Related papers: Singular value decomposition based matrix surgery
Affine rank minimization problem is the generalized version of low rank matrix completion problem where linear combinations of the entries of a low rank matrix are observed and the matrix is estimated from these measurements. We propose a…
This paper studies the problem of distributed computation over a network of wireless sensors. While this problem applies to many emerging applications, to keep our discussion concrete we will focus on sensor networks used for structural…
The oriented singular value decomposition (O-SVD) proposed by Zeng and Ng provides a hybrid approach to the t-product based third-order tensor singular value decomposition with the transform matrix being a factor matrix of the higher order…
Higher-order tensor decompositions are analogous to the familiar Singular Value Decomposition (SVD), but they transcend the limitations of matrices (second-order tensors). SVD is a powerful tool that has achieved impressive results in…
This work introduces Structured 3D-SVD as a practical framework for the reconstruction, compression, and analysis of biological volumetric data. Inspired by the logic of matrix singular value decomposition (SVD), the proposed approach…
We analyze sparse frame based regularization of inverse problems by means of a diagonal frame decomposition (DFD) for the forward operator, which generalizes the SVD. The DFD allows to define a non-iterative (direct) operator-adapted frame…
We address the reduction to compact band forms, via unitary similarity transformations, for the solution of symmetric eigenvalue problems and the computation of the singular value decomposition (SVD). Concretely, in the first case we…
Singular Value Decomposition (SVD) is a powerful tool in linear algebra.We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The paper illustrates nonlinear SVD…
We examine holographic renormalization by the singular value decomposition (SVD) of matrix data generated by the Monte Carlo snapshot of the 2D classical Ising model at criticality. To take the continuous limit of the SVD enables us to find…
A shift of paradigm is currently underway in biomedical ultrasound thanks to plane and diverging waves for ultrafast imaging. One remaining challenge consists in the correction of phase and amplitude aberrations induced during propagation…
We present a new restricted SVD-based CUR (RSVD-CUR) factorization for matrix triplets $(A, B, G)$ that aims to extract meaningful information by providing a low-rank approximation of the three matrices using a subset of their rows and…
In this paper we introduce the algorithm and the fixed point hardware to calculate the normalized singular value decomposition of a non-symmetric matrices using Givens fast (approximate) rotations. This algorithm only uses the basic…
Over the past decade, various matrix completion algorithms have been developed. Thresholded singular value decomposition (SVD) is a popular technique in implementing many of them. A sizable number of studies have shown its theoretical and…
The higher order singular value decomposition (HOSVD) of tensors is a generalization of matrix SVD. The perturbation analysis of HOSVD under random noise is more delicate than its matrix counterpart. Recently, polynomial time algorithms…
Storing data is particularly a challenge when dealing with image data which often involves large file sizes due to the high resolution and complexity of images. Efficient image compression algorithms are crucial to better manage data…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
Learning a dynamical system from input/output data is a fundamental task in the control design pipeline. In the partially observed setting there are two components to identification: parameter estimation to learn the Markov parameters, and…
The singular value decomposition (SVD) is a popular matrix factorization that has been used widely in applications ever since an efficient algorithm for its computation was developed in the 1970s. In recent years, the SVD has become even…
Higher-order singular value decomposition (HOSVD) is an efficient way for data reduction and also eliciting intrinsic structure of multi-dimensional array data. It has been used in many applications, and some of them involve incomplete…
Removing the aberrations introduced by the Point Spread Function (PSF) is a fundamental aspect of astronomical image processing. The presence of noise in observed images makes deconvolution a nontrivial task that necessitates the use of…