# Fully Symmetric Convolutional Network for Effective Image Denoising
## 3 Deep Symmetric Convolutional-Deconvolutional Network
### Model Visualization  
Visualizing outputs of each layer of a network can provide a good understanding of its behavior. The proposed FSCN model has demonstrated better denoising compared with other architectures. For a clear understanding of the superior performance, a visualization technique is employed to give insight into the function of intermediate feature layers. In Figure 3, we visualize the filters of the proposed model by taking each feature map separately. For visualization of the proposed architecture, the MNIST dataset with 28 \(\times\) 28 image resolution is used. Each layer consists of (i) convolution of the previous layer output (or, the noisy image input as shown in Figure 3a in the case of the first layer) with a set of filters and (ii) passing the responses through ReLu. The top-down nature of the model makes it easy to inspect what it has learned. The parameters in the network are trained and updated via [PERSON].  
Figure 3: Cont.  
Figure 3: (**a-l**) Visualizations of the filters learned in each layer of the proposed model.  
In Layer 1, convolution layer extracts the overall feature from the noisy image input while reducing the noise. The less denoised image output is then fed as an input to the next deconvolution layer (Layer 2) which captures the overall shape of the image suppressing the noisy activations. The same process is continued until the image is denoised completely. Layers 1, 3, 5, 7, 9 (Figure 3c,e,g,i,k) show the feature maps after the convolution operation is applied to the noisy image. It is clear that the convolution operation acts as a useful feature extractor which encodes the primary components while eliminating corruptions.  
Contrary to convolutional layers, which connect multiple input activations within a filter window to a single activation, deconvolutional layers associate a single input activation with multiple outputs. The learned filters in deconvolutional layers correspond to bases which reconstruct the shape of an input object. The deconvolutional layers are used to capture the different level of shape details. The filters in the lower layers tend to capture the overall shape of an object while the fine details are encoded in the filters of the higher layers. Layers 2, 4, 6, 8, 10 (Figure 3d,f,h,j,l) reveal that the deconvolutional layers decode the image abstraction from the convolutional layers to recover the details in the image. They also suppress noisy activations and make blurry images sharper. For each layer, it is apparent that the weights are not interpretable but are still smooth and well formed, with noisy patterns absent. Although all the layers share a similar form, they contribute different operations throughout the network. It gives some intuition for designing an end-to-end network in image processing. Well-trained networks display nice and smooth filters without any noisy patterns. Noisy patterns can be an indicator of a network that has not been trained for long enough or possibly may have led to overfitting. Therefore, it is evident that the image features are extracted by the layers and recovered efficiently in the intermediate layers.