Training Your Image Restoration Network Better with  Random Weight Network as Optimization Function
Authors: Man Zhou
Naishan Zheng
Yuan Xu
Chun-Le Guo
Chongyi Li
Venue: NeurIPS 2023 poster (2023)
Keywords: Image restoration
low-light image enhancement
image de-noising
TL;DR: This is a first time attempt to investigate the potential of ``Random Weights Networks can Be Acted as Loss Prior Constraint for Image Restoration''.

Abstract: The blooming progress made in deep learning-based image restoration has been largely attributed to the availability of high-quality, large-scale datasets and advanced network structures. However, optimization functions such as L_1 and L_2 are still de facto. In this study, we propose to  investigate new optimization functions to improve image restoration performance. Our key insight is  that ``random weight network can be acted as a constraint for training better image restoration networks''. However, not all random weight networks are suitable as constraints. We draw inspiration from Functional theory and show that alternative random weight networks should be represented in the form of a strict mathematical manifold. We explore the potential of our random weight network prototypes that satisfy this requirement:  Taylor's unfolding network, invertible neural network, central difference convolution, and zero-order filtering. We investigate these prototypes from four aspects: 1)   random weight strategies, 2)  network architectures, 3)   network depths, and 4) combinations of random weight networks. Furthermore, we devise the random weight in two variants:  the weights are randomly initialized only once during the entire training procedure, and  the weights are randomly initialized in each training epoch. Our approach can be directly integrated into existing networks without incurring additional training and testing computational costs. We perform extensive experiments across multiple image restoration tasks, including image denoising, low-light image enhancement, and guided image super-resolution to demonstrate the consistent performance gains achieved by our method.  Upon acceptance of this paper, we will release the code.

Training Your Image Restoration Network Better with Random Weight Network as Optimization Function
Man Zhou'
Naishan Zhenglo 1.2
Yuan Xu
Chunle Guo Chongyi Li
S-Laa, Nanyang Technological University 2 University of Science and Technology of China, China Nankai University, China
man. zhou@ntu..utmmmmm edu. 1ichongyi25dgail.. com
Abstract
The blooming progress made in deep learning- image restoration has been largely attributed to the availability of high-quality, large-scale datasets and ad- vanced network structures. However, optimization functions such as L1 and Le are still de facto. In this study, we propose to investigate new optimization functions improve image restoration performance. Our key insight is that "random weight network can acted as constraint for training better image restoration networks". However, not all random weight networks are suitable as constraints. We draw inspiration from Functional theory and show that alternative random weight net- works should be represented in the form of strict mathematical manifold. We explore the potential our random weight network prototypes that satisfy this requirement: Taylor's unfolding network, invertible neural network, central differ- ence convolution, and zero-order filtering. We investigate these prototypes from four aspects: 1) random weight strategies, 2) network architectures, 3) network depths, and 4) combinations random weight networks. Furthermore, we devise the random weight in two variants: the weights are randomly initialized only once during the entire training procedure, and the weights are randomly initialized each training epoch. Our approach can be directly integrated into existing networks without incurring additional training and testing computational costs. We perform extensive experiments across multiple image restoration tasks, including image denoising, low-light image enhancement, and guided image super-resolution to demonstrate the consistent performance gains achieved by our method.
Introduction
Image restoration challenging task that involves recovering latent clear image from given degraded observation. This task is highly ill-posed as there are infinite feasible results for a single de- graded image 2 Researchers have tackled this problem through two main approaches: traditional
optimization methods 4,4 and deep learning-based methods [2] 6 77.
Traditional methods formulate image restoration as optimization problem and various image priors to regularize the solution space of the latent clear image, such as low-rank prior 4 [),, dark
channel prior 8 9 [0], graph-based prior [12) total variation regularization [3 [4] and sparse
image priors 15 [6 However, these priors require carefully designed priors and involve iteration
optimization, making them computationally expensive.
In recent years, deep neural networks (DNNs) have shown promising results in image restoration tasks [7 18] These methods have three key components: data, model, and optimization function.
corresponding author.
37th Conference on Neural Information Processing Systems (NcurIPS 2023).

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Distribution Sampling
Random
Initialization
Task-speoific Model
cre-quallty Emage
Restored Image
F0o0 x0)
Hou tlas
Loss
MMxct dest + th
Your Win oue
Ground Truth Image
Loss
Prior Network
F Qty
Y1 X1 F(x2) y/2 X2 G(y))
Mathematical Manifolds
x=
F(y
Taylor's Manifolds
Invertible Manifolds
The flowchart of "Random Weight Networks Optimization Prior for Image Restoration". In detail, the output the task-specific model the ground truth are respectively fed into the random weight network to constrain the restoration network training, where the random weight network is required to satisfy a strict mathematical manifold, and its weights are randomly initialized.
Figure I:
While significant effort has been devoted to collecting high-quality and large-scale datasets and designing advanced network structures, the L1 and L2 losses remain the de facto optimization functions. In this study, we explore the potential of using random weight networks as a constraint for training better image restoration networks. By incorporating a random weight network during the training process, we aim to encourage the network to learn more robust features and produce better results. This approach may help to overcome some of the limitations of traditional and deep learning- based methods for image restoration.
constraint
Related Work. In terms of the prior loss function studies, the representative dual regression scheme for image super-resolution task in the form loss regularization term. This method introduces additional constraint on low-resolution data to reduce the space of the possible image super-resolution solutions. Similar to the loss regularization function, CycleGAN framework 21 22 23 exploited two sets of parallel generative adversarial networks formulate the image restoration function and the image degradation mechanism respectively where the corresponding cycle mechanism is modeled in the loss function by the form of regularization term. addition, this work [24] explored the Range-Null space decomposition to enable the relationship between realness and data consistency, and the consistency constraint is transferred into loss function. Despite the remarkable progress, the first two have been trained in a delicate manner while the remaining one only works on the particular forms of known degradation matrix. These issues leave room further study the potential of loss function for image restoration.
20 customized
In Figure D. we show the flowchart of random weight network as optimization prior to train an image restoration network, where the random weight network is treated as an optimization function without incurring additional training and testing computational costs. Despite the succinet idea, there still exists a question "whether any network architecture with random weights can be used as optimzation function?". With this question, we propose our analysis and solution. Specifically, we stand on the Functional theory and show that alternative random weight networks should be represented in the form of a strict mathematical manifold. We explore the potential of our random weight network prototypes that satisfy this requirement: Taylor's 's unfolding network, invertible neural network, central difference convolution, and zero-order filtering. We investigate these prototypes from four aspects: 1) random weight strategies, 2) network architectures, 3) network depths, and 4) combinations of random weight networks. Based on the above settings, we employ the random weight networks optimization functions to better optimize the task model in the following two variants: 1) the weights are randomly initialized only once during the entire training procedure, and 2) the weights are randomly initialized in each training iteration epoch. The illustration of random

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Epoch
Epach n
Sumple
Suaple
Model, 81
Moddl, 0g
Traming Sert
Raich Imsutts
Cutrue
Toiiiin Set
Ratch Imaqpce
Cuipes
Random
Random Initialization
Initialization
Loss, Pg
Loss, 9g
(a) randomly initializing only onee
(b) randomly initializing cach training epoch
Figure 2: Random Weight Strategies: (a) the weights randomly initialized only once during the entire training procedure; (b) the weights are randomly initialized in each training itcration epoch.
weights strategies is shown in Figure Our approach is verified over the representative baselines across multiple image restoration tasks including image denoising, low-light image enhancement, and guided image super-resolution and the extensive experimental results demonstrate its effectiveness.
To summarize, we make the following key contributions. 1) the first attempt to propose the insight that "random weight network can be acted constraint for training better image restoration networks". Our insight would spark the studies of optimization functions for image restoration. 2) Orthogonal to the existing data and model studies conducted in the field of deep toaring--bssed image restoration, our proposed approach is a plug-and-play, thus improving image restoration performance without changing the original model and data configurations. 3) Our approach improve the performance of multiple image restoration tasks without incurring additional training and testing computational costs.
Methodology
In this section, we will first introduce the prior image restoration optimization flowchart and discuss the limitation of current optimization functions. then detail the alternative random weight networks as optimization functions and show their feasibility. At last, present the random weights initialization strategies.
2.1 Image Restoration Flowchart
Suppose that the restoration task model as S(X) that transforms input image x to the output V the restoration process can be written
y f(X),
Suppose that the ground truth as GT, the commonly used optimization function egg, C1 or L2 can be written as
L = I|GT - 1
where ||-111,2 is the image-level Lı La loss.
Discussion. From the Bayesian perspective, it is well known that minimizing L1 or L2 can be equivalent to maximum likelihood estimation in regression. The prediction of regressor can be treated as the mean of a noisy prediction distribution, which modeled as a Gaussian or Laplace distribution in the classic probabilistic interpretation:
L2 p())X; 0) (NGGT; 2, I);
C P()X: 8) L(GT,),,)) b).
(4)
where Gnaise the scale of an i.i.d. error term e ~ (O, -2 go and b / / real distribution is more complex, making the model optimization difficult and pushing the model prediction biased. To solve this issue, we propose to customize the additional network as loss prior regularization term to better constrain the output close to the ground truth distribution.
However,

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2.2 Random Weight Network Manifold
In this study, we found that only random weight networks adhering specific mathematical manifold are suitable as optimization functions. To meet this requirement, we propose alternative random weight networks: Taylor's Unfolding Network. Invertible Neural Network, Central Difference Convolution, and Zero-order Filtering.
Taylor's Unfolding Network Manifold in Figure we leverage Taylor's unfolding (25) to formulate the manifold that is oriented towards decomposition
Drawing inspiration from image decomposition,
y = TX
(5)
where we denote the observation, latent clear image, transformation matrix, and error term V X, T, and N, respectively.
Let 3o- TX y - N, we learn X by the function F
x F(O) =F(Y- N).
N).
(6)
When only regarding n order Taylor's approximations, can be simplified as
F*F
X =
(7)
Jky
Recalling Equation for the l order derivative part, it can be written as
F*())+ = J² F²)(
(8)
Oky
To achieve this objective, employ Derivative function sub- network denoted as G, which operates in the aforementioned process. The kth order output of network G is represented as F= ()))** and conveniently recorded as yout Pout = Gl + k- Your
By combining the aforementioned two operational steps, can obtain the final output of the rith order deep Taylor's approximations framework as follows:
= =())
Σ ==1
k! Pout
(10)
Invertible Neural Network Manifold in Figure 3 Drawing inspiration from image transformation techniques such as Fourier transform and wavelet transform, we can designate the aforementioned invertible transformation as:
=x
(11)
where T is the wavelet function for wavelet transform while representing the Trigonometric basis for Fourier transform.
To capture the general invertible manifold, the fundamental units divide the input into Ii and ø2- Reversible blocks receive (X1, X2) and generate outputs (D/.3/) using additive coupling rules inspired by NICE's transformation [26] 27 28), as demonstrated in Figure righht):
> X1 + F(X2),
)/2 = X + 9(2)).
(12)
Central Difference Convolution Manifold Figure deep networks, the vanilla 2D convolution
a fundamental operator with two steps: 1) sampling, selecting local neighbor region R from input feature map æ;; and 2) aggregating, combining sampled values with learnable weights w. This process formulates the output feature map y
(po) Σ w(p)) X(po + Pa).
(13)
P.ER
Here, Po represents the current location both input and output feature maps, while pv, iterates over locations R. For example, convolution operator with 3x3 kernel and dilation 1, the local receptive field region is defined as R {(-1, -1),,,1), (-1,)), .,,, 1), 11)

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X2
1
Y/2
Mapping Function
Derivative Function
(F
Lea y)
X1
31
(a) Forward Process
x
x1
X.
X2
Y/2
F(Y)
Ya
F"(y
yal
FY0 Yol"
11
21
X1
Y1
Fau Bust
(b) Reverse Process
Taylor Framework's manifold
Invertible Network's manifold
Figure 3: The functional manifolds of deep Taylor's approximations framework (left) and invertible neural network (right).
Contrary to the vanilla convolution, the central difference convolution incorporates central gradient features to augment the representation and generalization capabilities. This can be formulated as:
Y(p)) = Σ w(p)) (X(po + pr.) X(po)).
(14)
PRER
Reverse Filtering Network Manifold inspired by [29] in Figure 4 Definition. Let (H, d) be a metric space, and T: : H - H be mapping function. For all x, y E H. if there exists constant e E [0, 1) such that the following formula holds:
d(T(x), T(y)) c. <c-d(x,))
(15)
mapping T : > H is called Contraction Mapping.
Theorem-l. Given a function 4 H H. variable x" considered a fixed point (x=) is a contraction mapping, it guarantees the existence of unique fixed point x' in H. Moreover, the fixed point x" can be determined using the the following iterative process. the initial guess be do and define sequence { } such that I., = =(Znn1). As the iterative process converges, we have lim,-+00 2n =x.
Reverse Filtering. The function F(.) can be viewed as a set of versatile filters used for image smoothing. This filtering process can be described as y F(X), where X represents the input image and y represents the filtering result. By performing reverse filtering, we can estimate X without explicitly computing F F-) and update the restored image based on the filtering effect, resulting in:
xk+1 x* + --xF((*),
(16)
Here, X represents the current estimation of in the k-th iteration. The iteration begins with X = ), and as the iteration count & increases, X gradually approaches the true X. To facilitate this process, we introduce the auxiliary function ip(-) as: (XX) x +
- F(X). Therefore, the above
iterative process can be regarded fixed point iteration
X (
(17)
In Figure right), the filtering process F(.) is realized using the Multi-scale Gaussian Convolution Module, which satisfies the necessary condition outlined in Theorem-1. Specifically, taking (21(t) (-) as an example, the sufficient condition for Theorem to hold is that 4i (H) constitutes a contraction mapping
| (H,) P1 (Ha)l
H + - (H.)) H, +1 (H,)
(18)
|H, f (H.)) - [H, f (H&) < c- H. - Ha] For linear filters, the condition further simplified as
H f(H]] < H (0.
(19)
5

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x
Sanpiiigg
x²
Festure Mapt
Gaussian kernel
Agoragation
fb
f()
f()
f()
Sunpping
f(x")
f(x1)
f(x))
Central Difference's manifold
Reverse Filtering's manifold
Figure 4: The functional manifolds of deep central difference convolution (left) and reverse filtering network (right).
2.3 Random Weight Strategies
Based on the above settings, we employ random weight networks as optimization functions to better optimize the image restoration models. In Figure we present the following two variants for the random weights initialization:
(1) the weights are randomly initialized only once during the entire training procedure, (2) the weights are randomly initialized in each training iteration epoch, denoted as "epochR";
We also discuss their effects in the experiment part.
2.4 Optimization Pipeline
Suppose that the randomly initialized manifold model as frandom (-), employed as the comple- mentary loss function to the original image-level loss function. The total loss function is remarked as
L GT yll1,2 + Al]Srandoo (GT) frandom (1),,
(20)
where À indicates the weighted factor, ||.||2,2 is the Lı or L2 loss, and GT denotes the ground truth.
3 Experiments
To demonstrate the efficacy of our proposed approach, we conduct extensive experiments on multiple image restoration tasks, including image denoising, low-light image enhancement, and guided image super-resolution. We provide more experimental results the Appendix.
3.1 Experimental Settings
Image Enhancement. We verify our approach on the image enhancement benchmarks, LOL Further, we adopt representative SID 31 and DRBN 32 as two baselines.
30
as the training benchmark. Further, the corresponding performance evaluation conducted on the remaining validation samples from the SIDD dataset. Two representative image denoising algorithms DnCNN 33 are selected as the baselines.
Image Denoising. Following 33 we employ the widely-used SIDD dataset 34
351 and MPRnet
Guided Image Super-resolution. Following 7 36], we adopt the pan-sharpening, the representative task of guided image super-resolution, for evaluations. The WorldView II and GaoFen2 datasets 36 are used for experiments. We employ INNformer 7 and SFINet [36] as the baselines.
Several widely-used image quality assessment (IQA) metrics are employed to evaluate the perfor- mance, including the relative dimensionless global error in synthesis (ERGAS) 37 PSNR, the spectral angle mapper (SAM) (38), SSIM.

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Table Quantitative comparison of different Table 2:
Quantitative comparison of different random weight networks with different random weight initialization strategies image enhance- ment task.
random weight networks with different random weight initialization strategies on image de-noising task.
SIDD
LOL
Model
Configurations
Model
Configurations
PSNR
SSIM
PSNR
SSIM
Original
37.1992
0.8954
Original
20.246
0.7920
+Taylor
37.3163
0.8955
+Taylor
20.5864
0.7971
+Taylor+epochR
37.3719
0.8954
+TaylortepochR
20.6018
0.7975
+CDC
37.2329
0.8958
+CDC
20.3298
0.7927
DrCNN
+CDC+epochR
37.2784
0.8955
SID
+CDC+epochR
20.4750
0.7999
+INN
37.3168
0.8970
+INN
20.3178
0.7944
+eNN+epochR
37.3318
0.8964
+ +NNN+epochR
20.3958
0.7924
+Reverse
37.3162
0.8965
+Reverse
20.5014
0.7941
+Reverse+epochk
37.3321
0.8955
+Reversc+epochh
20.5203
0.7943
Original
39.2372
0.9159
Original
19.8509
0.7769
+Taylor
39.2953
0.9161
+ +Taylor
20.1156
0.7778
+Taylor+epochR
39.3283
0.9161
+ +Taylor+epochR
20.2405
0.7791
+CDC
39.2609
0.9160
+CDC
19.7952
0.7851
MPRnet
+CDC+epochR
39.2821
0.9161
DRBN
+CDC+epochR
20.0756
0.7837
+INN
39,2729
0,9162
+INN
19.8543
0.7774
+NNN+po
39.3317
0,9162
+ INN++pochR
20.1913
0.7769
+Reverse
39.2446
0,9160
+ Revverse
19.9547
0.7765
+Roverse+epochk
39.2660
0.9161
Reverss+eppochR
20.1358
0.7751
Table 3: Quantitative comparison of different random weight networks on the guided image super-
resolution task.
WorldView-1 -Il
GaoFen2
Model
Configurations
PSNRT
SSIM
SAMI
ERGAS
PSNRT
SSIM
SAM
EGASJ
Original
41.6903
0.9704
0.0227
0.9514
47.3528
0.9893
0.0102
0.5479
+Taylor
41.8168
0.9716
0,0224
0,9276
47.4058
0.9901
0.0101
0.5356
INNformer
+CDC
41,8072
0.9715
0.0224
0.9276
47.4121
0,9902
0.0100
0.5354
+INN
41.8229
0.9717
0.0223
0.9276
47.4233
0.9904
0.0100
0.5353
+Reverse
41.7293
0,9711
0.0226
0,9276
47.4010
0.9901
0.0101
0,5354
Original
41.7244
0.9725
0.0220
0,9506
47.4712
0.9901
0.0102
0.5462
+Taylor
41.9314
0,9723
0.0219
0,9278
47,6132
0.9911
0.0101
0.5277
SFINet
+CDC
41.8943
0.9719
0.0220
0.9283
47.5990
0.9910
0.0101
0.5281
+INN
41.9521
0.9727
0,0217
0,9278
47,6316
0.9916
0.0101
0.5275
+Reverse
41.9217
0.9722
0.0218
0.9281
47.6227
0.9914
0.0101
0.5275
Table 4: Ablation study of the impact of network Table Ablation study of the impact network architecture on image denoising task.
architecture image enhancement task.
LoL
Model
Configurations
Model
Configurations
PSNR
SSIM
PSNR
SSIM
Original
37.1992
0.8954
Original
20.2461
0.7920
+ TTyloor-epochi
37.3719
0.8954
TaylortepochiR
20.6018
0.7975
DrCNN
+ Calaar-eppoch--Taanffeeee
37.3560
0.8958
SID
TaylortepochR-Traeee Transfomerr
20.5864
0.7971
INN+epochR
37.3318
0.8964
+ INN+epochR
20.3958
0.7924
ANN4eepchiR--Trasffor
37.3297
0.3961
-NNNepochl-Trannoome
20.3178
0.7944
Original
39.2372
0.9159
Original
19.8509
0.7769
+Taylor+epochIR
39,3283
0.9161
TaylortepochR
20,2405
0.7791
MPRnet
0.9160
T Transfforrre
20.1826
0.7784
+NNNeppcchR
0.9162
+ -NN+eppchaR
20.1913
0.7769
LINNeepochR--Trasfoor
39,2756
0.9159
20.1196
0.7772
3.2 Experimental Settings
Image Enhancement. We verify our approach on the image enhancement benchmarks, L.O..
Further, we adopt representative SID [1] and DRBN 32 two baselines.

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Table 6: Ablation study of the impact of network Table 7: Ablation study of the impact of network depth on image denoising task.
depth on image enhancement task.
Model
Configurations
SIDD
Model
Configurations
Lol.
PSNR
SSIM
PSNR
SSIM
Original
37.1992
0.8954
Original
20.2461
0.7920
+DC+eepochR
37.2784
0.8955
+CDC+epochR
20,4750
0.7999
37.2218
0.8921
20.3464
0.7915
DrCNN
37.2923
0.8930
20,4258
0.7857
INNtepochR
37.3218
0.8964
+INN+epochR
20.3858
0.7924
+NNGG)+<pochRR4Deppl
37,3213
0.8967
+INNG3)+epochR+DDppp
20.4946
0.7862
+INNT)HepochR++eppll
37.3142
0.8967
+NNN(7>+epccRR+Deelh
20.2816
0. 0.7959
Original
39.2372
0.9159
Original
19.8509
0.7769
+CDC+<pochR
39.2821
0.9161
+CDC+<pochR
20.0756
0.7837
+ DepohRReeot
39.2814
0.9160
DRBN
+CDDC(3)<ppccRR-Deept
19.9188
0.7808
MPRnet
+ +CDDCT7)
39.2740
0.9161
+CDCC7)+epcchR+Depll
19.9769
0.7795
+NN+epochR
39.2729
0.9162
+eNN+epochR
20.1913
0.7769
39.2758
0.9160
+NNN Depp
20,0330
0.7758
+DNN
39.2737
0.9160
+INN(TH+@pocuRR-Depphh
20.1153
0.7787
Table 8: Ablation study of the impact of initializa- Table 9: Ablation study of the impact of initializa- tion strategy image enhancement task.
tion strategy on image denoising task.
Model
Configurations
SIDD
Model
Configurations
LoL
PSNR1
SSIM
PSNR
SSIM
Original
37.1992
0.8954
Original
20.2461
0.7920
+CDC+epochR
37.2784
0.8925
+CDC+epochR
20.4750
0.7999
DnCNN
+CDC+epochR+xavierr
37,2567
0.8963
SID
+CIDCeqpochR-xxvin
20.3271
0.7847
+NN+eepohhR
37.3218
0.8964
+NN+epoohhR
20.3858
0.7924
+NNN+epochR-xavierr
37,2890
0.8957
-NNNeepochR-xavier
20.3257
0.7927
Original
39.2372
0.9159
Original
19.8509
0.7769
+CDC+epochR
39.2821
0,9161
+CDC+epochR
20.0756
0.7837
MPRnet
+CDC+epochR+xavier
39.2768
0.9160
DRBN
+CD+repoch+*xavve
20.0136
0.7760
+NNN+epochR
39.2729
0,9162
+NN++ppocRR
20.1913
0.7769
39.2779
0.9160
+NN+epoocR-xxavier
20.0948
0,7773
Table 10: Ablation studies of model numbers for Table 11: Ablation studies of model numbers for image enhancement.
image denoising.
Model
Configurations
Lol.
Model
Configurations
SIDD
PSNR
SSIM
NIQE
PSNR
SSIM
Original
20.2461
0.7920
4,1586
Original
0.8954
-CDC+epuchR
+CDC+epochR
37.2784
0.8925
SID
CDDC=spoclRRNNumberr
20.4879
0.7991
3.6793
DECNN
+CDCCeepccRR-Numbeer
37.4377
0.8969
4TCC=ppahlR+NNumki5555
20.5424
0.7889
3.7738
CCDCAepochR-Numberre.
37,3208
0,8948
-NN+epochRR
20.3858
0.7924
3,9210
+NNN+ppohhR
37.3218
0.8964
(NN4epcchR-Numnss55557
WWNN+epochR-Numbe(335))
37.3374
0.8937
(NN4gpcalR-Nunkor(555
20.3316
0.7911
4.1289
-INNeepchR--Mumher(55)
37.3581
0.8944
Original
19.8509
0.7769
4,7738
Original
39,2372
0.9159
CDCCepacchR
20.0756
0.7837
4.7850
+CDC++epoch
39.2821
0.9162
DRBN
CDDC<ppchBB-Nummlat3377
MPRnet
+CDC+epochR-Numberree
39,2704
0,9161
CDCCspuchR-NNumler555)
20.0603
0.7750
4,7060
ACTXCHepccR-NNumeer5555
39.2764
0.9160
-NN+epocchR
20.1913
0.7769
4,8067
+INN+epochR
39.2729
0.9162
INNrepchaR-Numker33377
20.0510
0.7779
4.6957
39,2767
0.9160
(NNNepocaR--Mumeer55555
-INNeepocRR-
39.2818
0.9160
Image Denoising. Following [33] we employ the widely-used SIDD dataset 34 as the training benchmark. Further, the corresponding performance evaluation is conducted on the remaining validation samples from the SIDD dataset. Two representative image denoising algorithms DnCNN 355 and MPRnet
33 are selected as the basclines.

---

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 and SFINet [36] as the baselines.
3.3 Implementation Details
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 L1 or L2);
2) Taylor: complementing the basic loss with the Taylor's unfolding network manifold:
3) +CDC: complementing the basic loss with the central difference convolution manifold;
4) +INN: complementing the basic loss with the invertible neural network manifold;
5) + Reverss:: 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 con- figurations. The quantitative results of image denoising, low-light image enhancement, and guided image super-resolution are respectively presented Table Table and 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.
4
Ablation Studies
To verify the stability of our approach, we conduct the following analysis from four aspects: initialization strategy, 2) model architecture, 3) model depth, and 4) model numbers.
Initielization Stratogy
Nasiec Initalizztinn
Model architecture. In the previous experiments, all of the random weight networks implemented by convolution networks as default. To explore the impact of network structures, we replace the default CNN with Transforner. The results in Table 4 and Table 5 demonstrate that replacing the network rarely affects performance.
Teansfeenc
Architecture
Depth
Kaimise
Inllialaation
Model depth. For model depth, change the model depth of the random weight network by adding more layers. To ensure fair comparison, other factors keep the same. The results in Table 6land and Table fur- ther demonstrate the stable and robust performance gains by introducing our designs.
Paratlel
Figure 5: The ablation studies: 1) initializa- tion strategy, 2) model architecture, 3) model depth and 4) model numbers.
Initialization strategy. In work, the default ini- tialization strategy Kaiming initialization.. To ex- plore the impact of the initialization mode, replace the default Kaiming initialization with Xavier initialization. Table g and Table 9 show that replacing the default initialization mode almost has little impact the performance.
Model numbers. our experiment, we use the single loss network as default and employ multiple parallel loss networks 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. attributes to the advantages of model ensemble.

---

Conclusion and Limitation
In this paper, we explore the potential optimization functions and present our insight that "random weight networks can serve 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.
Broader Impact
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 experiments show significant performance improvements, additional real-world testing and validation are necessary to ensure robustness and generalizability.
10

---

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13


Reviews:
[{"review_id": "6UNJfqdoKN", "reviewer": "Reviewer_d53F", "summary": "This paper explores the notion of using random weight networks as a constraint during the training process for image restoration. This approach aims to encourage the network to learn more robust features and produce better results, addressing the limitations of traditional optimisation methods and deep learning-based methods. By incorporating the random weight network as a constraint, the authors validate the approach towards improving image restoration performance.", "questions": "Kindly address the comments raised in weakness section", "limitations": "The authors have addressed the limitations arising from space but not the limitation of their methodology, which was the original objective.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The authors provide sufficient theoretical insights behind the formulation of using a randomly initialised network as an auxiliary loss function during the optimisation process. \n\n2. The ablation studies are elaborate and cover a wide variety of initialisation configurations and examine its effect on final restoration performance.", "weaknesses": "1. Experimental Setting section is repeated \n\n2. The proposed approach is similar to [1, 2, 3] and without discussion on differences, the contribution of the proposed work is weak. Specifically identification of different distributions and its impact on final restoration performance. \n\n3. The authors should discuss the impact of utilising multiple network architectures on the overall training period as well as memory requirements. \n\n4. The impact of initialisation distribution should be discussed, which is missing. Furthermore in the qualitative results the authors should also provide corresponding input and ground truth images for easier evaluation. \n\n5. While the authors evaluated the impact of network structures by replacing the CNN with transformer architectures in ablation. Other configurations such as using transformer based restoration networks and implications of using a lightweight optimisation network aren't considered. These ablations are necessary to identify the overall implication of using different strategies during optimisation.\n\n\n[1] Gallicchio, Claudio, and Simone Scardapane. \"Deep randomized neural networks.\" Recent Trends in Learning From Data: Tutorials from the INNS Big Data and Deep Learning Conference (INNSBDDL2019). Springer International Publishing, 2020.\n\n[2] Herrera, Calypso, et al. \"Optimal stopping via randomized neural networks.\" arXiv preprint arXiv:2104.13669 (2021).\n\n[3] Tarvainen, Antti, and Harri Valpola. \"Mean teachers are better role models: Weight-averaged consistency targets improve semi-supervised deep learning results.\" Advances in neural information processing systems 30 (2017).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**1, typos.**\n\nThanks for highlighting the issue! We'll thoroughly review the entire paper and correct all typos and grammar errors.\n\n**2, differences to other works.**\n\n1) Our method centers on designing the loss function, initially employing a random weights network with a strict mathematical manifold as a loss constraint, inspired by Functional theory. In contrast, the suggested works aim to explore a suitable subnet within the random network, known as ticket theory, to function as the working network. This leads to a distinction: our proposed random network serves the loss function, while theirs serves as a feed-forward network. Theoretical assurance for our approach is straightforward due to its strict mathematical foundation.\n\n2) As per your suggestion, we will incorporate a detailed discussion of the differences to enhance the content.\n\n3) Our work delves into identifying various distributions, as discussed in Tables 8 and 9.\n\n**3, memory requirements.**\n\nInitially, we explore the effects of employing diverse network architectures on training duration in our supplementary materials. Moreover, all random weights networks in our study are lightweight; specifics are outlined in the supplementary materials. Consequently, the utilization of multiple network architectures introduces minimal and inconsequential memory demands throughout the training process.\n\n**4, initialization distribution.**\n\nInitially, we address the initialization distribution impact, as demonstrated in Table 8 and Table 9 with analysis in the ablation studies section. Furthermore, we'll heed your advice to include input and ground truth images for qualitative results.\n\n**5, network structures.**\n\nAll our random weights networks are lightweight; see supplementary materials for detailed configurations. For model depth, specific experiments are in Table 6 and Table 7. In the transformed-based approach, we validate our claim using the INNformer model and its results. Additionally, due to time constraints, we tested the effectiveness of SWINIR for image denoising, as shown in the subsequent table.\n\n\n\n|dataset|SWINIR  |    +Taylor  |   +INN    |  +Zerofilter |\n|----|----|----|----|----|\n|Set12      |     31.01   |    31.22  |   31.29    | 31.27 |\n|BSD     |       29.50   |    29.63   |   29.67  |   29.65 |\n"}, {"review_id": "nPKUOUnxTD", "reviewer": "Reviewer_UxgD", "summary": "This paper introduces the idea that random weight networks can be used as loss functions for training image restoration networks. The paper proposes to use Taylor’s Unfolding Network, Invertible Neural Network, Central Difference Convolution, and Zero-order Filtering as random weight networks. The analysis and ablation studies show the effects of initialization strategy, model architecture, model depth, and model numbers. Experiments on image enhancement, image denoising, and guided image super-resolution validate that the proposed loss functions improve the performance of several existing image restoration methods.", "questions": "Please see the weaknesses section.", "limitations": "The paper does not mention any limitations of the proposed method. I believe some discussions on the perceptual quality are necessary since the quantitative improvements are limited and the visual results in the supplementary materials have negligible difference.", "rating": 4, "confidence": 5, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "+ The idea of using random weight networks as image restoration loss functions is interesting.\n+ The quantitative evaluation is performed on several image restoration tasks.\n", "weaknesses": "- The paper has a major technical flaw. The abstract states that the proposed loss functions do not incur additional training computational cost. This is unreasonable because the gradients of these loss functions require additional computation cost. To be effective, the proposed loss functions must be used in conjunction with a pixel loss and are more complex than the pixel loss. It consumes more GPU memory and time during training. The paper should report the additional training cost or the extra training time.\n- The quantitative improvements are not significant. From Table 1 to Table 9, the proposed loss functions have limited impact on the PSNR and SSIM results. For example, MPRNet is a representative denoising method, but its PSNR gain is less than 0.1 dB. In addition, the paper reports MPRNet achieves 39.24 dB on the SIDD dataset, which is far behind the PSNR result of 39.71 dB in the original paper of MPRNet. I suspect that this paper does not train MPRNet to convergence, and it is unreasonable to compare different loss functions without full convergence. As far as I know, NAFNet [a] achieves state-of-the-art 40.30 dB on the SIDD dataset. Are the proposed loss functions applicable to NAFNet?\n- Lack of visual results in the main paper. As a paper on image restoration, it is unreasonable that the main paper does not contain any visual results. Moreover, the visual results in the supplementary materials have negligible differences, which suggests the proposed loss functions are ineffective.\n- Lack of evaluation on more general image restoration tasks. The paper selects image enhancement, image denoising, and pan-sharpening as the image restoration tasks. Are the proposed loss functions applicable to more general image restoration tasks such as super-resolution? \n\n[a] Chen et al. “Simple Baselines for Image Restoration”, ECCV, 2022. \n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**1, technical flaw.**\n\n1) Since our proposed loss functions are used alongside pixel loss, there is no added computational burden. Pure pixel loss optimization can lead to local optima and oscillations. Conversely, our approach mitigates local oscillation and enhances model convergence. For instance, while DnCNN with pixel loss required 50K iterations to converge, integration with our designs only necessitated 30K iterations.\n\n2) Regarding training memory, our lightweight random weights networks, detailed in the supplementary materials, ensure minimal memory overhead. Thus, employing our designs introduces only marginal and inconsequential memory demands throughout training, compared to using pure pixel loss.\n\n**2, quantitative improvements.**\n\n1) To ensure comprehensive experimentation, we introduced a state-of-the-art model like MPRNet for validation. Given dataset limitations, the current top-performing model naturally approaches the dataset's upper bound. Despite minor impact from added efficient designs, this remains understandable.\n\n2) Our random weights network, serving as a loss function, counters data bias and offers theoretical generality across image restoration models. Following your advice and due to time constraints, we adopted NAFNet as the baseline for evaluating our operator's efficacy. Results are provided below:\n\n|dataset | NAFNet  |    taylor  |   INN   |   zerofilter |\n|----|----|----|----|----|\n|SIDD     |      40.30|       40.41  |   40.38  |    40.46|\n\n**3, visual results.**\n\nRegarding qualitative outcomes, we'll heed your suggestion to include an increased number of visual results in the main paper.\n\n**4,  general image restoration tasks.**\n\nFollowing your suggestion, we expanded the application of our proposed loss functions to broader image restoration tasks, including super-resolution. Due to time constraints, we focused on the representative image super-resolution model RCAN [1] with 2-4x scaling factors to assess effectiveness. These results further validate our assertions.\n\n|setting|  RCAN  |    +Taylor |    +INN  |    +Zerofilter |\n|----|----|----|----|----|\n|X2       |     38.27    |     38.35   |  38.35  |    38.36|\n|X4      |       32.63    |     32.71   |  32.69    |  32.69|\n\n[1] Image super-resolution using very deep residual channel attention networks, TPAMI 2020.\n\n"}, {"review_id": "iU6gkAqFNW", "reviewer": "Reviewer_Bde2", "summary": "This paper seeks to explore the untapped capabilities of random weights networks as a loss function. Inspired by mathematical manifolds, the authors propose innovative and straightforward solutions for random weights networks based on rigorous mathematical properties. Extensive experimental results across various image restoration tasks validate the efficacy of these solutions, showcasing their plug-and-play nature and ability to enhance model performance while preserving the original model and data configuration as the baseline. The novelty and interest of the idea are noteworthy.", "questions": "See weaknesses part. ", "limitations": "The authors adequately addressed the limitations and potential negative societal impact of their work.", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "1. Innovative approach: The authors propose a novel concept of utilizing a well-designed random weights network as a loss function, offering a plug-and-play solution that leads to remarkable performance improvements when integrated into existing baselines. This approach avoids the need for complex network architecture designs, making it highly appealing in the field of efficiency.\n2. Theoretical foundation: The design of the random weights network is derived from rigorous mathematical manifolds, ensuring a solid theoretical basis. Furthermore, the authors have tailored the random sampling strategies to enrich the manifold representation, adding depth to the approach.\n3. Comprehensive experiments: The paper provides extensive comparison experiments in both the main paper and the appendix, showcasing the advantages of the proposed flowchart. The inclusion of ablation studies and motivation analysis further strengthens the findings, ensuring convincing evidence of the method's effectiveness.\n", "weaknesses": "1. In all the tables, the authors have suggested to highlight the best results for a clear illustration. In addition, the more visual comparison is required to show the main body.\n2. The authors have performed sufficient ablation studies. However, the corresponding experimental configuration like convolution kernel sizes needs to be detailed.\n3. It would be better if the authors have presented more experimental analysis.\n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**1,visual comparison.**\n\nThanks for pointing out this issue. As you suggested, we will highlight the best results for a clear illustration. In addition, we will provide the more visual comparison in the main body to enrich this work.\n\n**2,experimental configuration.**\n\nThanks for pointing out this issue. First, due to the page limit, we have shown the corresponding experimental configuration like convolution kernel sizes of ablation studies in supplementary materials. Second, we will open the source code to highlight the details. Finally, we will check and detail the corresponding setting in revision.\n\n**3,experimental analysis.**\n\nThanks for pointing out this issue. Due to the page limit, we have provided the partial experimental analysis and we will add the underlying working mechanism of experimental analysis to enrich this work."}, {"review_id": "2xc4l9rcke", "reviewer": "Reviewer_VxMP", "summary": "This work introduces a novel and orthogonal approach by exploring the potential of using random weights network as a loss function. The authors have carefully designed the random weights network with theoretical constraints based on mathematical manifolds. To validate the proposed solutions, extensive experiments have been conducted on mainstream image restoration tasks. The results consistently demonstrate the effectiveness of the approach. ", "questions": "The authors are recommended to provide a detailed response addressing each concern raised in the weaknesses section. ", "limitations": "The authors adequately addressed the limitations and potential negative societal impact of their work.", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "There are several strengths here:\n1. This paper presents a pioneering exploration of the potential of using random weights network as a loss function. With a clear motivation and a series of interesting experiments, this study offers valuable insights into the applicability of the proposed approach, potentially shaping the direction of the loss function community.\n2. The proposed designs seamlessly integrate into existing methods, resulting in performance improvements. A thorough set of ablation studies provides strong evidence to validate these findings.\n3. The paper is well-written and maintains a high level of readability, ensuring that it is easily understandable and accessible to readers.\n", "weaknesses": "There are several weakness here:\n1. To ensure clarity, it is recommended to provide detailed information regarding the experimental settings, including the specific methodologies and procedures employed. This will allow readers to have a clear understanding of how the experiments were conducted.\n2. The figures and tables in the paper lack consistent style, indicating the need for a thorough review by the author to identify and correct any errors. Additionally, it would be beneficial to address potential limitations and investigate the extent to which the random weights network can be applied to various tasks or datasets. \n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**1,detailed information.**\n\nThanks for pointing out this issue. Initially, due to page constraints, we've presented the relevant methodologies and procedures in the supplementary materials. Furthermore, we will share the source code to elucidate the experimental setup details. Lastly, we'll thoroughly review and elaborate on the settings in the revision to ensure readers have a clear comprehension of the conducted experiments.\n\n**2,consistent style.**\n\nInitially, we will meticulously review the entire paper, ensuring uniform style for figures and tables, while rectifying any errors. Our proposed random weights network, serving as a loss function, addresses data bias and holds theoretical applicability across various image restoration models. \n\nFollowing your suggestion, we expanded the application of our proposed loss functions to broader image restoration tasks, including super-resolution. Due to time constraints, we focused on the representative image super-resolution model RCAN [1] with 2-4x scaling factors to assess effectiveness. These results further validate our assertions.\n\n|setting |\tRCAN |\t+Taylor|\t+INN|\t+Zerofilter|\n|----|----|----|----|----|\n|X2\t|38.27\t|38.35\t|38.35\t|38.36|\n|X4\t|32.63\t|32.71\t|32.69\t|32.69|\n\n[1] Image super-resolution using very deep residual channel attention networks, TPAMI 2020."}]

Author rebuttal:

Meta-review: The final ratings received for this paper were A, SA, SA, BR, indicating an overall positive trend in the evaluations. The majority of reviewers expressed positive opinions about the theoretical explanations in the work and commended the credibility of the experimental validation, and they noted that their concerns were appropriately addressed by the authors in their responses. As for the reviewer who tended to reject, there did not appear to be further comments after the author submitted the rebuttal. Nevertheless, the previous concerns raised by this reviewer regarding the technical feasibility and the breadth of experimental validation still need careful consideration. Above all, this work demonstrates an overall high quality, but there are some issues in the manuscript that require the author's careful consideration and improvement. Therefore, I believe that with some revisions, this work can meet the acceptance standards, and I have decided to accept it.
Decision: Accept (poster)