Quaternion Optimized Model with Sparse Regularization for Color Image Recovery

• URL: http://arxiv.org/abs/2204.08629v1
• Date: Tue, 19 Apr 2022 03:07:12 GMT
• Title: Quaternion Optimized Model with Sparse Regularization for Color Image Recovery
• Authors: Liqiao Yang, Yang Liu, Kit Ian Kou
• Abstract summary: 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.
• Score: 10.137095668835439
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper addresses the color image completion problem in accordance with low-rank quatenrion matrix optimization that is characterized by sparse regularization in a transformed domain. This research was 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. In addition, the representation of a low-rank structure that is intrinsic to the color image is a vital issue in the quaternion matrix completion problem. To achieve a more superior low-rank approximation, the quatenrion-based truncated nuclear norm (QTNN) is employed in the proposed model. Moreover, this model is facilitated by a competent alternating direction method of multipliers (ADMM) based on the algorithm. Extensive experimental results demonstrate that the proposed method can yield vastly superior completion performance in comparison with the state-of-the-art low-rank matrix/quaternion matrix approximation methods tested on color image recovery.

Related papers

• A Theoretically Guaranteed Quaternion Weighted Schatten p-norm Minimization Method for Color Image Restoration [11.47644299959152]
  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.
  arXiv  Detail & Related papers  (2023-07-24T09:54:49Z)
• Quaternion tensor left ring decomposition and application for color image inpainting [14.601163837840675]
  We propose the quaternion tensor left ring (QTLR) decomposition, which inherits the powerful and generalized representation abilities of the TR decomposition. 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.
  arXiv  Detail & Related papers  (2023-07-20T06:37:47Z)
• Data-Driven Bilateral Generalized Two-Dimensional Quaternion Principal Component Analysis with Application to Color Face Recognition [4.471812624045322]
  New data-driven bilateral generalized two-dimensional quaternion principal component analysis (BiG2DQPCA) is presented. BiG2DQPCA directly works on the 2D color images without vectorizing and well preserves the spatial and color information. New approach based on BiG2DQPCA is presented for color face recognition and image reconstruction with a new data-driven weighting technique.
  arXiv  Detail & Related papers  (2023-06-12T11:45:59Z)
• $PC^2$: Projection-Conditioned Point Cloud Diffusion for Single-Image 3D Reconstruction [97.06927852165464]
  Reconstructing the 3D shape of an object from a single RGB image is a long-standing and highly challenging problem in computer vision. We propose a novel method for single-image 3D reconstruction which generates a sparse point cloud via a conditional denoising diffusion process.
  arXiv  Detail & Related papers  (2023-02-21T13:37:07Z)
• 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)
• Hybrid Model-based / Data-driven Graph Transform for Image Coding [54.31406300524195]
  We present a hybrid model-based / data-driven approach to encode an intra-prediction residual block. The first $K$ eigenvectors of a transform matrix are derived from a statistical model, e.g., the asymmetric discrete sine transform (ADST) for stability. Using WebP as a baseline image, experimental results show that our hybrid graph transform achieved better energy compaction than default discrete cosine transform (DCT) and better stability than KLT.
  arXiv  Detail & Related papers  (2022-03-02T15:36:44Z)
• Quaternion-based dynamic mode decomposition for background modeling in color videos [1.0098114696565863]
  Dynamic mode decomposition (DMD) is a recently proposed method to robustly decompose a video sequence into the background model and the corresponding foreground part. We propose a quaternion-based DMD (Q-DMD), which extends the DMD by quaternion matrix analysis. We exploit the standard eigenvalues of the quaternion matrix to compute its spectral decomposition and calculate the corresponding Q-DMD modes and eigenvalues.
  arXiv  Detail & Related papers  (2021-12-28T03:35:39Z)
• Regularization by Denoising Sub-sampled Newton Method for Spectral CT Multi-Material Decomposition [78.37855832568569]
  We propose to solve a model-based maximum-a-posterior problem to reconstruct multi-materials images with application to spectral CT. In particular, we propose to solve a regularized optimization problem based on a plug-in image-denoising function. We show numerical and experimental results for spectral CT materials decomposition.
  arXiv  Detail & Related papers  (2021-03-25T15:20:10Z)
• Joint Estimation of Image Representations and their Lie Invariants [57.3768308075675]
  Images encode both the state of the world and its content. The automatic extraction of this information is challenging because of the high-dimensionality and entangled encoding inherent to the image representation. This article introduces two theoretical approaches aimed at the resolution of these challenges.
  arXiv  Detail & Related papers  (2020-12-05T00:07:41Z)
• Invariant Deep Compressible Covariance Pooling for Aerial Scene Categorization [80.55951673479237]
  We propose a novel invariant deep compressible covariance pooling (IDCCP) to solve nuisance variations in aerial scene categorization. We conduct extensive experiments on the publicly released aerial scene image data sets and demonstrate the superiority of this method compared with state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-11-11T11:13:07Z)
• Residual-Sparse Fuzzy $C$-Means Clustering Incorporating Morphological Reconstruction and Wavelet frames [146.63177174491082]
  Fuzzy $C$-Means (FCM) algorithm incorporates a morphological reconstruction operation and a tight wavelet frame transform. We present an improved FCM algorithm by imposing an $ell_0$ regularization term on the residual between the feature set and its ideal value. Experimental results reported for synthetic, medical, and color images show that the proposed algorithm is effective and efficient, and outperforms other algorithms.
  arXiv  Detail & Related papers  (2020-02-14T10:00:03Z)

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.