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Related papers: Principal Basis Analysis in Sparse Representation

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The research reported in this paper addresses the fundamental task of separation of locally moving or deforming image areas from a static or globally moving background. It builds on the latest developments in the field of robust principal…

Computer Vision and Pattern Recognition · Computer Science 2016-03-21 Salehe Erfanian Ebadi , Valia Guerra Ones , Ebroul Izquierdo

The problem of recovering a low-rank matrix from a set of observations corrupted with gross sparse error is known as the robust principal component analysis (RPCA) and has many applications in computer vision, image processing and web data…

Optimization and Control · Mathematics 2013-09-27 Necdet Serhat Aybat , Donald Goldfarb , Shiqian Ma

Our main objective is to develop a denoising strategy to increase the signal to noise ratio of individual spectral lines of stellar spectropolarimetric observations. We use a multivariate statistics technique called Principal Component…

In this paper, we study the problem of sparse Principal Component Analysis (PCA) in the high-dimensional setting with missing observations. Our goal is to estimate the first principal component when we only have access to partial…

Statistics Theory · Mathematics 2012-06-04 Karim Lounici

Sparse signal recovery from a small number of random measurements is a well known NP-hard to solve combinatorial optimization problem, with important applications in signal and image processing. The standard approach to the sparse signal…

Data Analysis, Statistics and Probability · Physics 2013-04-09 M. Andrecut

Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage constructs a regression model whose explanatory variables are replaced by principal components…

Machine Learning · Statistics 2021-11-22 Shuichi Kawano

We study the problem of demixing a pair of sparse signals from noisy, nonlinear observations of their superposition. Mathematically, we consider a nonlinear signal observation model, $y_i = g(a_i^Tx) + e_i, \ i=1,\ldots,m$, where $x = \Phi…

Machine Learning · Statistics 2017-08-02 Mohammadreza Soltani , Chinmay Hegde

In many scientific applications, measured time series are corrupted by noise or distortions. Traditional denoising techniques often fail to recover the signal of interest, particularly when the signal-to-noise ratio is low or when certain…

Machine Learning · Computer Science 2022-11-02 Natalie Klein , Amber J. Day , Harris Mason , Michael W. Malone , Sinead A. Williamson

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…

Machine Learning · Computer Science 2021-06-29 Zhao Kang , Hongfei Liu , Jiangxin Li , Xiaofeng Zhu , Ling Tian

We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…

Numerical Analysis · Computer Science 2009-01-08 Wei Dai , Olgica Milenkovic

This paper addresses the problem of noise reduction with simultaneous components extrac- tion in vibration signals for faults diagnosis of bearing. The observed vibration signal is modeled as a summation of two components contaminated by…

Sound · Computer Science 2016-08-09 Wangpeng He , Yin Ding , Yanyang Zi , Ivan W. Selesnick

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…

Machine Learning · Computer Science 2012-06-22 Alfredo Kalaitzis , Neil Lawrence

In this paper, a new method is proposed for sparse PCA based on the recursive divide-and-conquer methodology. The main idea is to separate the original sparse PCA problem into a series of much simpler sub-problems, each having a closed-form…

Computer Vision and Pattern Recognition · Computer Science 2012-12-03 Qian Zhao , Deyu Meng , Zongben Xu

Principal Component Analysis (PCA) has wide applications in machine learning, text mining and computer vision. Classical PCA based on a Gaussian noise model is fragile to noise of large magnitude. Laplace noise assumption based PCA methods…

Machine Learning · Computer Science 2014-12-22 Pengtao Xie , Eric Xing

A promising technique for the spectral design of acoustic metamaterials is based on the formulation of suitable constrained nonlinear optimization problems. Unfortunately, the straightforward application of classical gradient-based…

Computational Engineering, Finance, and Science · Computer Science 2021-12-08 Giorgio Gnecco , Andrea Bacigalupo , Francesca Fantoni , Daniela Selvi

Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…

Methodology · Statistics 2025-10-07 Jan O. Bauer

Tensor decomposition is a powerful tool for extracting physically meaningful latent factors from multi-dimensional nonnegative data, and has been an increasing interest in a variety of fields such as image processing, machine learning, and…

Machine Learning · Computer Science 2024-12-03 Xiongjun Zhang , Michael K. Ng

Sensor noise sources cause differences in the signal recorded across pixels in a single image and across multiple images. This paper presents a Bayesian approach to decomposing and characterizing the sensor noise sources involved in imaging…

In this paper we study the reconstruction of binary sparse signals from partial random circulant measurements. We show that the reconstruction via the least-squares algorithm is as good as the reconstruction via the usually used program…

Information Theory · Computer Science 2020-06-29 Sandra Keiper

We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component…

Computer Vision and Pattern Recognition · Computer Science 2025-08-06 Ling-Qi Zhang , Zahra Kadkhodaie , Eero P. Simoncelli , David H. Brainard