2015/08/03 by Rodrigo C. de Lamare, de Lamare, Rodrigo C.
Computer Science · Engineering · Mathematics · #Algorithm #Artificial intelligence #Blind Source Separation Techniques #Computer science #Covariance matrix #Curse of dimensionality #Digital signal processing #Dimensionality reduction #Direction-of-Arrival Estimation Techniques #FOS: Computer and information sciences #Image (mathematics) #Information Theory (cs.IT) #Iterative method #Krylov subspace #Linear algebra #Mathematics #Noise (video) #Rank (graph theory) #Reduction (mathematics) #SIGNAL (programming language) #Signal processing #Signal subspace #Sparse and Compressive Sensing Techniques #Synthetic Aperture Radar (SAR) Applications and Techniques #Transformation matrix #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1508.00636
23 pages, 6 figures
openalex publication_date 2015/08/03 · arxiv created 2015/08/04 · arxiv updated 2015/08/05 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28
We present a tutorial on reduced-rank signal processing, design methods and\nalgorithms for dimensionality reduction, and cover a number of important\napplications. A general framework based on linear algebra and linear estimation\nis employed to introduce the reader to the fundamentals of reduced-rank signal\nprocessing and to describe how dimensionality reduction is performed on an\nobserved discrete-time signal. A unified treatment of dimensionality reduction\nalgorithms is presented with the aid of least squares optimization techniques,\nin which several techniques for designing the transformation matrix that\nperforms dimensionality reduction are reviewed. Among the dimensionality\nreduction techniques are those based on the eigen-decomposition of the observed\ndata vector covariance matrix, Krylov subspace methods, joint and iterative\noptimization (JIO) algorithms and JIO with simplified structures and switching\n(JIOS) techniques. A number of applications are then considered using a unified\ntreatment, which includes wireless communications, sensor and array signal\nprocessing, and speech, audio, image and video processing. This tutorial\nconcludes with a discussion of future research directions and emerging topics.\n