Multi-channel nuclear norm minus Frobenius norm minimization for color image denoising

Shan, Yiwen; Dong, Hu; Wang, Zhi; Jia, Tao

doi:10.1016/j.sigpro.2023.108959

Cited by 15 publications

(3 citation statements)

References 34 publications

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“…To address the same issues encountered with WNNM, Huang et al [21] proposed the MCWSNM and achieved excellent results on real-world color image denoising. Shan et al [36] introduced a novel multi-channel optimization framework for color image denoising, utilizing nuclear norm minus Frobenius norm minimization. Furthermore, Chen et al [37] innovatively represented color images as pure quaternion matrices and then applied low-rank constraints to these constructed quaternion matrices, efectively harnessing the inherent cross-channel correlation within color channels.…”

Section: Introductionmentioning

confidence: 99%

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Nonconvex Regularization with Multi-Weighted Strategy for Real Color Image Denoising

Shi,

Liu,

et al. 2023

International Journal of Intelligent Systems

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Most existing image denoising methods commonly assume that the image is contaminated by additive white Gaussian noise (AWGN). However, real-world color image noise exhibits more complicated distribution properties, making it challenging to develop an accurate model. Consequently, denoising methods designed for AWGN often fail to achieve satisfactory performance on real-world images. In this paper, we present a novel multi-channel optimization model for real-world color images denoising within the multi-weighted Schatten p -norm minimization. Our proposed model utilizes the weighted Schatten p -norm as the regularization term, while the data fidelity term employs two weight matrices to balance the noise level across channels and regions. Besides, it helps to preserve as much detail as possible in the recovered image while removing noise. Although our proposed model is nonconvex and has no analytical solution, an accurate and efficient optimization algorithm is established based on the alternating direction method of multipliers (ADMMs) framework. Finally, we demonstrate the superior performance of our proposed method over existing state-of-the-art models on three real image datasets.

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Section: Introductionmentioning

confidence: 99%

“…Although WNNM has been shown to achieve good denoising results, several improved models have been proposed [20,35,36,41,42]. In [20], Xu et al proposed the MCWNNM, extending WNNM to perform color image denoising, which can be formulated as…”

mentioning

confidence: 99%

Nonconvex Regularization with Multi-Weighted Strategy for Real Color Image Denoising

Shi,

Liu,

et al. 2023

International Journal of Intelligent Systems

Self Cite

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“…Eq. ( 97) optimization problem can be solved using various algorithms subject to relevant constraints [71][72][73][74][75]. QAEs employ quantum circuits to encode and decode quantum states.…”

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confidence: 99%

Utilising Dimensionality Reduction for Improved Data Analysis with Quantum Feature Learning

Sihare

2024

Preprint

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This research explores the potential of quantum computing in data analysis, focusing on the efficient analysis of high-dimensional quantum datasets using dimensionality reduction techniques. The study aims to fill the knowledge gap by developing robust quantum dimensionality reduction techniques that can mitigate noise and errors. The research methodology involved a comprehensive review and analysis of existing quantum dimensionality reduction techniques, such as quantum principal component analysis, quantum linear discriminant analysis and quantum generative models. The study also explored the limitations imposed by NISQ devices and proposed strategies to adapt these techniques to work efficiently within these constraints. The key results demonstrate the potential of quantum dimensionality reduction techniques to effectively reduce the dimensionality of high-dimensional quantum datasets while preserving critical quantum information. The evaluation of quantum principal component analysis, quantum linear discriminant analysis and quantum generative models showed their effectiveness in improving quantum data analysis, particularly in improving simulation speed and predicting properties. Despite the challenges posed by noise and errors, robust quantum dimensionality reduction methods showed promise in mitigating these effects and preserving quantum information. Finally, this research contributes to the advancement of quantum data analysis by presenting a comprehensive analysis of quantum dimensionality reduction techniques and their applications. It highlights the importance of developing robust quantum feature learning methods that can operate efficiently in noisy quantum environments, especially in the NISQ era.

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Dimensionality Reduction for Data Analysis With Quantum Feature Learning

Sihare

2024

WIREs Data Min & Knowl

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To improve data analysis and feature learning, this study compares the effectiveness of quantum dimensionality reduction (qDR) techniques to classical ones. In this study, we investigate several qDR techniques on a variety of datasets such as quantum Gaussian distribution adaptation (qGDA), quantum principal component analysis (qPCA), quantum linear discriminant analysis (qLDA), and quantum t‐SNE (qt‐SNE). The Olivetti Faces, Wine, Breast Cancer, Digits, and Iris are among the datasets used in this investigation. Through comparison evaluations against well‐established classical approaches, such as classical PCA (cPCA), classical LDA (cLDA), and classical GDA (cGDA), and using well‐established metrics like loss, fidelity, and processing time, the effectiveness of these techniques is assessed. The findings show that cPCA produced positive results with the lowest loss and highest fidelity when used on the Iris dataset. On the other hand, quantum uniform manifold approximation and projection (qUMAP) performs well and shows strong fidelity when tested against the Wine dataset, but ct‐SNE shows mediocre performance against the Digits dataset. Isomap and locally linear embedding (LLE) function differently depending on the dataset. Notably, LLE showed the largest loss and lowest fidelity on the Olivetti Faces dataset. The hypothesis testing findings showed that the qDR strategies did not significantly outperform the classical techniques in terms of maintaining pertinent information from quantum datasets. More specifically, the outcomes of paired t‐tests show that when it comes to the ability to capture complex patterns, there are no statistically significant differences between the cPCA and qPCA, the cLDA and qLDA, and the cGDA and qGDA. According to the findings of the assessments of mutual information (MI) and clustering accuracy, qPCA may be able to recognize patterns more clearly than standardized cPCA. Nevertheless, there is no discernible improvement between the qLDA and qGDA approaches and their classical counterparts.

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Multi-channel nuclear norm minus Frobenius norm minimization for color image denoising

Cited by 15 publications

References 34 publications

Nonconvex Regularization with Multi-Weighted Strategy for Real Color Image Denoising

Nonconvex Regularization with Multi-Weighted Strategy for Real Color Image Denoising

Utilising Dimensionality Reduction for Improved Data Analysis with Quantum Feature Learning

Dimensionality Reduction for Data Analysis With Quantum Feature Learning

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