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Towards Perceptual Image Dehazing by Physics-Based Disentanglement and Adversarial Training

• 重建Loss，L1
  $\mathcal{L}_{r e c o n}\left(G_{J}, G_{t}, G_{A}\right)=\mathbb{E}_{I \sim \mathcal{I}}\|I-\hat{I}\|_{1}$Lrecon​(GJ​,Gt​,GA​)=EI∼I​∥I−I^∥1​

• GAN Loss，多尺度Discrimiation均值
  $\mathcal{L}_{G A N}(G, D)=\mathbb{E}_{J \sim \mathcal{J}}[\log D(J)]+\mathbb{E}_{I \sim \mathcal{I}}[\log (1-D(G(I)))]$LGAN​(G,D)=EJ∼J​[logD(J)]+EI∼I​[log(1−D(G(I)))]

  $\mathcal{L}_{a d v}\left(G_{J}, D\right)=\frac{1}{2}\left(\mathcal{L}_{G A N}\left(G_{J}, D^{l o c}\right)+\mathcal{L}_{G A N}\left(G_{J}, D^{g l o}\right)\right)$Ladv​(GJ​,D)=21​(LGAN​(GJ​,Dloc)+LGAN​(GJ​,Dglo))

• 正则Loss，TV Loss
  $\mathcal{L}_{r e g}\left(G_{t}\right)=T V(t)=\sum_{i, j}\left|t_{i+1, j}-t_{i, j}\right|+\left|t_{i, j+1}-t_{i, j}\right|$Lreg​(Gt​)=TV(t)=i,j∑​∣ti+1,j​−ti,j​∣+∣ti,j+1​−ti,j​∣

• 总Loss
  $\begin{array}{r}{\mathcal{L}\left(G_{J}, G_{t}, G_{A}, D\right)=\mathcal{L}_{a d v}\left(G_{J}, D\right) +\lambda \mathcal{L}_{r e c o n}\left(G_{J}, G_{t}, G_{A}\right)+\gamma \mathcal{L}_{r e g}\left(G_{t}\right)}\end{array}$L(GJ​,Gt​,GA​,D)=Ladv​(GJ​,D)+λLrecon​(GJ​,Gt​,GA​)+γLreg​(Gt​)​

权重未知

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Cycle-Dehaze: Enhanced CycleGAN for Single Image Dehazing

• Perceptual Loss（VGG16 feature extractor from 2nd and 5th pooling layers）

  $\begin{aligned} \mathcal{L}_{\text {Perceptual}} &=\|\phi(x)-\phi(F(G(x)))\|_{2}^{2}+\|\phi(y)-\phi(G(F(y)))\|_{2}^{2} \end{aligned}$LPerceptual​​=∥ϕ(x)−ϕ(F(G(x)))∥22​+∥ϕ(y)−ϕ(G(F(y)))∥22​​

• GAN Loss

• 总Loss
  $\begin{aligned} \mathcal{L}\left(G, F, D_{x}, D_{y}\right) &=\mathcal{L}_{C y c l e G A N}\left(G, F, D_{x}, D_{y}\right) +\gamma * \mathcal{L}_{P e r c e p t u a l}(G, F) \end{aligned}$L(G,F,Dx​,Dy​)​=LCycleGAN​(G,F,Dx​,Dy​)+γ∗LPerceptual​(G,F)​

• 超参数

  • adam optimizer
  • lr = 0.0001
  • 40 epoch
  • Perceptual Loss 权重 $\gamma=0.0001$γ=0.0001，采用VGG16 POOL2和POO5

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High-Resolution Image Dehazing with respect to Training Losses and Receptive Field Sizes

$L_{G}=\lambda_{1} L_{1}+\lambda_{V G G} L_{V G G}+\lambda_{A v g} L_{G A v g}+\lambda_{M a x} L_{G M a x}$LG​=λ1​L1​+λVGG​LVGG​+λAvg​LGAvg​+λMax​LGMax​

• input：512x512
• 500 epoch
• Adam optimizer （β 1 = 0.5）
• learning rate = 0.0002.
• batch size = 1
• 

注：这里的GMax指的是，在Discriminate的时候，原版是求输出的概率score map的平均值作为loss，这里文章提出用最大值做loss。

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Multi-scale Single Image Dehazing using Perceptual Pyramid Deep Network

• L_E reconstruction error
  $L_{E}=\frac{1}{C W H} \sum_{c=1}^{C} \sum_{w=1}^{W} \sum_{h=1}^{H}\left\|G(I(c, w, h), \Theta)-I_{t}(c, w, h)\right\|_{2}$LE​=CWH1​c=1∑C​w=1∑W​h=1∑H​∥G(I(c,w,h),Θ)−It​(c,w,h)∥2​

• perceptual Loss L_P
  $L_{P}=\frac{1}{C_{v} W_{v} H_{v}} \sum_{c=1}^{C_{v}} \sum_{w=1}^{W_{v}} \sum_{h=1}^{H_{v}}\left\|\phi_{V}(G(I, \Theta))-\phi_{V}\left(I_{t}\right)\right\|_{2}$LP​=Cv​Wv​Hv​1​c=1∑Cv​​w=1∑Wv​​h=1∑Hv​​∥ϕV​(G(I,Θ))−ϕV​(It​)∥2​
  采用VGG-16，relu3_1

• 总Loss
  $L=L_{E}+\lambda_{P} L_{P}$L=LE​+λP​LP​
  权重参数分别为1和0.5

• 超参数

  • ADAM
  • batch size = 1， input size = 640 x 640
  • lr = 0.002

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Recursive Deep Residual Learning for Single Image Dehazing

• epoch = 100
• lr = 0.001[0~60], lr=0.0001[61~100]
• Stochastic Gradient Descent (SGD). momentum parameter of 0.9.
• Loss: L2

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Single Image Dehazing via Conditional Generative Adversarial Network

• GAN Loss
  $L_{A}=\frac{1}{N} \sum_{i=1}^{N} \log \left(1-D\left(I_{i}, \widetilde{J}_{i}\right)\right)$LA​=N1​i=1∑N​log(1−D(Ii​,Ji​))

• VGG Loss

  $L_{P}=\frac{1}{N} \sum_{i=1}^{N}\left\|\mathcal{F}_{i}\left(G\left(I_{i}\right)\right)-\mathcal{F}_{i}\left(J_{i}\right)\right\|_{2}^{2}$LP​=N1​i=1∑N​∥Fi​(G(Ii​))−Fi​(Ji​)∥22​
  Vgg 具体的特征层未知

• 带正则的L1 重建Loss（实际就是L1 + TV Loss）
  $L_{T}=\frac{1}{N} \sum_{i=1}^{N}\left(\left\|G\left(I_{i}\right)-J_{i}\right\|_{1}+\lambda\left\|\nabla G\left(I_{i}\right)\right\|_{1}\right)$LT​=N1​i=1∑N​(∥G(Ii​)−Ji​∥1​+λ∥∇G(Ii​)∥1​)

• 总loss
  $\mathcal{L}=\alpha L_{A}+\beta L_{P}+\gamma L_{T}$L=αLA​+βLP​+γLT​

超参数

• $\alpha=1, \beta=150, \gamma=150, \lambda=10^{-5}$α=1,β=150,γ=150,λ=10−5

• input size：256x256

• lr = 0.0002

• Adam