Abstract. Low-rank matrix approximation plays an important role in various applications such as image processing, signal processing, and data analysis. The existing methods require a guess of the ranks of matrices that represent images or involve additional costs to determine the ranks. A novel efficient orthogonal decomposition with automatic basis extraction (EOD-ABE) is proposed to compute the optimal low-rank matrix approximation with adaptive identification of the optimal rank. By introducing a randomized basis extraction mechanism, EOD-ABE eliminates the need for additional rank determination steps and can compute a rank-revealing approximation to a low-rank matrix. With a computational complexity of [Formula: see text], where [Formula: see text] and [Formula: see text] are the dimensions of the matrix and [Formula: see text] is its computed numerical rank, EOD-ABE achieves significant speedups compared to the state-of-the-art methods. Experimental results demonstrate the superior speed, accuracy, and robustness of EOD-ABE and indicate that EOD-ABE is a powerful tool for fast image compression and reconstruction and hyperspectral image dimensionality reduction in large-scale applications.

The cross-channel deblurring problem in color image processing is difficult to solve due to the complex coupling and structural blurring of color pixels. Until now, there are few efficient algorithms that can reduce color artifacts in deblurring process. To solve this challenging problem, we present a novel cross-space total variation (CSTV) regularization model for color image deblurring by introducing a quaternion blur operator and a cross-color space regularization functional. The existence and uniqueness of the solution is proved and a new L-curve method is proposed to find a balance of regularization terms on different color spaces. The Euler-Lagrange equation is derived to show that CSTV has taken into account the coupling of all color channels and the local smoothing within each color channel. A quaternion operator splitting method is firstly proposed to enhance the ability of color artifacts reduction of the CSTV regularization model. This strategy also applies to the well-known color deblurring models. Numerical experiments on color image databases illustrate the efficiency and effectiveness of the new model and algorithms. The color images restored by them successfully maintain the color and spatial information and are of higher quality in terms of PSNR, SSIM, MSE and CIEde2000 than the restorations of the-state-of-the-art methods.

Quaternion singular value decomposition (QSVD) is a robust technique of digital watermarking that extracts high quality watermarks from watermarked images with low distortion. However, the existing QSVD-based watermarking schemes face the obstacle of "explosion of complexity" and have much room for improvement in terms of real-time, invisibility, and robustness. In this paper, we overcome such obstacle by introducing a new real structure-preserving QSVD algorithm and propose a novel QSVD-based watermarking scheme with high efficiency. Secret information is transmitted blindly by incorporating two new strategies: coefficient pair selection and adaptive embedding. The highly correlated coefficient pairs determined by the normalized cross-correlation method reduce the impact of embedding by reducing the maximum modification of the coefficient values, resulting in high fidelity of the watermarked image. Large-size 8-color binary watermark and QR code effectively verify that the proposed watermarking scheme can resist various image attacks in numerical experiments. Two keys designed by Logistic chaotic map ensure the security of the watermarking system. Under the premise of considering the correlation of color channels, the proposed watermarking scheme not only performs well in real-time and invisibility, but also has satisfactory advantages in robustness compared with the state-of-the-art methods.

Abstract ‘Health Cloud’ refers to the provision of hospital management and residents' health file management application services to all hospitals and related medical institutions in the area where the cloud computing industry base is located in the form of SaaS (software as a service). In the process of treating burn sepsis, it is particularly important to prevent burn sepsis. The purpose of this study is to diagnose burn sepsis early, after adding serum procalcitonin clinical research. First, use PCT during the experiment to observe the efficacy of antibiotics according to the situation and prognosis. In order to reduce the inappropriate use of antibiotics, it can be used as a reliable indicator to guide antibiotic management and allow patients with sepsis to receive accurate treatment. Second, according to the main observation indicators of burn sepsis, analyse the degree of injury of the patient. Finally, identifying burn sepsis as early as possible, and early intervention and prevention based on related technologies is a problem that needs to be solved by the research institute. The clinical symptoms and vital signs of burn sepsis are not particularly abnormal, and imaging examination may cause the focus of infection to be incorrect. As a result, the positive rate of positive results is low, which seriously affects the timely diagnosis and treatment of patients. Experimental data show that serum PCT of non‐septic patients is obvious during the six groups of experiments 1–5 days, 6–10 days, 11–15 days, 16–20 days, 21–25 days, 26–30 days after treatment serum PCT levels below sepsis. The data recorded during the experiment are in accordance with the relevant principles of statistics to ensure that the experiment is true and effective. The experimental results show that the PCT of burn sepsis group is higher than that of the cured group without burns, and the serum PCT level is crucial for the diagnosis of burn sepsis.

The image nonlocal self-similarity (NSS) prior refers to the fact that a local patch often has many nonlocal similar patches to it across the image and has been widely applied in many recently proposed machining learning algorithms for image processing. However, there is no theoretical analysis on its working principle in the literature. In this paper, we discover a potential causality between NSS and low-rank property of color images, which is also available to grey images. A new patch group based NSS prior scheme is proposed to learn explicit NSS models of natural color images. The numerical low-rank property of patched matrices is also rigorously proved. The NSS-based QMC algorithm computes an optimal low-rank approximation to the high-rank color image, resulting in high PSNR and SSIM measures and particularly the better visual quality. A new tensor NSS-based QMC method is also presented to solve the color video inpainting problem based on quaternion tensor representation. The numerical experiments on color images and videos indicate the advantages of NSS-based QMC over the state-of-the-art methods.

The two-dimensional principal component analysis (2DPCA) has been one of the basic methods of developing artificial intelligent algorithms. To increase the feasibility, we propose a new general ridge regression model for 2DPCA and variations, with extracting low dimensional features under two projection subspaces. A new relaxed 2DPCA under the quaternion framework is proposed to utilize the label (if known) and color information to compute the essential features of generalization ability with optimization algorithms. The 2DPCA-based approaches for face recognition are also improved by weighting each principle component a scatter measure, which increases efficiently the rate of face recognition. In numerical experiments on well-known standard databases, the R2DPCA approach has high generalization ability and achieves a higher recognition rate than the state-of-the-art 2DPCA-like methods, and has better performance than the basic deep learning methods such as CNNs , DBNs, and DNNs in the small-sample case.

Color image restoration is one of the important tasks in color image processing. Total variation regularizaton was proposed and employed for the recovery of edges in a grayscale image. In the literature, there are several methods for extension of total variation regularization for color images, for example, based on color channel coupling and tensor regularization. The main contribution of this paper is to propose and develop a new saturation-value (SV) color total variation regularization in the hue, saturation, amd value color space instead of in the original red, green, and blue color space. The development of this SV total variation can be studied via the representation of color images in the quaternion framework for color edge detection. We will investigate the properties of the SV total variation regularization and the resulting optimization model for color image restoration. Numerical examples are presented to demonstrate that the performance of the new SV total variation is better than that of existing color image total variation methods in terms of some criteria such as PSNR, SSIM, and S-CIELAB error.