[综述笔记]A Survey on Deep Learning for Neuroimaging-Based Brain Disorder Analysis

论文网址：Frontiers | A Survey on Deep Learning for Neuroimaging-Based Brain Disorder Analysis (frontiersin.org)

英文是纯手打的！论文原文的summarizing and paraphrasing。可能会出现难以避免的拼写错误和语法错误，若有发现欢迎评论指正！文章偏向于笔记，谨慎食用

1. 省流版

1.1. 心得

（1）上来直接就开模型介绍，文心吃这些东西吃多了吧

1.2. 论文总结图

2. 论文逐段精读

2.1. Abstract

①Structural magnetic resonance imaging (MRI), functional MRI, and positron emission tomography (PET) can all be used in neuroimage analysis

②Disease included: Alzheimer's disease, Parkinson's disease, Autism spectrum disorder, and Schizophrenia

2.2. Introduction

①Introducing medical imaging

②Therefore, the feature selection step is extremely important for complex medical image processing. Although sparse learning and dictionary learning have been used to extract features, their shallow architectures still limit their representation ability.

③The development of hardware promotes the improvement of deep learning in medical image analysis

④Categories of medical imaging analysis: classification, detection/localization, registration, and segmentation

⑤This survey mainly centers on brain disease

cardiac adj.心脏的;心脏病的 n.心脏病患者;强心剂;健胃剂

2.3. Deep Learning

2.3.1. Feed-Forward Neural Networks

①The function of FFNN:

$y_k(\boldsymbol{x};\boldsymbol{\theta})=f^{(2)}\left(\sum_{j=1}^Mw_{k,j}^{(2)}f^{(1)}\left(\sum_{i=1}^Nw_{j,i}^{(1)}x_i+b_j^{(1)}\right)+b_k^{(2)}\right)$

where the $\boldsymbol{x}$ is the input vector, $y_k$ is the output;

superscript denotes layer index, $M$ is the number of hidden units;

$b_j$ and $b_k$ are bias terms of input layer hidden layer respectively;

$f^{(1)}$ and $f^{(2)}$ denote non-linear activation function;

$\theta=\left\{w_{j}^{(1)},w_{k}^{(2)},b_{j}^{(1)},b_{k}^{(2)}\right\}$ represents parameter set

②Sketch map of (A) single and (B) multi layer neural networks:

2.3.2. Stacked Auto-Encoders

①Auto-encoder (AE), namely so called auto-associator, possesses the ability of encoding and decoding

②AE can be stacked as stacked auto-encoders (SAE) with better performance

③Sketch map of SAE:

where the blue and red dot boxes are encoder and decoder respectively

④To avoid being trapped in local optimal solution, SAE applies layer-wise pretraining methods

2.3.3. Deep Belief Networks

①By stacking multiple restricted Bolztman machines (RBMs), the Deep Belief Network (DBN) is constructed

②The joint distribution of DBN:

$P(v,h^{(1)},\ldots,h^{(L)})=P(v\mid h^{(1)})(\prod_{l=1}^{L-2}P(h^{(l)}\mid h^{(l+1)}))P(h^{(L-1)},h^{(L)})$

where $v$ denotes visible units and $h^{(1)},...,h^{(L)}$ denotes $L$ hidden layers

③Sketch map of (A) DBN and (B) DBM:

where the double-headed arrow denotes undirected connection and the single-headed arrow denotes directed connection

2.3.4. Deep Boltzmann Machine

①Futher stacking RBMs can get Deep Boltzmann Machine (DBM):

$\begin{gathered}P(v_i|\boldsymbol{h}^1)=\sigma(\sum_jW_{ij}^{(1)}h_j^{(1)})\quad\\\\P(h_k^{(l)}|\boldsymbol{h}^{(l-1)},\boldsymbol{h}^{(l+1)})=\sigma(\sum_mW_{m\boldsymbol{k}}^{(l)}\boldsymbol{h}_m^{(l-1)}+\sum_nW_{kn}^{(l+1)}h_n^{(l+1)})\quad\\\\P(h_t^{(L)}|\boldsymbol{h}^{(L-1)})=\sigma(\sum_sW_{st}^{(L)}\boldsymbol{h}_s^{(L-1)})\quad\end{gathered}$

2.3.5. Generative Adversarial Networks

①Simultaneously including generator $G$ and discriminator $D$ , Generative Adversarial Networks (GANs) achieves the task of training models with a small number of labeled samples:

$\begin{aligned}\min_G\max_DV(G,D)&=\mathbb{E}_{x-p_{data}(x)}\left[\log D(x)\right]\\&+\mathbb{E}_{x-p_z(z)}\left[\log(1-D(G(z)))\right]\end{aligned}$