Related papers: Separable Quaternion Matrix Factorization for Pola…

Quantum principal component analysis (qPCA) is commonly formulated as the extraction of eigenvalues and eigenvectors of a covariance-encoded density operator. Yet in many qPCA settings the practical goal is simpler: projection onto the…

Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity…

Matrices with low numerical rank are omnipresent in many signal processing and data analysis applications. The pivoted QLP (p-QLP) algorithm constructs a highly accurate approximation to an input low-rank matrix. However, it is…

Matrix completion is one of the most challenging problems in computer vision. Recently, quaternion representations of color images have achieved competitive performance in many fields. Because it treats the color image as a whole, the…

A novel low-rank completion algorithm based on the quaternion tensor is proposed in this paper. This approach uses the TQt-rank of quaternion tensor to maintain the structure of RGB channels throughout the entire process. In more detail,…

We propose a system for visual scene analysis and recognition based on encoding the sparse, latent feature-representation of an image into a high-dimensional vector that is subsequently factorized to parse scene content. The sparse feature…

Quaternion-valued wireless communication systems have been studied in the past. Although progress has been made in this promising area, a crucial missing link is lack of effective and efficient quaternion-valued signal processing algorithms…

Nonnegative matrix factorization (NMF) is a popular model in the field of pattern recognition. It aims to find a low rank approximation for nonnegative data M by a product of two nonnegative matrices W and H. In general, NMF is NP-hard to…

POLSAR image has an advantage over optical image because it can be acquired independently of cloud cover and solar illumination. PolSAR image classification is a hot and valuable topic for the interpretation of POLSAR image. In this paper,…

In the context of applying the Lorentz group theory to polarization optics in the frames of Stokes-Mueller formalism, some properties of the Lorentz group are investigated. We start with the factorized form of arbitrary Lorentz matrix as a…

Shape from Polarization (SfP) estimates surface normals using photos captured at different polarizer rotations. Fundamentally, the SfP model assumes that light is reflected either diffusely or specularly. However, this model is not valid…

This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian…

We present a stochastic description of multiple scattering of polarized waves in the regime of forward scattering. In this regime, if the source is polarized, polarization survives along a few transport mean free paths, making it possible…

We consider the problem of accurately and efficiently querying a remote server to retrieve information about images captured by a mobile device. In addition to reduced transmission overhead and computational complexity, the retrieval…

We introduce the probabilistic sequential matrix factorization (PSMF) method for factorizing time-varying and non-stationary datasets consisting of high-dimensional time-series. In particular, we consider nonlinear Gaussian state-space…

The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…

In this work we perform some mathematical analysis on non-negative matrix factorizations (NMF) and apply NMF to some imaging and inverse problems. We will propose a sparse low-rank approximation of big positive data and images in terms of…

In Gaussian model-based multichannel audio source separation, the likelihood of observed mixtures of source signals is parametrized by source spectral variances and by associated spatial covariance matrices. These parameters are estimated…

Compressed sensing of simultaneously sparse and low-rank matrices enables recovery of sparse signals from a few linear measurements of their bilinear form. One important question is how many measurements are needed for a stable…

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…