arXiv subjects

Lizhi Liu

Publications and source records attributed to Lizhi Liu.

4 recordsLinked to original sources

arXiv2025

A novel reverberation mapping method for blazars

Reverberation mapping (RM) is the most promising method to measure the masses of supermassive black holes in the center of active galaxy nuclei (AGNs). However, the dominant jet component hinders the application of RM method for blazars. In this work, we present a new algorithm to disentangle the contribution of the accretion disk from that of the relativistic jet in blazars by analyzing the spectral break of the optical spectroscopic data. We applied this method to two flat-spectrum radio quasars (FSRQs), PKS 1510-089 and PKS 0736+017. In PKS 1510-089, the variability of the H$γ$ line is delayed with respect to the disk emission by approximately 94 days, while the H$β$ line shows a lag of about 111 days relative to the disk. In PKS 0736+017, the H$γ$ variability is delayed with respect to the disk by roughly 66 days, and the H$β$ line exhibits a lag of about 67 days. Based on these measured time lags, we estimate black hole masses of $\sim1.4\times10^{8}\,M_{\odot}$ for PKS 1510-089 and $\sim8.1\times10^{7}\,M_{\odot}$ for PKS 0736+017. This method paves the way to apply the RM method for blazars, and improves the understanding of disk and jet activities.

astro-ph.HE↗

arXiv2023

Quaternion tensor left ring decomposition and application for color image inpainting

In recent years, tensor networks have emerged as powerful tools for solving large-scale optimization problems. One of the most promising tensor networks is the tensor ring (TR) decomposition, which achieves circular dimensional permutation invariance in the model through the utilization of the trace operation and equitable treatment of the latent cores. On the other hand, more recently, quaternions have gained significant attention and have been widely utilized in color image processing tasks due to their effectiveness in encoding color pixels by considering the three color channels as a unified entity. Therefore, in this paper, based on the left quaternion matrix multiplication, we propose the quaternion tensor left ring (QTLR) decomposition, which inherits the powerful and generalized representation abilities of the TR decomposition while leveraging the advantages of quaternions for color pixel representation. In addition to providing the definition of QTLR decomposition and an algorithm for learning the QTLR format, the paper further proposes a low-rank quaternion tensor completion (LRQTC) model and its algorithm for color image inpainting based on the defined QTLR decomposition. Finally, extensive experiments on color image inpainting demonstrate that the proposed LRQTC method is highly competitive.

cs.CV↗

arXiv2023

$L_{2,1}$-Norm Regularized Quaternion Matrix Completion Using Sparse Representation and Quaternion QR Decomposition

Color image completion is a challenging problem in computer vision, but recent research has shown that quaternion representations of color images perform well in many areas. These representations consider the entire color image and effectively utilize coupling information between the three color channels. Consequently, low-rank quaternion matrix completion (LRQMC) algorithms have gained significant attention. We propose a method based on quaternion Qatar Riyal decomposition (QQR) and quaternion $L_{2,1}$-norm called QLNM-QQR. This new approach reduces computational complexity by avoiding the need to calculate the QSVD of large quaternion matrices. We also present two improvements to the QLNM-QQR method: an enhanced version called IRQLNM-QQR that uses iteratively reweighted quaternion $L_{2,1}$-norm minimization and a method called QLNM-QQR-SR that integrates sparse regularization. Our experiments on natural color images and color medical images show that IRQLNM-QQR outperforms QLNM-QQR and that the proposed QLNM-QQR-SR method is superior to several state-of-the-art methods.

cs.CV↗

arXiv2022

Low Rank Quaternion Matrix Completion Based on Quaternion QR Decomposition and Sparse Regularizer

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 coupling information between the three channels of the color image is better utilized. Due to this, low-rank quaternion matrix completion (LRQMC) algorithms have gained considerable attention from researchers. In contrast to the traditional quaternion matrix completion algorithms based on quaternion singular value decomposition (QSVD), we propose a novel method based on quaternion Qatar Riyal decomposition (QQR). In the first part of the paper, a novel method for calculating an approximate QSVD based on iterative QQR is proposed (CQSVD-QQR), whose computational complexity is lower than that of QSVD. The largest $r \ (r>0)$ singular values of a given quaternion matrix can be computed by using CQSVD-QQR. Then, we propose a new quaternion matrix completion method based on CQSVD-QQR which combines low-rank and sparse priors of color images. Experimental results on color images and color medical images demonstrate that our model outperforms those state-of-the-art methods.

eess.IV↗