2016/10/27 by Hong Sun, Sun, Hong, Cheng-Wei Sang +4
Computer Science · Engineering · Mathematics · #Algorithm #Artificial intelligence #Basis (linear algebra) #Computer science #Decomposition #FOS: Computer and information sciences #Image (mathematics) #Image and Signal Denoising Methods #K-SVD #Machine Learning (stat.ML) #Mathematics #Matrix decomposition #Noise (video) #Noise reduction #Pattern recognition (psychology) #Representation (politics) #SIGNAL (programming language) #Set (abstract data type) #Signal subspace #Sparse and Compressive Sensing Techniques #Sparse approximation #Structural Health Monitoring Techniques #Subspace topology #stat.ML
paper · pdf · doi:10.48550/arxiv.1610.08813
published in arXiv (Cornell University) (Cornell University)
arxiv created 2016/10/27 · openalex publication_date 2016/10/27 · arxiv updated 2016/10/28 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/09
This paper proposes a subspace decomposition method based on an over-complete dictionary in sparse representation, called "Sparse Signal Subspace Decomposition" (or 3SD) method. This method makes use of a novel criterion based on the occurrence frequency of atoms of the dictionary over the data set. This criterion, well adapted to subspace-decomposition over a dependent basis set, adequately re ects the intrinsic characteristic of regularity of the signal. The 3SD method combines variance, sparsity and component frequency criteria into an unified framework. It takes benefits from using an over-complete dictionary which preserves details and from subspace decomposition which rejects strong noise. The 3SD method is very simple with a linear retrieval operation. It does not require any prior knowledge on distributions or parameters. When applied to image denoising, it demonstrates high performances both at preserving fine details and suppressing strong noise.