SlowGuess/NeurIPS_2023_OCR huggingface dataset:
where  $\mathbf{A}_i\in \{\mathbf{A}_j\}_{j = 1}^8$  is an augmentation operation, which is the random combination of a 90-degree rotation, a horizontal and a vertical flip on the input image  $\mathbf{x}_c$ .  $\mathbf{R}_i$  is the inverse operation of  $\mathbf{A}_i$  that rolls back the image  $\mathbf{A}_i(\mathbf{x}_c)$  to its original version  $\mathbf{x}_c$ . With  $\omega (\theta_i^0)$ , we select the most important parameters using a ratio of  $\rho$  and freeze these parameters during the adaptation. The set of selected parameters  $S$  can be formulated as
$$
\mathcal {S} = \left\{\theta_ {i} ^ {0} \mid \omega \left(\theta_ {i} ^ {0}\right) > \tau_ {\rho}, \theta_ {i} ^ {0} \in \theta^ {0} \right\}, \tag {9}
$$
where  $\tau_{\rho}$  denotes the first  $\rho$ -ratio largest value obtained by ranking the value  $\omega(\theta_i^0)$ ,  $\rho$  is a hyperparameter to control the ratio of parameters to be frozen. Note that we only need to select the set of significant parameters  $S$  once before performing test-time adaptation.
5.1 Experimental Details
Testing data. Following ImageNet-C [18], we degraded 100 validation images from the DIV2K [1] dataset into eight domains. We select the eight degradation types that do not extremely change the image content, including Gaussian Blur, Defocus Blur, Glass Blur, Gaussian Noise, Poisson Noise (Shot Noise), Impulse Noise, Speckle Noise, and JPEG compression. In total, we create a new benchmark dataset DIV2K-C, which contains 800 images with different single degradation, to evaluate the performance of different SR methods. Besides, we further construct a dataset named DIV2K-MC, which consists of four domains with mixed multiple degradations, including BlurNoise, BlurJPEG, NoiseJPEG, and BlurNoiseJPEG. Specifically, test images from the BlurNoiseJPEG domain contain the combined degradation of Gaussian Blur, Gaussian Noise and JPEG simultaneously. Moreover, we also evaluate our SRTTA on real-world images from DPED [23], ADE20K [61] and OST300 [50], whose corresponding ground-truth HR images can not be found. To evaluate the anti-forgetting performance, we use a benchmark dataset Set5 [3].
Table 1: Comparison with existing state-of-the-art SR methods on DIV2K-C for  $2 \times$  SR regarding PSNR ( $\uparrow$ ) and inference time (second/image), which is measured on a single TITAN XP GPU. The bold number indicates the best result and the underlined number indicates the second best result.
Method	Gaussian Blur	Defocus Blur	Glass Blur	Gaussian Noise	Poisson Noise	Impulse Noise	Speckle Noise	JPEG	Mean	GPU Time (seconds/image)
SwinIR [29]	30.40	25.52	27.82	25.35	22.36	15.34	30.45	30.74	26.00	13.08
IPT [7]	28.93	24.08	26.39	22.96	20.08	13.06	28.27	28.36	24.02	55.36
HAT [8]	29.00	24.08	26.40	22.31	19.33	11.91	28.02	28.25	23.66	25.01
DAN [21]	34.32	25.58	31.77	26.36	23.28	11.46	30.64	31.08	26.81	3.10
DCLS-SR [34]	33.93	25.55	31.98	25.45	21.59	8.12	30.66	30.86	26.02	1.45
ZSSR [43]	29.91	25.54	27.79	26.79	24.24	19.14	30.95	31.01	26.92	117.65
KernelGAN [15]+ZSSR	30.18	25.87	29.01	21.45	19.32	17.93	25.07	26.11	24.37	231.41
MZSR [45]	30.14	25.54	28.03	25.94	23.48	17.05	30.00	30.49	26.33	3.34
DualSR [12]	29.00	24.40	28.18	22.30	20.11	17.22	24.99	24.74	23.87	210.85
DDNM [51]	28.46	24.09	26.39	24.37	21.92	13.98	28.60	28.26	24.51	2,288.55
EDSR [31]	30.28	25.52	27.82	25.87	22.96	15.87	30.52	30.83	26.21	-
TTA-C	30.21	25.50	27.79	26.37	23.57	16.41	30.25	30.91	26.38	13.59
SRTTA (ours)	31.07	25.86	29.01	29.65	26.69	16.15	32.33	31.30	27.76	5.38
SRTTA-lifelong (ours)	31.07	25.83	29.18	29.48	27.10	16.27	31.71	31.22	27.73	5.38
Implementation details and evaluation metric. We evaluate our approach using the baseline model of EDSR [31] with only  $1.37\mathrm{M}$  parameters for  $2\times \mathrm{SR}$ . To demonstrate the effectiveness of our SRTTA, we conduct experiments in two settings, including a parameter-reset setting and a lifelong setting. In the parameter-reset setting, the model parameters will be reset after the adaptation of each domain, which is the default setting of our SRTTA. In the lifelong setting, the model parameters will never be reset in the long-term adaptation, in this case, we call our methods as SRTTA-lifelong. For the balance weight in Eqn. (6), we set  $\alpha$  to 1. For the ratio of parameters to be frozen, we set the  $\rho$  to 0.50. Please refer to more details in the supplementary materials.
To compare the inference times of different SR methods, we measure all methods on a TITAN XP with 12G graphics memory for a fair comparison. Due to the memory overload of HAT [8] and DDNM [51], we chop the whole image into smaller patches and process them individually for these two methods. To evaluate the performance of different methods, we use the common metrics PSNR [20] and SSIM [20] and report the results of all methods on the DIV2K-C dataset. Due to the page limit, we mainly report PSNR results and put more results in the supplementary materials.
Compared methods. We compare our SRTTA with several state-of-the-art methods including supervised pre-trained SR methods, blind SR methods, zero-shot SR methods, and a TTA baseline method. 1) The supervised pre-trained SR models learn super-resolution knowledge with a predefined degradation process, i.e., the Bicubic downsampling. These methods include SwinIR [29], IPT [7] and HAT [8], and the EDSR baseline [31]. 2) Blind SR models predict the blur kernel of test images and generate HR images simultaneously, e.g., DAN [21] and DCLS-SR [34]. 3) Zero-shot SR models often use a predefined/estimated degradation kernel to construct the LR-HR paired images based on the assumption of the cross-scale patch recurrence [14, 62, 37], and they use the LR-HR paired images to train/update the SR models for each test image. These methods include ZSSR [43], KernelGAN [2] + ZSSR [43], MZSR [9], DualSR [12], DDNM [51]. 4) Moreover, we implement a baseline TTA method (dubbed TTA-C) that utilizes the augmentation consistency loss  $\mathcal{L}_c$  in Eqn. (8) to adapt the pre-trained model, similar to MEMO [57] and CoTTA [48].
We evaluate the effectiveness of our methods in terms of quantitative results and visual results. We report the PSNR results of our SRTTA and existing methods on the DIV2K-C dataset for  $2 \times \mathrm{SR}$  in Table 1 (more results are put in the supplementary materials). Since DAN [21] and DCLS-SR [34] are trained on paired images with Gaussian Blur degradation, they achieve the best results in Gaussian Blur and Glass Blur degradation. However, they merely achieve a limited performance on average due to the ignoring of the noise and JPEG degradations in their degradation model. Moreover, ZSSR [43] achieves state-of-the-art performance on average due to the thousands of iterations of training steps for each image. Though KernelGAN [15] estimates a more accurate blur kernel and helps to generate more plausible HR images for Gaussian Blur and Glass Blur degradation images, it is harmful to the performance of ZSSR [43] on the noise images, since the degradation model of KernelGAN [15] does not cover the noise degradation. Moreover, the baseline TTA-C may be harmful to adapting the pre-trained model to blur degradation due to the simple augmentation, resulting in a limited
Ground-truth HR
DAN
KernelGAN+ZSSR
DDNM
SRTTA(ours)
ZSSR
DualSR
EDSR SRTTA-lifelong(ours)
(a) Visualizations under Gaussian Noise for  $2\times$  SR
Ground-truth HR
(b) Visualizations under JEPG Compression for  $2\times$  SR
Figure 2: Visualization comparison on DIV2K-C test images with degradation for  $2 \times$  SR.
adaptation performance. Instead, our methods achieve the best performance in terms of PSNR on average. For quality comparison, we provide the visual results of our SRTTA and the compared methods in Figure 2. As shown in Figure 2, our SRTTA is able to remove the degradation and reconstruct clearer SR images with less noise or fewer JPEG artifacts.
Comparison of inference time. Moreover, we also compare the inference time of different methods in Table 1. Due to the additional time for test-time adaptation, our SRTTA cannot achieve the best inference speed. However, those methods with less inference time are mostly trained on domains with Gaussian blur degradation only, such as DAN [21], DCLS-SR [34], and MZSR [45], which still suffer from the domain shift issue under noise or JPEG degradation. Instead, with comparable efficiency, our SRTTA achieves an impressive improvement on average for all domains (see results in Table 1). In conclusion, our SRTTA achieves a better tradeoff between performance and efficiency.
More results on test domains with mixed multiple degradations. In this part, we evaluate our SRTTA on DIV2K-MC to further investigate the effectiveness of SRTTA under mixed multiple degradations. In Table 2, our SRTTA achieves the best performance on four domains with different mixed degradations, e.g., 26.47 (ZSSR)  $\rightarrow$  28.48 (our SRTTA-lifelong) regarding the average PSNR metric. These results further validate the effectiveness of our proposed methods.
Evaluation in terms of human eye-related metrics. In this part, we further evaluate different methods in terms of the Fréchet Inception Distance (FID) [19] and the Learned Perceptual Image Patch Similarity (LPIPS) distance [58], which correlate well with perceived image quality and are commonly used to evaluate the quality of generated images [10, 55]. We evaluate different methods on two synthesized datasets, including DIV2K-C and DIV2K-MC. As shown in Table 3, our SRTTA achieves the lowest values of both FID and LPIPS scores, demonstrating our SRTTA is able to generate images with higher visual quality.
5.3 Further Experiments
In this part, we further conduct several ablation studies to demonstrate the effectiveness of each component of our SRTTA. Last, we evaluate our SRTTA on several datasets with real-world test images and provide the visual comparison results of different methods.
Table 2: Comparison with different SR methods on the synthesized DIV2K-MC dataset. We report the PSNR(↑) values of different methods.
Methods	Blur Noise	Blur JPEG	Noise JPEG	BlurNoise JPEG	Mean
SwinIR [29]	20.91	26.83	23.86	22.77	23.59
IPT [7]	21.28	26.83	24.15	22.96	23.81
HAT [8]	23.41	28.86	25.69	24.42	25.59
DAN [21]	24.14	28.95	26.20	24.82	26.03
DCLS-SR [34]	23.84	28.93	26.37	24.92	26.02
ZSSR [43]	24.9	29.02	26.68	25.24	26.47
KernelGAN [2]+ZSSR	23.08	28.32	21.90	22.76	24.02
MZSR [9]	18.73	24.90	20.37	20.62	21.16
DualSR [12]	25.59	28.24	23.78	24.62	25.56
DDNM [51]	22.62	26.82	25.11	23.81	24.59
EDSR [31]	24.02	28.93	26.08	24.73	25.94
TTA-C	24.29	28.93	26.35	24.91	26.12
SRTTA (ours)	26.93	28.93	29.13	27.12	28.02
SRTTA-lifelong (ours)	27.67	29.02	29.70	27.52	28.48
Table 3: Comparison with different methods in terms of  $\mathrm{{FID}}\left( \downarrow \right)$  and LPIPS  $\left( \downarrow \right)$  on both DIV2K-C and DIV2K-MC datasets.
Methods	DIV2K-C
FID / LPIPS	DIV2K-MC
FID / LPIPS
SwinIR [29]	72.90 / 0.2441	60.62 / 0.2781
IPT [7]	68.22 / 0.2345	58.24 / 0.2453
HAT [8]	64.92 / 0.2352	60.73 / 0.2640
DAN [21]	73.59 / 0.2260	56.96 / 0.2263
DCLS-SR [34]	83.44 / 0.2472	57.93 / 0.2299
ZSSR [43]	56.66 / 0.1931	52.78 / 0.2152
KernelGAN [2]+ZSSR	88.28 / 0.2160	80.19 / 0.2371
MZSR [9]	68.27 / 0.2085	162.72 / 0.4463
DDNM [51]	70.80 / 0.2101	59.64 / 0.2083
EDSR [31]	69.70 / 0.2242	57.95 / 0.2338
TTA-C	66.95 / 0.2188	56.32 / 0.2293
SRTTA (ours)	54.37 / 0.1877	36.88 / 0.1915
SRTTA-lifelong (ours)	53.30 / 0.1828	35.72 / 0.1832
Table 4: Effectiveness of components in SRTTA on DIV2K-C.
Method	Avg. PSNR
SRTTA (ours)	27.76
- w/o classifier C(·)	26.06
- w/o Ls	27.15
- w/o La	10.24
Table 5: Effects of different  $\alpha$  (in Eqn. (6)) under parameterreset setting. We report average PSNR  $(\uparrow)$  on DIV2K-C (with degradation shift) and Set5 (w/o degradation shift).
α	0	0.1	0.5	1	2	5
DIV2K-C	10.24	13.96	22.63	27.76	27.52	27.31
Set5	11.42	37.66	37.75	34.59	35.41	35.89
Effect of the degradation classifier  $C(\cdot)$ . To investigate the effect of the degradation classifier, we compare our SRTTA with a baseline that does not use the degradation classifier. Specifically, this baseline generates the second-order degraded images with the random degradation type. In this case, a test image with blur degradation can be randomly degraded with blur, noise, or JPEG degradation. We report the PSRN results of our SRTTA and this baseline in Table 4. Experimental results demonstrate the necessity of the degradation classifier in our second-order degradation scheme.
Effect of  $\mathcal{L}_s$  and  $\mathcal{L}_a$  in Eqn. (6). To investigate the effect of the self-supervised adaptation loss  $\mathcal{L}_s$  and adaptation consistency loss  $\mathcal{L}_a$  in Eqn. (6), we report the mean PSNR results of our SRTTA with  $\mathcal{L}_s$ -only and  $\mathcal{L}_a$ -only. As shown in Table 4, without the adaptation consistency loss  $\mathcal{L}_a$ , the SR models with only the  $\mathcal{L}_s$  will inevitably result in a model collapse. This is because the SR model is prone to output the same output for any input images without meaning. When we remove the  $\mathcal{L}_s$  loss, SRTTA can only achieve a limited performance, which demonstrates that  $\mathcal{L}_s$  truly helps to encourage the SR models to learn how to remove the degradation during the adaptation process. These experimental results demonstrate the effectiveness of the  $\mathcal{L}_s$  and  $\mathcal{L}_a$  in our framework.
Effect of the hyper-parameters  $\alpha$  in Eqn. (6). To investigate the effect of the weight of adaptation consistency loss  $\alpha$  in Eqn. (6), we report the mean PSNR results of our SRTTA with different  $\alpha$  in Table 5. When the  $\alpha$  is too small ( $\alpha < 1$ ), the self-supervised degradation loss  $\mathcal{L}_s$  dominates the adaptation process and often results in the collapse of SR models. When the  $\alpha$  is too large ( $\alpha > 1$ ), the adaptation consistency loss  $\mathcal{L}_a$  may have a great constraint on the adapted SR model to be the same as the pre-trained model, which may be harmful to the adaptation of the SR performance. With  $\alpha = 1$ , our SRTTA achieves the best results on the DIV2K-C dataset on average. Therefore, we simply set the  $\alpha$  to be 1 for all other experiments.
Effect of adaptive parameter preservation in Eqn. (9). In this part, we investigate the effect of our adaptive parameter preservation (APP) strategy on test-time adaptation. We compare our APP with the existing anti-forgetting method Stochastic Restoration (STO) [48], which randomly restores a different set of parameters (1% parameters) after each adaptation step. Moreover, we also compare our APP with the random selection (RS) baseline, which randomly selects a fixed set of parameters to freeze before adaptation. As shown in Table 6, though STO achieves the best anti-forgetting performance on the clean Set5 dataset, the STO severely hinders the TTA performance. The random selection baseline only achieves a limited performance of both TTA and anti-forgetting. Instead, our APP consistently outperforms the random selection baseline with the same ratio of frozen parameters. Moreover, our APP with  $\rho = 0.5$  achieves the best adaptation performance on DIV2K-C (see more
Table 6: Ablation studies of adaptive parameter preservation (APP) strategy on DIV2K-C and Set5 under the lifelong setting. We report PSNR  $(\uparrow)$  and results on DIV2K-C are averaged over 8 different degradation types. The compared stochastic restoration (STO) [48] select  $1\%$  parameters for each adaptation iteration and Random Selection (RS) is evaluated by selecting different  $\rho$  parameters.
Dataset	STO [48]	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	27.52	27.62	27.68	27.72	27.73	27.73
Set5 (w/o degradation shift)	35.57	33.95	34.02	34.24	34.11	34.23	34.38
(a) Visualization results of the image from DPED [23].
(b) Visualization results of the image from ADE20K [61].
Figure 3: Visualization comparison on real-world test images from DPED [23] and ADE20K [61].
results in the supplementary materials), thus we set the ratio of preservation parameters to be 0.5 in our SRTTA by default. These results demonstrate the effectiveness of our APP strategy.
Visualization results on the real-world images. We also provide the visual results of different methods on the real-world images from DPED [23] and ADE20K [61]. We use our SRTTA-lifelong model that has been adapted on DIV2K-C to perform test-time adaptation on the real-world images from DPED [23] and ADE20K [61], respectively. As shown in Figure 3, SRTTA-lifelong is able to generate HR images with fewer artifacts. These results demonstrate that our method is able to be applied to real-world applications. Please refer to more results in the supplementary materials.
In this paper, we propose a super-resolution test-time adaptation (SRTTA) framework to quickly alleviate the degradation shift issue for image super-resolution (SR). Specifically, we propose a second-order degradation scheme to construct paired data for each test image. Then, our second-order reconstruction loss is able to quickly adapt the pre-trained SR model to the test domains with unknown degradation. To evaluate the effectiveness of our SRTTA, we use eight different types of degradations to synthesize two new datasets named DIV2K-C and DIV2K-MC. Experiments on the synthesized datasets and several real-world datasets demonstrate that our SRTTA is able to quickly adapt the SR model for each image and generate plausible high-resolution images.
This work was partially supported by the National Natural Science Foundation of China (NSFC) (62072190), National Natural Science Foundation of China (NSFC) 61836003 (key project), Program for Guangdong Introducing Innovative and Entrepreneurial Teams 2017ZT07X183, and CCF-Tencent Open Research Fund (CCF-Tencent RAGR20220108).
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Supplementary Materials for " Efficient Test-Time Adaptation for Super-Resolution with Second-Order Degradation and Reconstruction
A More Details of the Second-Order Degradation 2
A.1 Random Blur Degradation 2
A.2 Random Noise Degradation 2
A.3 Random JPEG Degradation 2
B The Difference from Real-ESRGAN 2
B.1 Solving Different Problems 2
B.2 Different Construction Schemes 2
C Experimental Datasets 3
C.1 Construction Details of the DIV2K-C Dataset 3
C.2 Construction Details of the DIV2K-MC Dataset 4
C.3 More Test Datasets for Test-Time Image Super-Resolution 5
D Implementation Details 5
D.1 Implementation Details of the Degradation Classifier 5
D.2 More Details of Super-Resolution Test-Time Adaptation 5
E More Experimental Results 6