# Synthetic Image Generation Using Conditional GAN-Provided Single-Sample Face Image
## 1 Introduction  
Facial recognition has emerged as an important area in various fields, including image processing, cognitive sciences, computer vision, machine learning, and pattern recognition, driven by its application in bio-metric verification technology. The human face can be recognized from a video stream or a static image using human face databases containing many different individuals. While humans have the natural ability to recognize faces with ease, machines struggle to do so due to the presence of complex features within each face, making every individual distinct from one another [1]. In recent decades, machine learning and deep learning models have shown promising results in automatic face recognition. This process is critical for tasks such as identifying terrorists, military personnel, monitoring general surveillance, identifying criminals, border security, and immigration control. Due to its significant applications, facial recognition has been a focal point of research for many years. The automatic recognition of faces is a complex task due to various challenges such as illumination, pose, expressions, occlusion, and demographic differences such as gender and race [2]. A wide range of deep learning-based methods [3, 4] have been developed for face recognition. However, an effective facial recognition system must profitently extract the key features that minimize both inter-class variation and intra-class variation between the subjects. Despite considerable progress, managing these variations, particularly inter-class variations such as age, appearances, racial features, and gender, as well as intra-class variations like illumination, disguise, expressions, and occlusion, remains a challenge. While deep learning has shown promising results in various domains,including facial recognition, training these models requires extensive datasets, posing considerable challenges. The key issue for deep learning-based facial recognition systems is the scarcity of training samples. Often, there is only a single training sample per person (SSPP). This scenario becomes more challenging when attempting to recognize a query image under varying conditions such as occlusion, illumination, pose, and expression, with only one image per subject in the gallery set. Consequently, recognition systems struggle to identify the facial variations due to the limited data availability. Two fundamental approaches typically employed by researchers to address the SSPP issue, i.e., holistic, and local methods. Holistic methods include subspace models like Principal Component Analysis (PCA) [5] and Linear Discriminant Analysis (LDA) [6]. However these methods relied on large amounts of training data, which is the primary issue with the SSPP scenario. Generative models play a crucial role when training data is scarce or difficult to obtain. A key generative model approach is the Generative Adversarial Network (GAN) [7]; it is comprised of two competing neural networks, a generator, and a discriminator [8] trained in an adversarial manner, where the generator network receives random noise as input and produces synthetic samples designed to mimic real data. Concurrently, the discriminator is trained to distinguish these generated samples from actual training data samples. During the adversarial training process, the generator aims to produce increasingly realistic fake samples to deceive the discriminator, while the discriminator aims to enhance its ability to differentiate these generated samples from actual data. The generator and discriminator are involved in a min-max game where the generator seeks to minimize the discriminator's ability to detect fake samples, while the discriminator aims to maximize its accuracy in classifying the samples as either real or fake. This iterative process results in the generator gradually learning to create synthetic data that become indistinguishable from real data for the discriminator. The trained generator generates new realistic samples aimed at extending the limited training data.