# Brief Review — Natural Image Denoising with Convolutional Networks

## Convolutional Network for Image Denoising in Year of 2008

Natural Image Denoising with Convolutional Networks

Jain NIPS’08, by Massachusetts Institute of Technology2008 NIPS, Over 900 Citations(Sik-Ho Tsang @ Medium)

Image Denoising

# Outline

**Convolutional Networks for Image Denoising****Results**

# 1. Convolutional Networks for Image Denoising

## 1.1. Network Architecture

- A convolutional network is an alternating sequence of linear filtering and nonlinear transformation operations. The input and output layers include one or more images, while intermediate layers contain “hidden” units with images called feature maps that are the internal computations of the algorithm.
- The activity of
**feature map**is given by:*a*in layer*k*

- with
*f*(*x*)**sigmoid**activation function:

- where
*Ik*-1,*b*are feature maps that provide input to*Ik*,*a*, ⊗ denotes the convolution operation, and*θk*,*a*is a bias parameter **Input**and**target**values are in the**range of 0 to 1**, and hence the 8-bit integer intensity values of the dataset**(values from 0 to 255) were normalized to lie between 0 and 1.**- The
**border**of the image is explicitly encoded by**padding**an area surrounding the image with values of**-1**.

- The network has
**4 hidden layers**and**24 feature maps**in each hidden layer. In layers 2, 3, and 4, each feature map is connected to 8 randomly chosen feature maps in the previous layer. - Each arrow represents a single convolution associated with a 5×5 filter, and hence this network has
**15,697 free parameters**and requires 624 convolutions to process its forward pass.

## 1.2. Training Details

- A
**noise process**is used that*n*(*x*)**operates on an image**drawn from a distribution of natural images*xi**X*. **Reconstruction error**is minimized:

**Mini-batch**training is used where a**gradient update**is computed from**6×6 patches**randomly sampled from**6 different images**in the training set.- Finally, when learning networks with two or more hidden layers it was important to use a
**very small learning rate**for the**final layer (0.001)**and a**larger learning rate (0.1)**in**all other layers**.

# 2. Results

**CN1**and CNBlind are learned using the**same forty image training set**as the Field of Experts model (FoE).**CN2**is learned using a training set with an**additional sixty images**.

The convolutional network has the

highest average PSNRusing either training set.

- A visual comparison of these results is shown above.

This paper was appeared after LeNet (1989, 1998), earlier than AlexNet (2012). ReLU is not used. No Caffe, TensorFlow, PyTorch, etc. Awesome!

## Reference

[2008 NIPS] [Jain NIPS’08]

Natural Image Denoising with Convolutional Networks

## Image Restoration

**2008** [Jain NIPS’08] **2016** [RED-Net] [GDN] **2017 **[DnCNN] [MemNet] [IRCNN] [WDRN / WavResNet] **2018 **[MWCNN] **2019 **[IDBP-CNN-IA]