR methods on test images of the DIV2K-C dataset for both  $2 \times$  and  $4 \times$  SR. As shown in Figures D and E, our SRTTA is able to reduce the degradation from the test images and generate more plausible HR images.
F.2 Visualization Results on the Real-World Images
In this part, we conduct a comprehensive comparison of our SRTTA with existing approaches on two real-world datasets, including DPED [13], ADE20K [28] and OST300 [23]. As shown in Figures F and G, our SRTTA methods consistently generate more satisfactory HR images with less degradation of unknown noise or artifacts.
EDSR
EDSR-B
EDSR-N
EDSR-J
Figure C: Visualization of the domain shift issue under different domains for  $2\times \mathrm{SR}$
Ground-truth HR
KernelGAN+ZSSR
TA-lifelong(ours)
(a) Visualizations under Gaussian Noise for  $2\times$  SR
Ground-truth HR
Figure D: Visualization comparison on DIV2K-C test images with degradation for  $2 \times$  SR.
G Limitation Analysis and Border Impacts
G.1 Limitation Analysis
In this part, we analyze the limitations of our SRTTA and existing SR methods. When test images are corrupted at a high level, our SRTTA may not be able to completely remove the degradation and result in generated HR images with the existing degradation. For example, we show more visualization results of different methods on test images with Impulse Noise degradation in Figure H.
SRDiff
IPT
EDSR SR
TTA-lifelong(ours)
Ground-truth HR
Figure E: Visualization comparison on DIV2K-C test images with degradation for  $4 \times$  SR.
(a) Visualizations under PossionNoise for  $4\times$  SR
Bicubic
Since Real-ESRGAN [22] uses several different degradation types to construct training data, this model is able to remove the degradation in many cases. However, this model still suffers from the degradation shift issue, such as it cannot remove the gray Impulse noise from the test images as shown in Figure H(a). Moreover, Real-ESRGAN may generate HR images with over-smooth regions when removing the noise degradation and introduce some unpleasant artifacts due to the GAN training [22], which are shown in Figure H(b) and Figure H(c), respectively. Although our SRTTA cannot also completely remove the degradation from the test images in these cases, our SRTTA often preserves the original information of the test images. These results show the limitations of our SRTTA and existing methods and have a great impact on the practical application. Thus, these drawbacks are in urgent need to address in future works.
G.2 Broader Impacts
Our proposed SRTTA method is capable of improving the resolution of low-resolution test images in real-world applications, resulting in enhanced image clarity and enabling a precise understanding of image content. However, it is important to exercise caution during aggressive TTA adaptation, as this may result in the introduction of artifacts or distortions that have the potential to negatively impact downstream analyses such as microscopy, remote sensing, and surveillance.
kernelGAN+ZSSR DCLS-SR
CLS-SR
kernelGAN+ZSSR
EDSR S
DAN
kernelGAN+ZSSR
DCLS-SR
DAN
kernelGAN+ZSSI
LR
ZSSR
Figure F: Visualization comparison of different methods on real-world test images from DPED [13].
DAN
kernelGAN+Z
(b) Visualization comparisons on OST300 [23] test images.
LR
Figure G: Visualization comparison on real-world test images from for  $2 \times \mathrm{SR}$ .
RealesrGAN
(a) Limitation visualization under Impulse Noise.
Bicubic
KernelGAN+ZSSR
SRDiff
Ground-truth HR
Figure H: Limitations visualization on DIV2K-C test images with degradation for  $4 \times$  SR.
IPT
KernelGAN+ZSSR
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