SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Table 7: Ablation study of the impact of network depth on image enhancement task.
Model	Configurations	LoL
PSNR	SSIM
Original	20.2461	0.7920
SID	+CDC+epochR	20.4750	0.7999
+CDC(3)+epochR+Depth	20.3464	0.7915
+CDC(7)+epochR+Depth	20.4258	0.7857
+INN+epochR	20.3858	0.7924
+INN(3)+epochR+Depth	20.4946	0.7862
+INN(7)+epochR+Depth	20.2816	0.7959
Original	19.8509	0.7769
DRBN	+CDC+epochR	20.0756	0.7837
+CDC(3)+epochR+Depth	19.9188	0.7808
+CDC(7)+epochR+Depth	19.9769	0.7795
+INN+epochR	20.1913	0.7769
+INN(3)+epochR+Depth	20.0330	0.7758
+INN(7)+epochR+Depth	20.1153	0.7787
Table 8: Ablation study of the impact of initialization strategy on image denoising task.
Model	Configurations	SIDD
PSNR↑	SSIM↑
Original	37.1992	0.8954
DnCNN	+CDC+epochR	37.2784	0.8925
+CDC+epochR+xavier	37.2567	0.8963
+INN+epochR	37.3218	0.8964
+INN+epochR+xavier	37.2890	0.8957
Original	39.2372	0.9159
MPRnet	+CDC+epochR	39.2821	0.9161
+CDC+epochR+xavier	39.2768	0.9160
+INN+epochR	39.2729	0.9162
+INN+epochR+xavier	39.2779	0.9160
Table 9: Ablation study of the impact of initialization strategy on image enhancement task.
Model	Configurations	LoL
PSNR	SSIM
Original	20.2461	0.7920
SID	+CDC+epochR	20.4750	0.7999
+CDC+epochR+xavier	20.3271	0.7847
+INN+epochR	20.3858	0.7924
+INN+epochR+xavier	20.3257	0.7927
Original	19.8509	0.7769
DRBN	+CDC+epochR	20.0756	0.7837
+CDC+epochR+xavier	20.0136	0.7760
+INN+epochR	20.1913	0.7769
+INN+epochR+xavier	20.0948	0.7773
Table 10: Ablation studies of model numbers for image enhancement.
Model	Configurations	LoL
PSNR	SSIM	NIQE
Original	20.2461	0.7920	4.1586
SID	+CDC+epochR	20.4750	0.7999	3.6636
+CDC+epochR+Number(357)	20.4879	0.7991	3.6793
+CDC+epochR+Number(555)	20.5424	0.7889	3.7738
+INN+epochR	20.3858	0.7924	3.9210
+INN+epochR+Number(357)	20.3516	0.7843	4.2365
+INN+epochR+Number(555)	20.3316	0.7911	4.1289
Original	19.8509	0.7769	4.7738
DRBN	+CDC+epochR	20.0756	0.7837	4.7850
+CDC+epochR+Number(357)	20.0200	0.7789	4.6900
+CDC+epochR+Number(555)	20.0403	0.7750	4.7060
+INN+epochR	20.1913	0.7769	4.8067
+INN+epochR+Number(357)	20.0510	0.7779	4.6957
+INN+epochR+Number(555)	20.2572	0.7767	4.6169
Table 11: Ablation studies of model numbers for image denoising.
Model	Configurations	SIDD
PSNR↑	SSIM↑
Original	37.1992	0.8954
DnCNN	+CDC+epochR	37.2784	0.8925
+CDC+epochR+Number(357)	37.4377	0.8969
+CDC+epochR+Number(555)	37.3208	0.8948
+INN+epochR	37.3218	0.8964
+INN+epochR+Number(357)	37.3374	0.8937
+INN+epochR+Number(555)	37.3581	0.8944
Original	39.2372	0.9159
MPRnet	+CDC+epochR	39.2821	0.9162
+CDC+epochR+Number(357)	39.2704	0.9161
+CDC+epochR+Number(555)	39.2764	0.9160
+INN+epochR	39.2729	0.9162
+INN+epochR+Number(357)	39.2767	0.9160
+INN+epochR+Number(555)	39.2818	0.9160
Guided Image Super-resolution. Following [39, 40], we adopt the pan-sharpening, the representative task of guided image super-resolution, for evaluations. The WorldView II and GaoFen2 datasets [7, 36] are used for experiments. We employ the representative INNformer [7] and SFINet [36] as the baselines.
For concision, we denote some annotations of the proposed alternative solutions in strict mathematical manifolds before our presentation, and the implementation variants of the baselines are organized as the five configurations:
1) Original: the baseline with the basic loss  $(\mathcal{L}_1$  or  $\mathcal{L}_2)$
2) +Taylor: complementing the basic loss with the Taylor's unfolding network manifold;
3)  $+\mathbf{CDC}$ : complementing the basic loss with the central difference convolution manifold;
4) +INN: complementing the basic loss with the invertible neural network manifold;
5) +Reverse: complementing the basic loss with the reverse filtering network manifold.
3.4 Comparison and Analysis
For quantitative Comparison, we perform the model performance comparison over different configurations. The quantitative results of image denoising, low-light image enhancement, and guided image super-resolution are respectively presented in Table 1, Table 2, and 3. From the results, we can observe performance gain against the baselines across all the datasets in the corresponding tasks, suggesting the effectiveness of our approach. For example, in terms of image enhancement, the baseline DRBN with “+Taylor”, “+CDC”, “INN” and “Reverse” has obtained the 0.4dB, 0.3dB, 0.2dB, 0.2dB PSNR gains over LoL dataset respectively.
Figure 5: The ablation studies: 1) initialization strategy, 2) model architecture, 3) model depth and 4) model numbers.
To verify the stability of our approach, we conduct the following analysis from four aspects: 1) initialization strategy, 2) model architecture, 3) model depth, and 4) model numbers.
Model architecture. In the previous experiments, all of the random weight networks are implemented by convolution networks as default. To explore the impact of network structures, we replace the default CNN with Transformer. The results in Table 4 and Table 5 demonstrate that replacing the network rarely affects performance.
Model depth. For model depth, we change the model depth of the random weight network by adding more layers. To ensure a fair comparison, other factors keep the same. The results in Table 6 and Table 7 further demonstrate the stable and robust performance gains by introducing our designs.
Initialization strategy. In our work, the default initialization strategy is Kaiming initialization. To ex
plore the impact of the initialization mode, we replace the default Kaiming initialization with Xavier initialization. Table 8 and Table 9 show that replacing the default initialization mode almost has little impact on the performance.
Model numbers. In our experiment, we use the single loss network as default and employ multiple parallel loss networks to verify the impact of model numbers. The results in Table 10 and Table 11 indicate that increasing the number of models will improve the performance. It attributes to the advantages of model ensemble.
In this paper, we explore the potential of optimization functions and present our insight that "random weight networks can serve as a constraint for training improved image restoration networks." Drawing inspiration from Functional theory, we offer several alternative solutions within strict mathematical manifolds, known as "random weights network prototypes." Our approach seamlessly integrates into existing image restoration networks, and extensive experiments across multiple tasks validate its effectiveness. While our experiments are extensive, limitations in space prevent us from conducting more comprehensive evaluations, such as including experiments on image de-blurring and additional representative baselines.
Our work demonstrates the potential of random weight networks as optimization functions for low-level image restoration tasks, with applications in mobile photography, healthcare, entertainment, and other fields that rely on high-quality images. We observe no apparent negative societal consequences. While our experiments show significant performance improvements, additional real-world testing and validation are necessary to ensure robustness and generalizability.
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