## 3 High-Dimensional Medical Imaging Analysis Based on Deep Learning
### Semi-Supervised Deep Learning Strategies for MRI
#### 3.2.5 Outlook for a Unified Multi-Dimensional Data Model from DCE-MRI via Multi-Task Learning
At the end of the network, a feature distillation module is positioned for automatically fusing all image features and removing redundant features, reducing the network model parameters for improved network performance. In the design of the loss function, we intended to fully consider the content, texture, color (intensity) and other characteristics of magnetic resonance images. A series of new loss functions, such as spatial content loss (Content Loss, referred to as \(\text{Loss}_{\text{C}}\)), TV loss (Total Variation Loss, referred to as \(\text{Loss}_{TV}\)), and focal loss (\(\text{Loss}_{\text{Focal}}\)) can be expressed by using a generic partial loss function as follows:  
\[\text{Loss}_{\text{C}}=\|G(u^{\prime})-u\|_{1} \tag{1}\]  
\[\text{Loss}_{\text{T}^{0}}=\frac{1}{CHW}\|\
abla_{X}G(u)+\
abla_{y}G(u)\|. \tag{2}\]  
here, \(u^{\prime}\) indicates the image to be enhanced, \(u\) denotes the target image, \(G(u)\) denotes the output of the multi-task classification network and \(CHW\) indicates the spatial dimension of the enhanced image. The focal loss can be expressed as:  
\[\text{Loss}_{\text{Focal}}=-\frac{1}{N}\sum_{i=1}^{N}\left(\xi y_{i}(1-p_{i})^{ \gamma}\log p_{i}+(1-\xi)(1-y_{i})p_{i}^{\gamma}\log(1-p_{i})\right) \tag{3}\]  
here, \(y_{i}\) is the real category of the input instance, \(p_{i}\) is the predicted probability that the input instance belongs to the category \(i\) and N is the number of pixels in the image space. The purpose of invoking the loss function is to reduce the loss of samples with a high probability of networks prediction under extremely unbalanced conditions of tumour categories, thereby enhancing the focus on positive samples and solving the problem of serious imbalance regarding the proportion of positive and negative samples. An adversarial network can be utilised as a perceptual discriminant network. In order to function in this way, the output of the generated model and the numerically weighted images are used as the training set of the discriminant model. This model consists of two parts: the self-encoding module and the perceptual discriminating module. The self-encoding module is used to encode its own image features so that the input image retains only its most important features, reducing computational complexity. The perceptual discriminant module introduces an improved VGG convolutional neural network architecture for extracting high-level semantic features of the image, and further judges the authenticity of the generated image from the high-level semantic feature level, so as to alleviate the difficulty of network training. The discriminant model is an important auxiliary training part of the generative model and the output of the discriminant model is an important condition for generating the update weight of the network. For the adversarial network, we planned to design a series of new loss functions to enhance color loss (Adversarial Color Loss, denoted as \(\text{Loss}_{\text{AC}}\)), adversarial semantic loss (Adversarial Semantic Loss, denoted as \(\text{Loss}_{\text{AS}}\)) and adversarial loss (Adversarial Loss, denoted as \(\text{Loss}_{\text{A}}\)), for the image to be further discriminated. The partial loss function can be expressed as:  
\[\text{Loss}_{\text{AS}}=-\|F_{j}(G(u^{\prime}))+F_{j}(u)\| \tag{4}\]\[\text{Loss}_{A}=-\sum_{j}\log D((G(u))) \tag{5}\]  
where \(F_{j}(\bullet)\) represents the \(j\)th convolutional layer of the perception discrimination module and \(D(\bullet)\) represents the adversarial network. The medical image enhancement framework completes the end-to-end magnetic resonance image enhancement task by jointly training the generation network (multi-task enhancement network) and the confrontation network (perceptual discrimination network). Through the cooperation of multiple modules, the proposed model can extract the unique data features of medical images and achieve high-quality magnetic resonance image tumour classification from multiple feature spaces such as spatial structure, spatial signals and position details.