電腦斷層(Computed Tomography, CT)是現代醫學常用的診斷工具，使用低劑量電腦斷層可以降低接收劑量，但會產生雜訊影響影像品質，從而降低診斷價值。為了提昇影像品質，一般會使用三種方法：正弦濾波器、迭代重建、和影像後處理，然而這些方法都各有其優缺點與限制。卷積神經網路是一種具有非線性和多層卷積層組合的神經網路，已被證明在各種任務中有效，運用於去雜訊其優點是可以從低劑量和正常劑量的影像對中學習非線性轉換函數。
早期的研究集中於架構的優化上，然而損失函數也是影響生成影像品質的原因之一，一般常用的損失函數包含像素級損失函數、感知損失函數……等。不同的損失函數擁有不同性質，此研究的目標是設計一個損失函數組合可以保留各別的優點，最終得到最適合使用於低劑量電腦斷層影像去雜訊的組合。
本篇研究裡我使用了不同種類的神經網路架構，包含殘差學習的卷積神經網絡與生成對抗神經網路，並結合平均絕對誤差(Mean absolute error , MAE)、使用VGG-net計算的感知損失函數、和結構相似性損失函數。
最終我們得到的結果是MAE對於模型的訓練有很大的幫助，感知損失在影像上可以得到和正常劑量電腦斷層影像類似的紋理特徵，結構相似性損失函數對於像素值的準確性佔有重要的角色。

Computed tomography (CT) is a popular medical imaging modality. Low-dose CT is a way to reduce the radiation dose, but it will increase the noise and artifacts which significantly degrade the image quality and can compromise diagnostic information. To improve image quality, three methods are generally used: sinogram filtering, iterative reconstruction, and image post-processing. However, these methods have their advantages, disadvantages, and limitations. A Convolutional neural network (CNN) is a neural network that has one or more convolutional layers and is used mainly for image processing, classification, segmentation, and also for other tasks. The advantage of applying CNN to denoising is that it can learn non-linear transfer functions from low-dose and normal-dose image pairs.
Early research focused on the optimization of the architecture, but the loss function is also one of the reasons that affect the quality. Generally, the commonly used loss functions include pixel-level loss functions, perceptual loss functions, etc. Different loss functions have different properties. The goal of the study is to design a combination of loss functions that preserves the respective advantages and finally obtains the combination that is most suitable for use in low-dose CT denoising.
In this study, we used two kinds of neural network architectures, including residual convolutional neural networks and generative neural networks. Combined with mean absolute error (MAE), perceptual loss function, and structural similarity loss function.
At the end, our research shows that MAE is very helpful for the training of the model. Perceptual loss function can obtain texture similar to normal dose CT images. Structural similarity loss function plays an important role in the accuracy of pixel values.

1. 前言 - 1 -
2. 卷積神經網路 - 5 -
2.1 卷積層(Convolution layer) - 7 -
2.2 池化層(Pooling layer) - 9 -
2.3 神經網路訓練流程 - 10 -
2.3.1 參數 - 10 -
2.3.2 梯度下降(Gradient descent) - 11 -
2.3.3 反向傳播演算法(Backpropagation) - 12 -
2.3.4 梯度消失和梯度爆炸 - 14 -
2.4 優化器(Optimizer) - 15 -
2.4.1 SGD (Stochastic Gradient Decent) - 16 -
2.4.2 Adagrad (Adaptive gradient algorithm) [26] - 16 -
2.4.3 RMSprop (Root Mean Square Propagation) - 17 -
2.4.4 Adam (Adaptive Moment Estimation) [27] - 17 -
2.5 激活函數(Activation function) - 18 -
2.5.1 Sigmoid - 18 -
2.5.2 Tanh - 19 -
2.5.3 ReLU - 20 -
2.5.4 Leaky ReLU - 20 -
2.6 過擬合 (Over-fitting) 和欠擬合 (Under-fitting) - 21 -
2.7 正規化(Regularization) - 22 -
2.7.1 L1 和 L2 正規化 - 22 -
2.7.2 Dropout - 23 -
2.7.3 Batch Normalization - 24 -
2.8 殘差學習(Residual learning) - 25 -
2.8.1 RED-CNN - 26 -
3. 生成對抗神經網路 (Generative Adversarial Network) - 27 -
3.1 原始生成對抗神經網路 - 27 -
3.2 WGAN - 29 -
3.3 PatchGAN - 31 -
4. 損失函數 (Loss function) - 32 -
4.1 像素級別損失函數 (Pixel-level loss function) - 32 -
4.1.1 MAE - 33 -
4.1.2 MSE - 33 -
4.1.3 將像素級別損失函數使用於深度學習訓練 - 33 -
4.2 結構相似性損失函數 - 34 -
4.2.1 結構相似性(Structural similarity index , SSIM) - 34 -
4.2.2 將結構相似性損失函數使用於深度學習訓練 - 34 -
4.3 感知損失函數 (Perceptual loss function) - 35 -
4.3.1 VGG Net - 36 -
4.3.2 將感知損失函數使用於深度學習訓練 - 37 -
4.4 Adversarial loss function - 37 -
5. 實驗設計 - 38 -
5.1 神經網路架構 - 39 -
5.1.1 去雜訊部份 - 39 -
5.1.2 特徵提取部份 - 40 -
5.1.3 鑑別器部份 - 40 -
5.2 訓練設備 - 41 -
5.3 訓練資料集與資料預處理 - 41 -
5.3.1 Mayo Clinic data - 41 -
5.4 Quantitative Analysis - 43 -
5.4.1 PSNR - 43 -
5.4.2 RMSE - 44 -
5.4.3 PSNR-HVS - 44 -
6. 實驗結果與討論 - 46 -
6.1 實驗一: 透過使用不同損失函數的神經網路模型，探討其對低劑量電腦斷層影像去雜訊的影響 - 46 -
6.1.1 單獨使用一種損失函數，觀察其對去雜訊的影響 - 46 -
6.1.2 單獨比較MAE和MSE - 50 -
6.2 實驗二: 透過組合不同損失函數的神經網路模型，探討其對低劑量電腦斷層影像去雜訊的影響 - 53 -
6.2.1 MAE與其他兩種損失函數的組合 - 53 -
6.2.2 添加GAN是否提升性能得到更好的結果 - 60 -
6.3 實驗三: 透過改變損失函數之間的占比，探討其對低劑量電腦斷層影像去雜訊的影響 - 65 -
6.3.1 改變VGG的占比 - 65 -
6.3.2 改變MAE的占比 - 70 -
6.3.3 改變DSSIM的占比 - 75 -
6.4 將實驗三的結果套用在GAN的架構上，探討其與未使用GAN有什麼樣的差異 - 81 -
6.4.1 調整G_MAE_ALL中損失函數的比例 - 81 -
7. 結論 - 85 -
8. 未來展望 - 87 -
9. 參考文獻 - 88 -

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