2021/04/23 by Palle E. T. Jørgensen, Jorgensen, Palle E. T., Myung-Sin Song +3
Computer Science · Engineering · Mathematics · #41A65 #42A82 #42C15 #46E22 #47A05 #47N10 #60G15 #62H25 #68T07 #90C20 #94A08 #94A12 #94A20 #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Numerical Analysis (math.NA) #Primary: 47B32. Secondary: 41A15 #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2104.11807
openalex publication_date 2021/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main purpose of our paper is a new approach to design of algorithms of Kaczmarz type in the framework of operators in Hilbert space. Our applications include a diverse list of optimization problems, new Karhunen-Loève transforms, and Principal Component Analysis (PCA) for digital images. A key feature of our algorithms is our use of recursive systems of projection operators. Specifically, we apply our recursive projection algorithms for new computations of PCA probabilities and of variance data. For this we also make use of specific reproducing kernel Hilbert spaces, factorization for kernels, and finite-dimensional approximations. Our projection algorithms are designed with view to maximum likelihood solutions, minimization of "cost" problems, identification of principal components, and data-dimension reduction.