Federated Learning for COVID-19 Detection with Generative Adversarial Networks in Edge Cloud Computing

Several studies using GAN and FL have been proposed for supporting COVID-19 detection tasks. Specifically, the authors in [15], [16] developed a GAN-based approach to detect COVID-19 X-ray images, along with using transfer learning for lung segmentation for facilitating classification. The study in [17] implemented an image synthesis approach to produce high-quality and realistic COVID-19 chest tomography (CT) images for the use in DL-based semantic segmentation and classification. Moreover, the application of GAN for synthetic chest X-ray image augmentation was also investigated in [18] by using a conditional GAN, which helps speed up the COVID-19 detection with enhanced classification performances. The potential of GAN in solving data limitation in the COVID-19 pandemic was demonstrated in [19], where DL-based models, e.g., Alexnet, Googlenet, and Restnet18, are employed to evaluate the synthetic data quality and perform COVID-19-related predictions. Another work in [20] employed GANs for mobility estimation in the COVID-19 pandemic under complex social contexts and constrained training datasets with multiple data sources.

Furthermore, the applications of FL in COVID-19 diagnosis and detection have been investigated in recent works. For example, the study in [21] proposed a novel dynamic fusion-based FL approach for diagnostic image analytics to identify COVID-19 cases. The main focus of this work is on designing a client selection mechanism which allows for deciding clients to join the FL training based on their local model performances, and developing a model fusion solution to perform FL aggregation. The research in [22] proposed an FL scheme for federated COVID region segmentation using chest computed tomography (CT) images by the collaboration of hospitals from China, Italy, and Japan. A multi-national database consisting of 1704 scans distributed among these countries is built to build a global COVID-19 detection model via a federated semi-supervised learning technique. Another work in [23] developed a federated DL framework for privacy-enhanced detection of lung abnormalities caused by COVID-19. Each institution runs a CNN model to detect lesions from COVID-19 CT images, and update the gradients to a data centre for building a generalizable, low-cost, and scalable AI model for COVID-19 disease diagnosis and management. Furthermore, the authors in [24] leveraged FL to build a COVID-19 infection screening scheme based on chest X-ray images. Several CNN-based models are employed in the FL setting, showing promising results on COVID-19 classification compared to standalone schemes without federation. The feasibility of FL was also evaluated via real-world experiments in [25] for COVID-19 X-ray image analytics and classification.

In terms of blockchain-based FL, the work in [26] suggested an FL model with blockchain for COVID-19 CT imaging by the cooperation of multiple hospitals. The focus of this work was on developing a data normalization-based FL technique to accurately train the collaborative deep CNN model using the datasets collected from different hospitals and CT scan machines. The work in [27] introduced a conceptual concept of the blockchain, edge computing, and FL integration for controlling the COVID-19 pandemic. The potential of blockchain and FL was also investigated in [28] for health data analytics, where the benefits of the integration of these technologies were analyzed. However, no implementation and simulation results have been reported in these works [27], [28]. Other related works in [29], [30] proposed blockchain-based FL schemes for health Internet of Things (IoT) networks, but their roles in COVID-19 detection have not been investigated. The studies in [31], [32] also paid attention to blockchain-based FL designs, where the proposed solutions were used to mostly address attack issues in the data communication and model aggregation. Nonetheless, all existing works [26, 27, 28, 29, 31, 32] have not addressed the latency issue caused by blockchain mining in the blockchain-FL systems. Moreover, the integrated design of blockchain, FL, and GANs and the investigation of this integrated model in the COVID-19 context are still missing in the above literature studies.

The motivations of our work can be explained as follows. Firstly, despite these research efforts, most existing GAN algorithms [15, 16, 17, 18] for COVID-19 analytics are trained using limited and imbalanced datasets from a single institution which cannot achieve a desired COVID-19 detection accuracy. Secondly, during a pandemic, due to the increasing user privacy concerns and strict regulations, medical institutions such as hospitals are not willing to share their COVID-19 image data with a data centre for AI training, which calls for COVID-19 data training without data sharing. Thirdly, the convergence of FL and GANs is a very interesting research direction, which can achieve better COVID-19 image augmentation with privacy enhancement for better disease detection and diagnosis. However, its potential has not been explored for the COVID-19 detection domain in the open literature [21, 22, 23, 24]. Finally, how to develop a new blockchain solution for secure and low-latency federated data training is an urgent need, aiming to support efficient COVID-19 detection in the pandemic.

Motivated by these limitations, we here propose a novel scheme called FedGAN for privacy-ensured and efficient COVID-19 detection by enabling a joint design of GAN and FL across medical institutions in edge cloud computing. The key purpose of our proposed scheme is to generate high-quality synthetic image data for supporting COVID-19 detection tasks without the need for COVID-19 image data sharing. Our proposed solution not only solves the problems of data limitation and imbalance thanks to generative learning but also enhances COVID-19 data privacy, as well as enhances the COVID-19 detection performance due to the collaboration of multiple data sources from distributed institutions. Moreover, we propose a new blockchain-based FedGAN framework for secure COVID-19 data analytics, by decentralizing the FL process with a new mining solution for low running latency. The comparison of our paper and the related works via several key features is summarized in Table I. In a nutshell, the unique contributions of this article are highlighted as follows:

• •

  We propose a novel FedGAN scheme for COVID-19 detection, by enabling a joint design of GAN and FL across the distributed medical institutions in edge cloud computing. This model is highly effective in generating realistic COVID-19 X-ray images and thus facilitating the automatic COVID-19 detection in the current pandemic scenario with COVID-19 data scarcity at each institution.

• •

  We propose a collaborative data augmentation scheme where a discriminator and a generator of the GAN at each edge-based institution alternatively train their model and update their trained parameters to a cloud server without disclosing the actual image samples. The proposed solution thus enables GANs to federate the training for building the global GAN model which is used to generate synthetic COVID-19 X-ray images. To enhance the privacy in federated COVID-19 data analytics, we integrate a differential privacy solution at each hospital institution.

• •

  We then further propose a new blockchain-based FedGAN framework for secure COVID-19 data analytics, by decentralizing the FL process over the hospital institutions. Particularly, we propose a novel mining mechanism to mitigate the mining latency caused by the blockchain adoption in the FL system that has not been addressed in the literature works. Further, we investigate the potential of blockchain-based FedGAN in COVID-19 detection scenarios with real-world datasets.

• •

  We also design an efficient CNN-based classifier which can flexibly perform COVID-19 classification in three labelled classes (COVID-19 positive, normal, and pneumonia). Finally, we implement extensive simulations to evaluate the effectiveness of our designs, showing the significant improvement of the proposed scheme in COVID-19 detection with low running latency, compared to existing methods.

The remainder of this article is organized as follows. Section II describes the system model and explains the standalone GAN model as the basic solution for COVID-19 image augmentation. Next, in Section III, we present our FedGAN model that enhances the COVID-19 image augmentation with privacy awareness and then provide its theoretical analysis. We also propose a new blockchain-based FedGAN framework for decentralized COVID-19 data analytics. We provide the simulations and evaluate the efficiency of our scheme as well as compare with other related schemes in Section V. Finally, Section VI concludes the paper.

We consider a FedGAN model for COVID-19 detection as illustrated in Fig. 1, including a set $\mathcal{N}$ of edge nodes (ENs) located at medical institutions (e.g., hospitals) and a cloud server. Note that ENs can be local computers or powerful IoT devices installed in hospitals for data training. Each EN (or institution) $n\in\mathcal{N}$ participates in the FL process using its own COVID-19 image dataset to build a global GAN with the help of a cloud server, aiming to generate high-quality synthetic COVID-19 X-ray images for improving the overall COVID-19 detection. We assume that each institution $n$ has its own dataset, denoted as $D_{n}$ which follows a distribution $p_{n}(x)$ where $x$ is the real data samples acquired from the real COVID-19 image dataset.

We design a GAN at each EN including a generator and a discriminator by using CNNs. Particularly, each institution trains a generator to learn a generative data distribution $p^{g}_{n}$ based on its dataset $D_{n}$, aiming to mimic the real data distribution $p^{d}_{n}$ which is $p^{g}_{n}=p^{d}_{n}$¹¹1At this optimal condition, the discriminator cannot distinguish the real samples from the synthetic samples generated by a well-functioning generator.. To do so, given a random noise $z$ from a probability distribution $p^{z}_{n}(z)$, the generator learns to generate a fake COVID-19 image data point $G_{n}(z,\theta_{n}^{g})$ where $G_{n}$ represents the CNN with parameters $\theta_{n}^{g}$. Moreover, we design another CNN as a discriminator $D_{n}(x,\theta_{n}^{d})$ at each institution which tries to classify the real COVID-19 image data point $x$ from the distribution $p_{n}(x)$ against the one produced from the generator. The discriminator outputs a value 1 if the input is $x$ or 0 if the input is $G_{n}(z,\theta_{n}^{g})$. Accordingly, the generator and the discriminator at each hospital interact to derive the parameters $\theta_{n}^{g},\theta_{n}^{d}$ so that the generator produces the synthetic data distribution $p^{g}_{n}$ similar to the real data distribution $p^{d}_{n}$ to fool the discriminator. Mathematically, the objective function of the GAN at each institution $n$ can be formulated via a min-max game with a value function $V_{n}(D,G)$ as:

where $\mathds{E}$ is the expectation, $D_{n}(x)$ denotes the probability that $D_{n}$ distinguishes $x$ as real data samples, and $D_{n}(G_{n}(z))$ represents the probability that $D_{n}$ determines the data generated by $G_{n}$. In (1), the first term implies that the $D$ controls how the synthetic sample should be close to the real sample, while the second term penalizes the implausible points generated from the generator. Therefore, the discriminator $D_{n}$ aims to maximize the value function $V_{n}(D,G)$ in 1, while the generator tries to minimize this value.

In this subsection, we analyze the standalone GAN, a traditional approach used in [15, 16, 17] for COVID-19 detection. In this case, every institution $n$ only trains the GAN using its own dataset without the federation.
Proposition 1: For a given generator $G_{n}$, the optimal discriminator is

Proof. For a given generator $G_{n}$, we can derive the probability distribution function for the generator $p^{g}_{n}$. Based on [33], we can express the value function $V_{n}$ in 1 as below

We know that the function $a\log(y)+b\log(1-y)$ achieves its minimum value at $\frac{a}{a+b}$, $\forall(a,b)\in(0,1]$, which thus leads to the result in 2. Next, we derive the optimum of the standalone GAN.
Theorem 1: The optimal value of a standalone GAN for COVID-19 detection is

where $JSD(p^{d}_{n}\parallel p^{g}_{n})$ is the Jensen-Shannon divergence between distributions $p^{d}_{n}$ and $p^{g}_{n}$ [33].
Proof. From 2 and 3, we have

where $KL$ is the Kullback-Leibler divergence. Based on [33], we know that the Jensen-Shannon divergence between probability distributions $A(x)$ and $B(x)$ is $JSD(A\parallel B)$ which is a symmetrized and smoothed version of the all important divergence measure of Kullback-Leibler divergence $KL~{}(~{}A~{}\parallel~{}B)$ which is defined as: $KL~{}(~{}A~{}\parallel~{}C)+KL(B\parallel C)=2*JSD(A\parallel B)$, where $C=\frac{1}{2}(A+B)$. Accordingly, from 4 we derive $V^{*}_{n}(D,G)=-\log 4+2*JSD(p^{d}_{n}||p^{g}_{n})$, completing the proof.

Since $JSD(p^{d}_{n}||p^{g}_{n})$ is always non-negative [33], the global minimum of $V^{*}_{n}(D,G)$ in the standalone GAN-based COVID-19 detection is $-\log 4$. In the following, we will present the proposed FedGAN and prove theoretically its advantages in training the GAN for efficient COVID-19 detection.

In FedGAN, the value function can be defined as a multi-agent game of discriminators and generators of all institutions $n\in\mathcal{N}$. The generators cooperatively learn to generate fake COVID-19 X-ray images in order to fool all discriminators of institutions, whereas the discriminators attempt to differentiate the real data from fake images generated by generators. Then, the value function of the FedGAN can be defined as

Moreover, for any given generators $G_{n}$, the optimal discriminator $D_{n}^{*}$ for the FedGAN is also similar to the standalone GAN which is given by 2. Accordingly, the optimal value of the FedGAN for COVID-19 detection can be calculated as follows:

In the multi-agent game, each generator at each institution $n$ is trained to learn perfectly the contribution of the actual data $p^{d}_{n}$ where the minimum of the value function $V^{fed}(D,G)$ can be achieved at $p^{d}_{n}=p^{g}_{n}$ for $n\in\mathcal{N}$. Thus, the solution of 7 yields $\sum_{n=1}^{N}JSD(p^{g}_{n}||p^{g}_{n})=0$. As a result, the optimal value function for FedGAN can achieve as $V^{fed*}_{n}(D,G)=-n\log 4$.

Based on the above analysis, we can see that the federated approach can achieve a better global minimum of the GAN value function, compared to the standalone approach, due to the federation of multiple institutions which enables learning the data distribution over the entire population. In order words, the proposed FedGAN approach can learn better the COVID-19 image distribution to produce better synthetic image data which facilitates the detection tasks. We will provide extensive simulations to verify the advantage of the FedGAN.

We denote the global training iteration horizon as $T$ and index time by $t$. Each institution $n\in\mathcal{N}$ joins the FedGAN training with the cloud server, by updating the parameters of the discriminator and the generator $\theta^{d}_{n,t}$ and $\theta^{g}_{n,t}$ in each global round and exchange them with the cloud server for aggregation. We assume that the COVID-19 image data in this work is independent and identically distributed (iid) across the institutions, while the non-iid data case will be considered in future works. For every global epoch $t$, each institution $n$ collaboratively trains its discriminator $D_{n}$ and generator $G_{n}$. Specifically, the generator $G_{n}$ produces $k$ minibatchs of fake samples from the noise probability distribution $p^{z}_{n}(z)$ as $\{z^{(1)},z^{(2)},...,z^{(k)}\}$. Also, the discriminator $D_{n}$ samples $k$ minibatchs of real data from the actual image distribution $p^{d}_{n}(x)$ as $\{x^{(1)},x^{(2)},...,x^{(k)}\}$. Then, each institution $n$ updates simultaneously the discriminator $D_{n}$ by ascending its stochastic gradient:

and updates the generator $G_{n}$ by descending its stochastic gradient:

to update its own weights $\theta_{n}^{d},\theta_{n}^{g}$. These stochastic gradient calculations also characterize the approximation of the value function defined in 6.

After the training, the institutions upload their updates $\theta_{n}^{d},\theta_{n}^{g}$ to the cloud server for model aggregation. In this work, we adopt the popular model averaging approach [13] to aggregate the local model parameters: $\theta^{d}\leftarrow\frac{1}{N}\sum_{1}^{N}\theta_{n}^{d}$, $\theta^{g}\leftarrow\frac{1}{N}\sum_{1}^{N}\theta_{n}^{g}$. Then, the cloud server broadcasts the new global updates $\theta^{d},\theta^{g}$ to all institutions for the next round of GAN learning. The FedGAN process is iterated until the global loss function converges with a desired accuracy. The training procedure of the proposed FedGAN is summarized in Algorithm 1.

In FedGAN, the computational complexity mostly comes from the computation at each institution since the cloud server only implements the parameter aggregation and does not result in much computational costs. Thus, we here focus on analyzing the computational complexity at each institution. In every global training round, each institution $n$ collaboratively trains its discriminator and generator to compute its $\theta_{n}^{d}$ and $\theta_{n}^{g}$, respectively. To do that, the generator $G_{n}$ produces $k$ minibatchs of fake samples of batch size $b^{g}$, and the discriminator $D_{n}$ samples $k$ minibatchs of real data of batch size $b^{d}$. Accordingly, in the generator, the batch generation requires $kb^{g}G_{fp}$ floating point operations, where $G_{fp}$ is the number of floating operations to generate a fake data sample of the generator, and a memory of $kb^{g}G_{neu}$, where $G_{neu}$ is the number of neurons of the generator. Therefore, the computational complexity of the generator can be determined as $kb^{g}G_{fp}+kb^{g}G_{neu}=\mathcal{O}\left(kb^{g}(G_{fp}+G_{neu})\right)$. Similarly, the computational complexity of the discriminator can be specified as $\mathcal{O}\left(kb^{d}(D_{fp}+D_{neu})\right)$, where $D_{fp}$ and $D_{neu}$ are the number of floating operations to generate a real data sample and the number of neurons of the generator. To sum up, the computational complexity at an institution in the FedGAN framework after $T$ global training round is $\mathcal{O}\left(Tk\left[\left(b^{g}(G_{fp}+G_{neu})\right)+\left(b^{d}(D_{fp}+D_{neu})\right)\right]\right)$.

To further enhance privacy for FedGAN training, we integrate an $\epsilon$-differential privacy solution at each hospital site, where $\epsilon$ is the distinguishable bound of all outputs on two adjacent datasets $D,D^{\prime}$ in a database. A randomized function $\mathcal{A}$ is $\epsilon$-differential privacy if

where $\mathcal{S}\in range(\mathcal{A})$. To guarantee $\epsilon$-differential privacy, we here apply a gradient perturbation technique with differentially-private stochastic gradient descent (DP-SGD) [12], where Gaussian noises are added to the gradient during the training. Accordingly, we can determine the gradient descent update at training round $t$ as

where $L$ is the loss function of GAN and $\zeta$ is the noise guaranteeing differential privacy.

The working procedure of our blockchain-based FedGAN framework is explained in the following steps:

1. 1.

   The EN that is willing to join the FL process downloads an initial model from the blockchain. Note that each EN also needs to set up a wallet account that contains a public key for identification and a private key for transaction signature.

2. 2.

   Each EN performs the training of the GAN model (i.e., a generator and a discriminator) to compute the gradients using its own local COVID-19 X-ray image dataset. In the case of using differential privacy, an amount of $\epsilon$-differential privacy noises is added to the gradient during the training. After local training, each EN submits its model updates to the blockchain by creating a transaction.

3. 3.

   The miners will aggregate the transactions uploaded from ENs to construct a block after a certain period of time. Then, the miners perform the mining to verify the block using a consensus mechanism.

4. 4.

   After the mining, if all miners achieve an agreement on the verified block, this block is then appended to the blockchain. Now each EN can download the block that contains all FL updates of other ENs to compute the global model. In this regard, the global model is constructed locally instead of in the central cloud server like in the traditional FL architecture. The GAN training is iterated until the desired accuracy performance is achieved.

Based on the working procedure, we can see that the total running latency costs of blockchain-based FedGAN training mostly come from the FedGAN training latency and blockchain mining latency. In this particular work, we focus on addressing the blockchain mining latency, by proposing a novel block consensus mechanism as presented in the following.

In the blockchain-based FedGAN system, when the number of transactions (e.g., local GAN updates) to the blockchain increases, the consensus workload to validate and append them into the blockchain also increases significantly. Although consensus mechanisms such as Delegated Proof-of-Stake (DPoS) have been applied to replace computationally expensive consensus schemes like Proof-of-Work, these solutions still have high latency costs. Indeed, in current consensus algorithms, e.g., DPoS [36], each miner must contact at least more than half of the total nodes in the miner group, which consequently increases latency and alleviates the scalability of the blockchain system. Moreover, each miner node must implement a repeated verification process across the miner network, which results in unnecessary consensus latency. A possible solution is to reduce the number of miner nodes to mitigate the consensus latency, but it potentially compromises the security of blockchain because of the higher probability of adding compromised transactions from malicious nodes [36]. To solve these mining issues, here we propose a new lightweight consensus mechanism called Proof of Reputation (PoR) for our blockchain-FedGAN system. Compared to the DPoS scheme, here we make a significant improvement in the miner selection based on a reputation score evaluation approach. Moreover, instead of using a repeated verification among miner nodes, we implement a lightweight block verification solution that allows each miner to only verify once with another node during the consensus process, which would significantly reduce the verification latency. There are two main parts to our PoR consensus, including miner node selection and block verification.

We use two popular COVID-19 X-ray datasets for simulations, including a DarkCOVID dataset [7] with total 620 X-ray images and a ChestCOVID dataset [39] with total 950 X-ray images for three classes (COVID-19, normal (no pneumonia), and pneumonia (with no COVID-19 infection)) which have been collected from different regions which makes them suitable for our FedGAN setting. For each dataset, we divide into the training and testing set with a 80:20 ratio.

In the FedGAN system, we set up five institutions where each of them has a discriminator and a generator based on CNNs, as shown in Fig. 1. Each discriminator $D$ takes COVID-19 X-ray images in the form of 64x64x1 size where the mini-batch is set to 32. The discriminator is configured with five hidden layers, each having 128 dimensions along with LeakyRELU and dropout. Furthermore, each generator $G$ takes 64-dimensional noise samples from a standard Gaussian distribution. Every generator has five hidden layers, where the first three layers have 256 dimensions and the last two layers have 128 dimensions. These parameters are selected based on preliminary experimental results. The FedGAN is trained for 500 global rounds where each local GAN is trained for 20 epochs.

Moreover, we design a CNN-based classifier for COVID-19 detection with three classes: COVID-19 positive, normal, and pneumonia. The CNN architecture consists of an input layer with the shape of 32x32x3 and three hidden convolutional layers with kernel 3x3, ReLU activation functions and max pooling. Here, the first hidden layer has 32 dimensions, the second layer has 128 dimensions with Relu as the activation in each layer. The final layer has three dimensions, with SGD as the optimizer, a softmax function as the activation to output prediction results over three classes. Moreover, batch normalization and dropout (0.5) are added to avoid overfitting on the training set. The CNN classifier is trained with the learning rate of 0.001. These hyperparameters are selected via multiple training trials for reliable classification results. All simulations were implemented in Pytorch on a desktop server with an Intel Core i7 4.7GHz CPU and 128 GB memory with Nvidia Pascal Titan X and CUDA 8.0.

We investigate the performance of our proposed FedGAN scheme and compare it with the state-of-the-art schemes, including: the standalone scheme [5], the standalone scheme with GAN [18], the FL scheme without GAN [24], and the centralized scheme (all datasets are transmitted to the cloud for classification). All considered schemes use a CNN-based classifier for evaluating the COVID-19 detection. For reliable evaluation, the reported results are averaged from five runs of numerical simulations.

Here, we evaluate the performance of our proposed PoR consensus scheme via numerical simulations and compare it with the traditional DPoS scheme via the verification block latency metric. We set up 10 transactions per block and vary the numbers of miners from 2 to 100. Motivated by [38], the mining parameters are set up as follows: edge computation resources $c_{m}=[10^{3}-10^{6}]$ CPU cycles/s, input/output block data sizes $B=500$ KB, $B^{re}=50$ KB, the uplink transmission rate $r_{m}^{u}=[100-250]$ kbps, the downlink transmission rate $r_{m}^{d}=[100-250]$ kbps, $\xi=0.5$, $\tau_{m}=1000$ ms.