相关论文: Steerable $e$PCA: Rotationally Invariant Exponenti…

Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…

In this paper, we study the problem of computing a Principal Component Analysis of data affected by Poisson noise. We assume samples are drawn from independent Poisson distributions. We want to estimate principle components of a fixed…

Sparse principal component analysis (sPCA) has become one of the most widely used techniques for dimensionality reduction in high-dimensional datasets. The main challenge underlying sPCA is to estimate the first vector of loadings of the…

In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at $p$ locations and $n$ time points with the possibility that $p>n$. While principal component analysis…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Sparse PCA is the optimization problem obtained from PCA by adding a sparsity constraint on the principal components. Sparse PCA is NP-hard and hard to approximate even in the single-component case. In this paper we settle the computational…

Accurate, unified models for event cameras (ECs) remain elusive, hampering calibration and algorithm design. We develop a foundational probabilistic model for EC event detection, grounded in photon statistics, that unifies the description…

High-dimensional data often exhibit dependencies among variables that violate the isotropic-noise assumption under which principal component analysis (PCA) is optimal. For cases where the noise is not independent and identically distributed…

Sparse local feature matching is pivotal for many computer vision and robotics tasks. To improve their invariance to challenging appearance conditions and viewing angles, and hence their usefulness, existing learning-based methods have…

How do statistical dependencies in measurement noise influence high-dimensional inference? To answer this, we study the paradigmatic spiked matrix model of principal components analysis (PCA), where a rank-one matrix is corrupted by…

This paper discusses new methods for processing images in the photon-limited regime where the number of photons per pixel is binary. We present a new Bayesian denoising method for binary, single-photon images. Each pixel measurement is…

This work presents a novel approach for robust PCA with total variation regularization for foreground-background separation and denoising on noisy, moving camera video. Our proposed algorithm registers the raw (possibly corrupted) frames of…

Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…

The in vitro clonogenic assay is a technique to study the ability of a cell to form a colony in a culture dish. By optical imaging, dishes with stained colonies can be scanned and assessed digitally. Identification, segmentation and…

Fourier ptychography is a new computational microscopy technique that provides gigapixel-scale intensity and phase images with both wide field-of-view and high resolution. By capturing a stack of low-resolution images under different…

Accurate estimation of the relative concentrations of chromophores in a spectroscopic photoacoustic (sPA) image can reveal immense structural, functional, and molecular information about physiological processes. However, due to…

Singular value decomposition (SVD) based principal component analysis (PCA) breaks down in the high-dimensional and limited sample size regime below a certain critical eigen-SNR that depends on the dimensionality of the system and the…

Despite the advances of deep learning in specific tasks using images, the principled assessment of image fidelity and similarity is still a critical ability to develop. As it has been shown that Mean Squared Error (MSE) is insufficient for…

The principal component analysis (PCA) is widely used for data decorrelation and dimensionality reduction. However, the use of PCA may be impractical in real-time applications, or in situations were energy and computing constraints are…

Principal component analysis (PCA) is a fundamental tool in multivariate statistics, yet its sensitivity to outliers and limitations in distributed environments restrict its effectiveness in modern large-scale applications. To address these…