Related papers: Distributions of Singular Values for Some Random M…
Truncated Singular Value Decomposition (SVD) calculates the closest rank-$k$ approximation of a given input matrix. Selecting the appropriate rank $k$ defines a critical model order choice in most applications of SVD. To obtain a principled…
Removing speckle noise from SAR images is still an open issue. It is well know that the interpretation of SAR images is very challenging and despeckling algorithms are necessary to improve the ability of extracting information. An urban…
In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
This paper focus on recovering multi-dimensional data called tensor from randomly corrupted incomplete observation. Inspired by reweighted $l_1$ norm minimization for sparsity enhancement, this paper proposes a reweighted singular value…
We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across…
Relationships in scientific data, such as the numerical and spatial distribution relations of features in univariate data, the scalar-value combinations' relations in multivariate data, and the association of volumes in time-varying and…
We investigate a general matrix factorization for deviance-based data losses, extending the ubiquitous singular value decomposition beyond squared error loss. While similar approaches have been explored before, our method leverages…
In convolutional neural networks, the linear transformation of multi-channel two-dimensional convolutional layers with linear convolution is a block matrix with doubly Toeplitz blocks. Although a "wrapping around" operation can transform…
Low-rankness of amplitude spectrograms has been effectively utilized in audio signal processing methods including non-negative matrix factorization. However, such methods have a fundamental limitation owing to their amplitude-only treatment…
We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this…
The statistical properties of Synthetic Aperture Radar (SAR) image texture reveals useful target characteristics. It is well-known that these images are affected by speckle, and prone to contamination as double bounce and corner reflectors.…
Deep learning methods achieve great success recently on many computer vision problems, with image classification and object detection as the prominent examples. In spite of these practical successes, optimization of deep networks remains an…
We develop a data-driven optimal shrinkage algorithm for matrix denoising in the presence of high-dimensional noise with a separable covariance structure; that is, the noise is colored and dependent across samples. The algorithm, coined…
This article investigates the problem of noisy low-rank matrix completion with a shared factor structure, leveraging the auxiliary information from the missing indicator matrix to enhance prediction accuracy. Despite decades of development…
We propose an approximation method for thresholding of singular values using Chebyshev polynomial approximation (CPA). Many signal processing problems require iterative application of singular value decomposition (SVD) for minimizing the…
In this paper, we consider multivariate response regression models with high dimensional predictor variables. One way to model the correlation among the response variables is through the low rank decomposition of the coefficient matrix,…
This note considers the spectral estimation problems of sparse spectral measures under unknown noise levels. The main technical tool is the eigenmatrix method for solving unstructured sparse recovery problems. When the noise level is…
Singular spectrum analysis is developed as a nonparametric spectral decomposition of a time series. It can be easily extended to the decomposition of multidimensional lattice-like data through the filtering interpretation. In this…
Deep neural networks used for image classification often use convolutional filters to extract distinguishing features before passing them to a linear classifier. Most interpretability literature focuses on providing semantic meaning to…