An Invitation to Hypercomplex Phase Retrieval: Theory and Applications

Hypercomplex signal processing (HSP) provides state-of-the-art tools to handle multidimensional signals by harnessing intrinsic correlation of the signal dimensions through Clifford algebra. Recently, the hypercomplex representation of the phase retrieval (PR) problem, wherein a complex-valued signal is estimated through its intensity-only projections, has attracted significant interest. The hypercomplex PR (HPR) arises in many optical imaging and computational sensing applications that usually comprise quaternion and octonion-valued signals. Analogous to the traditional PR, measurements in HPR may involve complex, hypercomplex, Fourier, and other sensing matrices. This set of problems opens opportunities for developing novel HSP tools and algorithms. This article provides a synopsis of the emerging areas and applications of HPR with a focus on optical imaging.Comment: 10 pages, 4 figures, 2 table

Enhancing Facial Emotion Recognition with a Modified Deep Convolutional Neural Network

Understanding and predicting human character traits play a crucial role in various domains ranging from psychology to human resources. With the advent of artificial intelligence (AI) and deep learning algorithms, researchers have explored the potential of analyzing facial images to predict human character traits accurately. In this paper, we present a comprehensive study of the application of AI techniques for human character recognition. We review the existing literature on facial image analysis, AI algorithms, and personality prediction. Furthermore, we propose a methodology that leverages deep learning and convolutional neural networks (CNNs) to extract meaningful features from facial images. Our experiments demonstrate the effectiveness of our approach in accurately predicting character traits and showcasing promising results using small-scale datasets. We discuss the implications of our findings in psychology, human resources, and personalized user experiences. Additionally, ethical considerations, such as privacy and bias, are addressed. This research contributes to the growing field of AI-driven character recognition, providing insights for further advancements and practical applications in understanding human behavio

Enhancing Facial Emotion Recognition with a Modified Deep Convolutional Neural Network

Understanding and predicting human character traits play a crucial role in various domains ranging from psychology to human resources. With the advent of artificial intelligence (AI) and deep learning algorithms, researchers have explored the potential of analyzing facial images to predict human character traits accurately. In this paper, we present a comprehensive study of the application of AI techniques for human character recognition. We review the existing literature on facial image analysis, AI algorithms, and personality prediction. Furthermore, we propose a methodology that leverages deep learning and convolutional neural networks (CNNs) to extract meaningful features from facial images. Our experiments demonstrate the effectiveness of our approach in accurately predicting character traits and showcasing promising results using small-scale datasets. We discuss the implications of our findings in psychology, human resources, and personalized user experiences. Additionally, ethical considerations, such as privacy and bias, are addressed. This research contributes to the growing field of AI-driven character recognition, providing insights for further advancements and practical applications in understanding human behavio

PHNNs: Lightweight Neural Networks via Parameterized Hypercomplex Convolutions

Hypercomplex neural networks have proven to reduce the overall number of parameters while ensuring valuable performance by leveraging the properties of Clifford algebras. Recently, hypercomplex linear layers have been further improved by involving efficient parameterized Kronecker products. In this article, we define the parameterization of hypercomplex convolutional layers and introduce the family of parameterized hypercomplex neural networks (PHNNs) that are lightweight and efficient large-scale models. Our method grasps the convolution rules and the filter organization directly from data without requiring a rigidly predefined domain structure to follow. PHNNs are flexible to operate in any user-defined or tuned domain, from 1-D to nD regardless of whether the algebra rules are preset. Such a malleability allows processing multidimensional inputs in their natural domain without annexing further dimensions, as done, instead, in quaternion neural networks (QNNs) for 3-D inputs like color images. As a result, the proposed family of PHNNs operates with 1/n free parameters as regards its analog in the real domain. We demonstrate the versatility of this approach to multiple domains of application by performing experiments on various image datasets and audio datasets in which our method outperforms real and quaternion-valued counterparts