A Theoretically Guaranteed Quaternion Weighted Schatten p-norm Minimization Method for Color Image Restoration

• URL: http://arxiv.org/abs/2307.12656v1
• Date: Mon, 24 Jul 2023 09:54:49 GMT
• Title: A Theoretically Guaranteed Quaternion Weighted Schatten p-norm Minimization Method for Color Image Restoration
• Authors: Qing-Hua Zhang, Liang-Tian He, Yi-Lun Wang, Liang-Jian Deng, Jun Liu
• Abstract summary: We propose a novel quaternion-based WSNM model (QWSNM) for tackling the color image restoration problems. Extensive experiments on two representative CIR tasks, including color image denoising and deblurring, demonstrate that the proposed QWSNM method performs favorably against many state-of-the-art alternatives.
• Score: 11.47644299959152
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Inspired by the fact that the matrix formulated by nonlocal similar patches in a natural image is of low rank, the rank approximation issue have been extensively investigated over the past decades, among which weighted nuclear norm minimization (WNNM) and weighted Schatten $p$-norm minimization (WSNM) are two prevailing methods have shown great superiority in various image restoration (IR) problems. Due to the physical characteristic of color images, color image restoration (CIR) is often a much more difficult task than its grayscale image counterpart. However, when applied to CIR, the traditional WNNM/WSNM method only processes three color channels individually and fails to consider their cross-channel correlations. Very recently, a quaternion-based WNNM approach (QWNNM) has been developed to mitigate this issue, which is capable of representing the color image as a whole in the quaternion domain and preserving the inherent correlation among the three color channels. Despite its empirical success, unfortunately, the convergence behavior of QWNNM has not been strictly studied yet. In this paper, on the one side, we extend the WSNM into quaternion domain and correspondingly propose a novel quaternion-based WSNM model (QWSNM) for tackling the CIR problems. Extensive experiments on two representative CIR tasks, including color image denoising and deblurring, demonstrate that the proposed QWSNM method performs favorably against many state-of-the-art alternatives, in both quantitative and qualitative evaluations. On the other side, more importantly, we preliminarily provide a theoretical convergence analysis, that is, by modifying the quaternion alternating direction method of multipliers (QADMM) through a simple continuation strategy, we theoretically prove that both the solution sequences generated by the QWNNM and QWSNM have fixed-point convergence guarantees.

Related papers

• Quaternion Nuclear Norm minus Frobenius Norm Minimization for color image reconstruction [20.11953064373745]
  Quaternion Nuclear Norm Minus Frobenius Norm Minimization (QNMF) is a novel approach for color image reconstruction. By employing a regularization technique that involves nuclear norm minus Frobenius norm, QNMF approximates the underlying low-rank structure of quaternion-encoded color images.
  arXiv  Detail & Related papers  (2024-09-12T06:57:00Z)
• Retinex-RAWMamba: Bridging Demosaicing and Denoising for Low-Light RAW Image Enhancement [71.13353154514418]
  Low-light image enhancement, particularly in cross-domain tasks such as mapping from the raw domain to the sRGB domain, remains a significant challenge. We present a novel Mamba scanning mechanism, called RAWMamba, to effectively handle raw images with different CFAs. We also present a Retinex Decomposition Module (RDM) grounded in Retinex prior, which decouples illumination from reflectance to facilitate more effective denoising and automatic non-linear exposure correction.
  arXiv  Detail & Related papers  (2024-09-11T06:12:03Z)
• A New Cross-Space Total Variation Regularization Model for Color Image Restoration with Quaternion Blur Operator [20.00683294783224]
  Cross-channel deblurring problem in color image processing is difficult to solve due to complex coupling and structural blurring of color pixels. We present a novel cross-space total variation (CSTV) regularization model for color image deblurring. New L-curve method is proposed to find a sweet balance of regularization functionals on different color spaces.
  arXiv  Detail & Related papers  (2024-05-20T15:29:26Z)
• $L_{2,1}$-Norm Regularized Quaternion Matrix Completion Using Sparse Representation and Quaternion QR Decomposition [7.344370881751104]
  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
  arXiv  Detail & Related papers  (2023-09-07T15:08:12Z)
• DARC: Distribution-Aware Re-Coloring Model for Generalizable Nucleus Segmentation [68.43628183890007]
  We argue that domain gaps can also be caused by different foreground (nucleus)-background ratios. First, we introduce a re-coloring method that relieves dramatic image color variations between different domains. Second, we propose a new instance normalization method that is robust to the variation in the foreground-background ratios.
  arXiv  Detail & Related papers  (2023-09-01T01:01:13Z)
• Quasi Non-Negative Quaternion Matrix Factorization with Application to Color Face Recognition [0.0]
  A novel quasi-negative quaternion matrix factorization (QNQMF) is presented for color image processing. The accuracy of the rate of face recognition on the quaternion model is better than on the red, green and blue channels of color image.
  arXiv  Detail & Related papers  (2022-11-30T04:51:09Z)
• A Unified Framework for Contrastive Learning from a Perspective of Affinity Matrix [80.2675125037624]
  We present a new unified contrastive learning representation framework (named UniCLR) suitable for all the above four kinds of methods. Three variants, i.e., SimAffinity, SimWhitening and SimTrace, are presented based on UniCLR. In addition, a simple symmetric loss, as a new consistency regularization term, is proposed based on this framework.
  arXiv  Detail & Related papers  (2022-11-26T08:55:30Z)
• Quaternion Optimized Model with Sparse Regularization for Color Image Recovery [10.137095668835439]
  This paper is inspired by an appreciation of the fact that different signal types, including audio formats and images, possess structures that are inherently sparse in respect of their respective bases. Since color images can be processed as a whole in the quaternion domain, we depicted the sparsity of the color image in the quaternion discrete cosine transform (QDCT) domain. To achieve a more superior low-rank approximation, the quatenrion-based truncated nuclear norm (QTNN) is employed in the proposed model.
  arXiv  Detail & Related papers  (2022-04-19T03:07:12Z)
• Leveraging Spatial and Photometric Context for Calibrated Non-Lambertian Photometric Stereo [61.6260594326246]
  We introduce an efficient fully-convolutional architecture that can leverage both spatial and photometric context simultaneously. Using separable 4D convolutions and 2D heat-maps reduces the size and makes more efficient.
  arXiv  Detail & Related papers  (2021-03-22T18:06:58Z)
• Deep Variational Network Toward Blind Image Restoration [60.45350399661175]
  Blind image restoration is a common yet challenging problem in computer vision. We propose a novel blind image restoration method, aiming to integrate both the advantages of them. Experiments on two typical blind IR tasks, namely image denoising and super-resolution, demonstrate that the proposed method achieves superior performance over current state-of-the-arts.
  arXiv  Detail & Related papers  (2020-08-25T03:30:53Z)
• Single-Image HDR Reconstruction by Learning to Reverse the Camera Pipeline [100.5353614588565]
  We propose to incorporate the domain knowledge of the LDR image formation pipeline into our model. We model the HDRto-LDR image formation pipeline as the (1) dynamic range clipping, (2) non-linear mapping from a camera response function, and (3) quantization. We demonstrate that the proposed method performs favorably against state-of-the-art single-image HDR reconstruction algorithms.
  arXiv  Detail & Related papers  (2020-04-02T17:59:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.