Pub Date : 2024-03-01DOI: 10.1109/MSP.2024.3379732
Wenyuan Wang;Kutluyil Doğançay
In this article, we present a powerful unifying framework for widely linear (WL) adaptive filters building on the concept of geometric algebra (GA), including recently proposed complex-valued (CV), quaternion-valued, and GA WL adaptive filters (WLAFs). We also consider and review WL adaptive filtering methods that feature robustness against impulsive noise, noisy input measurements, partial coefficient updates, subband structures, censoring, and composite structures under the unified framework. Furthermore, we propose innovative WL adaptive filtering algorithms for functional link polynomial (FLP) nonlinear filters, infinite-impulse response (IIR) systems, and kernel-based nonlinear system identification, showcasing the advantages of the unified framework. The article also investigates the relationship among WLAFs, graph filters, and Cayley–Dickson (CD)-valued adaptive filters, offering new insights into how the unified framework can be extended to graph signals and CD numbers. Finally, the article motivates future work on WL adaptive filtering based on GA and its special cases.
在本文中，我们以几何代数（GA）的概念为基础，为广泛线性（WL）自适应滤波器提出了一个强大的统一框架，包括最近提出的复值（CV）、四元数值和 GA WL 自适应滤波器（WLAF）。我们还考虑并评述了 WL 自适应滤波方法，这些方法的特点是在统一框架下对脉冲噪声、噪声输入测量、部分系数更新、子带结构、删减和复合结构具有鲁棒性。此外，我们还针对函数链路多项式（FLP）非线性滤波器、无穷脉冲响应（IIR）系统和基于核的非线性系统识别提出了创新的 WL 自适应滤波算法，展示了统一框架的优势。文章还研究了 WLAF、图滤波器和 Cayley-Dickson (CD) 值自适应滤波器之间的关系，为如何将统一框架扩展到图信号和 CD 数提供了新的见解。最后，文章激励了基于 GA 及其特例的 WL 自适应滤波的未来工作。
{"title":"Widely Linear Adaptive Filtering Based on Clifford Geometric Algebra: A unified framework [Hypercomplex Signal and Image Processing]","authors":"Wenyuan Wang;Kutluyil Doğançay","doi":"10.1109/MSP.2024.3379732","DOIUrl":"https://doi.org/10.1109/MSP.2024.3379732","url":null,"abstract":"In this article, we present a powerful unifying framework for widely linear (WL) adaptive filters building on the concept of geometric algebra (GA), including recently proposed complex-valued (CV), quaternion-valued, and GA WL adaptive filters (WLAFs). We also consider and review WL adaptive filtering methods that feature robustness against impulsive noise, noisy input measurements, partial coefficient updates, subband structures, censoring, and composite structures under the unified framework. Furthermore, we propose innovative WL adaptive filtering algorithms for functional link polynomial (FLP) nonlinear filters, infinite-impulse response (IIR) systems, and kernel-based nonlinear system identification, showcasing the advantages of the unified framework. The article also investigates the relationship among WLAFs, graph filters, and Cayley–Dickson (CD)-valued adaptive filters, offering new insights into how the unified framework can be extended to graph signals and CD numbers. Finally, the article motivates future work on WL adaptive filtering based on GA and its special cases.","PeriodicalId":13246,"journal":{"name":"IEEE Signal Processing Magazine","volume":"41 2","pages":"86-101"},"PeriodicalIF":14.9,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141326256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A hybrid model called the geometric (Clifford) quanvolutional neural network ( GQNN ) that merges elements of geometric (Clifford) convolutional neural networks (GCNNs) and variational quantum circuits (VQCs) is presented. In this model, a randomized quantum convolution operation is applied to the input image, giving as a result four output channels, which are treated as a single entity (quaternion image) by the subsequent quaternion layers. This approach is extended to Clifford algebras by choosing the number of qubits of the quantum circuit according to the dimension of the Clifford algebra so that the resulting output channels are regarded as the components of a multivector image to be further processed by Clifford layers.
{"title":"Geometric Algebra Quantum Convolutional Neural Network: A model using geometric (Clifford) algebras and quantum computing [Hypercomplex Signal and Image Processing]","authors":"Guillermo Altamirano-Escobedo;Eduardo Bayro-Corrochano","doi":"10.1109/MSP.2024.3369015","DOIUrl":"https://doi.org/10.1109/MSP.2024.3369015","url":null,"abstract":"A hybrid model called the \u0000<italic>geometric (Clifford) quanvolutional neural network</i>\u0000 (\u0000<italic>GQNN</i>\u0000) that merges elements of geometric (Clifford) convolutional neural networks (GCNNs) and variational quantum circuits (VQCs) is presented. In this model, a randomized quantum convolution operation is applied to the input image, giving as a result four output channels, which are treated as a single entity (quaternion image) by the subsequent quaternion layers. This approach is extended to Clifford algebras by choosing the number of qubits of the quantum circuit according to the dimension of the Clifford algebra so that the resulting output channels are regarded as the components of a multivector image to be further processed by Clifford layers.","PeriodicalId":13246,"journal":{"name":"IEEE Signal Processing Magazine","volume":"41 2","pages":"75-85"},"PeriodicalIF":14.9,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141326299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-01DOI: 10.1109/MSP.2024.3349460
Michel Berthier;Nicoletta Prencipe;Edoardo Provenzi
We propose a perceptual chromatic adaptation transform (CAT) for white balance that makes use of split-quaternions. The novelty of the present work, which is motivated by a recently developed quantumlike model of color perception, consists of stressing the link between the algebraic structures appearing in this model and a certain subalgebra of the split-quaternions. We show the potential of this approach for color image processing applications by proposing a CAT implemented via an appropriate use of the split-quaternion multiplication. Moreover, quantitative comparisons with the widely used state-of-the art von Kries CAT are provided.
我们提出了一种利用分四元数进行白平衡的感知色度适应变换（CAT）。本研究的新颖之处在于强调了该模型中出现的代数结构与分四元数的某个子代数之间的联系。我们提出了一种通过适当使用分裂四元数乘法实现的 CAT，从而展示了这种方法在彩色图像处理应用中的潜力。此外，我们还提供了与广泛使用的最先进的 von Kries CAT 的定量比较。
{"title":"Split-Quaternions for Perceptual White Balance: A quantum information-based chromatic adaptation transform [Hypercomplex Signal and Image Processing]","authors":"Michel Berthier;Nicoletta Prencipe;Edoardo Provenzi","doi":"10.1109/MSP.2024.3349460","DOIUrl":"https://doi.org/10.1109/MSP.2024.3349460","url":null,"abstract":"We propose a perceptual chromatic adaptation transform (CAT) for white balance that makes use of split-quaternions. The novelty of the present work, which is motivated by a recently developed quantumlike model of color perception, consists of stressing the link between the algebraic structures appearing in this model and a certain subalgebra of the split-quaternions. We show the potential of this approach for color image processing applications by proposing a CAT implemented via an appropriate use of the split-quaternion multiplication. Moreover, quantitative comparisons with the widely used state-of-the art von Kries CAT are provided.","PeriodicalId":13246,"journal":{"name":"IEEE Signal Processing Magazine","volume":"41 2","pages":"42-50"},"PeriodicalIF":14.9,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141326316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-01DOI: 10.1109/MSP.2023.3327627
Artyom M. Grigoryan;Sos S. Agaian
Classical color image processing, image recognition, and machine learning introduce nonlinearity, causing the collapse of the quantum state into classical probability perceptrons after measurements, due to the inherent linearity of quantum computing. To address this challenge, quaternion-based arithmetic offers a promising approach. By treating the primary color components as a single unit using quaternion algebra, nonlinear relationships can be implemented, effectively manipulating higher-dimensional color data. This article aims to achieve efficient and accurate color quantum image processing (QIP) by introducing new quaternion quantum-based color imaging tools based on multiplicative arithmetic on two-qubits and quantum superpositions. The approach includes the concept of a quaternion Fourier transform (QFT) in two-qubit-based color image representation. To end, we discuss possible applications of the proposed methods in color quantum imaging.
{"title":"Quaternion-Based Arithmetic in Quantum Information Processing: A promising approach for efficient color quantum imaging [Hypercomplex Signal and Image Processing]","authors":"Artyom M. Grigoryan;Sos S. Agaian","doi":"10.1109/MSP.2023.3327627","DOIUrl":"https://doi.org/10.1109/MSP.2023.3327627","url":null,"abstract":"Classical color image processing, image recognition, and machine learning introduce nonlinearity, causing the collapse of the quantum state into classical probability perceptrons after measurements, due to the inherent linearity of quantum computing. To address this challenge, quaternion-based arithmetic offers a promising approach. By treating the primary color components as a single unit using quaternion algebra, nonlinear relationships can be implemented, effectively manipulating higher-dimensional color data. This article aims to achieve efficient and accurate color quantum image processing (QIP) by introducing new quaternion quantum-based color imaging tools based on multiplicative arithmetic on two-qubits and quantum superpositions. The approach includes the concept of a quaternion Fourier transform (QFT) in two-qubit-based color image representation. To end, we discuss possible applications of the proposed methods in color quantum imaging.","PeriodicalId":13246,"journal":{"name":"IEEE Signal Processing Magazine","volume":"41 2","pages":"64-74"},"PeriodicalIF":14.9,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141326255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-01DOI: 10.1109/MSP.2024.3408368
{"title":"Signal Processing Society Social Media","authors":"","doi":"10.1109/MSP.2024.3408368","DOIUrl":"https://doi.org/10.1109/MSP.2024.3408368","url":null,"abstract":"","PeriodicalId":13246,"journal":{"name":"IEEE Signal Processing Magazine","volume":"41 2","pages":"5-5"},"PeriodicalIF":14.9,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10558734","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141326298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-01DOI: 10.1109/MSP.2024.3388166
Richard J. Radke
How did an “old dog” signal processing professor approach learning and teaching the “new tricks” of generative artificial intelligence (AI)? This article overviews my recent experience in preparing and delivering a new course called “Computational Creativity,” reflecting on the methods I adopted compared to a traditional equations-on-a-whiteboard course. The technical material is qualitatively different from traditional signal processing, and the types of students who took the class and their approach to learning were different too. I learned a lot from the experience but also came away with bigger questions about the role of educators in the age of generative AI.
{"title":"A Signal Processor Teaches Generative Artificial Intelligence [SP Education]","authors":"Richard J. Radke","doi":"10.1109/MSP.2024.3388166","DOIUrl":"https://doi.org/10.1109/MSP.2024.3388166","url":null,"abstract":"How did an “old dog” signal processing professor approach learning and teaching the “new tricks” of generative artificial intelligence (AI)? This article overviews my recent experience in preparing and delivering a new course called “Computational Creativity,” reflecting on the methods I adopted compared to a traditional equations-on-a-whiteboard course. The technical material is qualitatively different from traditional signal processing, and the types of students who took the class and their approach to learning were different too. I learned a lot from the experience but also came away with bigger questions about the role of educators in the age of generative AI.","PeriodicalId":13246,"journal":{"name":"IEEE Signal Processing Magazine","volume":"41 2","pages":"6-10"},"PeriodicalIF":14.9,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141326318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-01DOI: 10.1109/MSP.2024.3396646
Recounts the career and contributions of H. Joel Trussell.
介绍乔尔-特鲁塞尔（H. Joel Trussell）的职业生涯和贡献。
{"title":"In Memoriam: H. Joel Trussell [In Memoriam]","authors":"","doi":"10.1109/MSP.2024.3396646","DOIUrl":"https://doi.org/10.1109/MSP.2024.3396646","url":null,"abstract":"Recounts the career and contributions of H. Joel Trussell.","PeriodicalId":13246,"journal":{"name":"IEEE Signal Processing Magazine","volume":"41 2","pages":"102-102"},"PeriodicalIF":14.9,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10558735","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141326320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-01DOI: 10.1109/MSP.2024.3349456
Breno Bahia;Arash JafarGandomi;Mauricio D. Sacchi
Vector-valued signals are crucial in science and engineering. The evolving field of hypercomplex signal processing, particularly quaternion algebra, offers a concise and natural approach to handling vectorial data. In multicomponent seismology, for instance, vector-valued signal processing finds a natural fit that has been exploited in several applications. This article provides a concise and practical review of quaternionic methods for handling vector-valued seismic datasets, from historical origins to key concepts and tools in the field of quaternion signal processing, such as the quaternion Fourier transform and quaternion singular value decomposition (SVD). While highlighting existing results, this review also showcases novel developments through source separation applications with quaternions, discussing encountered challenges and outlining potential future trends.
{"title":"Hypercomplex Processing of Vector Field Seismic Data: Toward vector-valued signal processing [Hypercomplex Signal and Image Processing]","authors":"Breno Bahia;Arash JafarGandomi;Mauricio D. Sacchi","doi":"10.1109/MSP.2024.3349456","DOIUrl":"https://doi.org/10.1109/MSP.2024.3349456","url":null,"abstract":"Vector-valued signals are crucial in science and engineering. The evolving field of hypercomplex signal processing, particularly quaternion algebra, offers a concise and natural approach to handling vectorial data. In multicomponent seismology, for instance, vector-valued signal processing finds a natural fit that has been exploited in several applications. This article provides a concise and practical review of quaternionic methods for handling vector-valued seismic datasets, from historical origins to key concepts and tools in the field of quaternion signal processing, such as the quaternion Fourier transform and quaternion singular value decomposition (SVD). While highlighting existing results, this review also showcases novel developments through source separation applications with quaternions, discussing encountered challenges and outlining potential future trends.","PeriodicalId":13246,"journal":{"name":"IEEE Signal Processing Magazine","volume":"41 2","pages":"29-41"},"PeriodicalIF":14.9,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141326339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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