Blind Source Separation Based on Sparsity

• URL: http://arxiv.org/abs/2504.19124v1
• Date: Sun, 27 Apr 2025 06:42:06 GMT
• Title: Blind Source Separation Based on Sparsity
• Authors: Zhongxuan Li,
• Abstract summary: Blind source separation (BSS) is a key technique in array processing and data analysis.<n>Box coordinate relaxation MCA algorithm is used in Multichannel MCA and Generalized MCA.<n>We propose an improved algorithm, SAC+BK-SVD, which enhances K-SVD by learning a block-sparsifying dictionary.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Blind source separation (BSS) is a key technique in array processing and data analysis, aiming to recover unknown sources from observed mixtures without knowledge of the mixing matrix. Classical independent component analysis (ICA) methods rely on the assumption that sources are mutually independent. To address limitations of ICA, sparsity-based methods have been introduced, which decompose source signals sparsely in a predefined dictionary. Morphological Component Analysis (MCA), based on sparse representation theory, assumes that a signal is a linear combination of components with distinct geometries, each sparsely representable in one dictionary and not in others. This approach has recently been applied to BSS with promising results. This report reviews key approaches derived from classical ICA and explores sparsity-based methods for BSS. It introduces the theory of sparse representation and decomposition, followed by a block coordinate relaxation MCA algorithm, whose variants are used in Multichannel MCA (MMCA) and Generalized MCA (GMCA). A local dictionary learning method using K-SVD is then presented. Finally, we propose an improved algorithm, SAC+BK-SVD, which enhances K-SVD by learning a block-sparsifying dictionary that clusters and updates similar atoms in blocks. The implementation includes experiments on image segmentation and blind image source separation using the discussed techniques. We also compare the proposed block-sparse dictionary learning algorithm with K-SVD. Simulation results demonstrate that our method yields improved blind image separation quality.

Related papers

• Fast Semisupervised Unmixing Using Nonconvex Optimization [80.11512905623417]
  We introduce a novel convex convex model for semi/library-based unmixing. We demonstrate the efficacy of Alternating Methods of sparse unsupervised unmixing.
  arXiv  Detail & Related papers  (2024-01-23T10:07:41Z)
• Nonparametric Evaluation of Noisy ICA Solutions [5.749787074942513]
  Independent Component Analysis (ICA) was introduced in the 1980's as a model for Blind Source Separation (BSS) We develop a nonparametric score to adaptively pick the right algorithm for ICA with arbitrary Gaussian noise.
  arXiv  Detail & Related papers  (2024-01-16T16:18:17Z)
• Score-based Source Separation with Applications to Digital Communication Signals [72.6570125649502]
  We propose a new method for separating superimposed sources using diffusion-based generative models. Motivated by applications in radio-frequency (RF) systems, we are interested in sources with underlying discrete nature. Our method can be viewed as a multi-source extension to the recently proposed score distillation sampling scheme.
  arXiv  Detail & Related papers  (2023-06-26T04:12:40Z)
• Rethinking k-means from manifold learning perspective [122.38667613245151]
  We present a new clustering algorithm which directly detects clusters of data without mean estimation. Specifically, we construct distance matrix between data points by Butterworth filter. To well exploit the complementary information embedded in different views, we leverage the tensor Schatten p-norm regularization.
  arXiv  Detail & Related papers  (2023-05-12T03:01:41Z)
• Semi-Blind Source Separation with Learned Constraints [1.2891210250935146]
  Blind source separation (BSS) algorithms are unsupervised methods for hyperspectral data analysis. In this article, we investigate a semi-supervised source separation approach in which we combine a projected alternating least-square algorithm with a learning-based regularization scheme. We show that this allows for an innovative BSS algorithm, with improved accuracy, which provides physically interpretable solutions.
  arXiv  Detail & Related papers  (2022-09-27T17:58:23Z)
• Mining Relations among Cross-Frame Affinities for Video Semantic Segmentation [87.4854250338374]
  We explore relations among affinities in two aspects: single-scale intrinsic correlations and multi-scale relations. Our experiments demonstrate that the proposed method performs favorably against state-of-the-art VSS methods.
  arXiv  Detail & Related papers  (2022-07-21T12:12:36Z)
• Deep Equilibrium Assisted Block Sparse Coding of Inter-dependent Signals: Application to Hyperspectral Imaging [71.57324258813675]
  A dataset of inter-dependent signals is defined as a matrix whose columns demonstrate strong dependencies. A neural network is employed to act as structure prior and reveal the underlying signal interdependencies. Deep unrolling and Deep equilibrium based algorithms are developed, forming highly interpretable and concise deep-learning-based architectures.
  arXiv  Detail & Related papers  (2022-03-29T21:00:39Z)
• Dictionary-based Low-Rank Approximations and the Mixed Sparse Coding problem [7.132368785057316]
  I show how to adapt an efficient MSC solver based on the LASSO to compute Dictionary-based Matrix Factorization and Canonical Polyadic Decomposition. I show how to adapt an efficient MSC solver based on the LASSO to compute Dictionary-based Matrix Factorization and Canonical Polyadic Decomposition in the context of hyperspectral image processing and chemometrics.
  arXiv  Detail & Related papers  (2021-11-24T10:32:48Z)
• Discriminative Dictionary Learning based on Statistical Methods [0.0]
  Sparse Representation (SR) of signals or data has a well founded theory with rigorous mathematical error bounds and proofs. Training dictionaries such that they represent each class of signals with minimal loss is called Dictionary Learning (DL) MOD and K-SVD have been successfully used in reconstruction based applications in image processing like image "denoising", "inpainting"
  arXiv  Detail & Related papers  (2021-11-17T10:45:10Z)
• Deep learning based dictionary learning and tomographic image reconstruction [0.0]
  This work presents an approach for image reconstruction in clinical low-dose tomography that combines principles from sparse signal processing with ideas from deep learning. First, we describe sparse signal representation in terms of dictionaries from a statistical perspective and interpret dictionary learning as a process of aligning distribution that arises from a generative model with empirical distribution of true signals. As a result we can see that sparse coding with learned dictionaries resembles a specific variational autoencoder, where the decoder is a linear function and the encoder is a sparse coding algorithm.
  arXiv  Detail & Related papers  (2021-08-26T12:10:17Z)
• Locality Constrained Analysis Dictionary Learning via K-SVD Algorithm [6.162666237389167]
  We propose a novel locality constrained analysis dictionary learning model with a synthesis K-SVD algorithm (SK-LADL) It considers intrinsic geometric properties by imposing graph regularization to uncover the geometric structure for the image data. Through the learned analysis dictionary, we transform the image to a new and compact space where the manifold assumption can be further guaranteed.
  arXiv  Detail & Related papers  (2021-04-29T05:58:34Z)
• CIMON: Towards High-quality Hash Codes [63.37321228830102]
  We propose a new method named textbfComprehensive stextbfImilarity textbfMining and ctextbfOnsistency leartextbfNing (CIMON) First, we use global refinement and similarity statistical distribution to obtain reliable and smooth guidance. Second, both semantic and contrastive consistency learning are introduced to derive both disturb-invariant and discriminative hash codes.
  arXiv  Detail & Related papers  (2020-10-15T14:47:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.