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Abstract Image restoration with impulse noise is an important task in image processing. Taking into account the statistical distribution of impulse noise, the ℓ1‐norm data fidelity and total variation (ℓ1TV) model has been widely used in this area. However, the ℓ1TV model usually performs worse when the noise level is high. To overcome this drawback, several nonconvex models have been proposed. In this paper, an efficient iterative algorithm is proposed to solve nonconvex models arising in impulse noise. Compared to existing algorithms, the proposed algorithm is a completely explicit algorithm in which every subproblem has a closed‐form solution. The key idea is to transform the original nonconvex models into an equivalent constrained minimization problem with two separable objective functions, where one is differentiable but nonconvex. As a consequence, the proximal linearized alternating direction method of multipliers is employed to solve it. Extensive numerical experiments are presented to demonstrate the efficiency and effectiveness of the proposed algorithm.

In this paper, we propose a non-convex model with fractional-order applied to image deblurring problems. In the new model, fractional-order gradients have been introduced to preserve detailed features, and a source term with a blurry kernel is used for deblurring. This aspect of the model ensures that it can handle various blurring scenarios. Additionally, we devise an algorithm that maintains the non-expansiveness of the support set for image gradients, serving as a critical component in our approach to address image deblurring issues. After approximate linearization, the algorithm can be easily implemented. Some standard image processing techniques similar to fast Fourier transform can be utilized. Global convergence has likewise been confirmed and established. Moreover, we have also demonstrated that the proposed deblurring algorithm exhibits edge preservation properties. Compared with several existing classic models, the proposed method maintains a good balance between detail preservation, edge preservation, and deblurring. In addition, compared with several classic methods, the proposed method improved PSNR and SSIM by 0.9733 and 0.0111, respectively.

Lilium brownii var. viridulum is one of the main traditional edible and medicinal lily in China. This study aimed to explore the extraction technology, physicochemical properties and functional activity of polysaccharide from Lilium brownii var. viridulum, used Lilium brownii var. viridulum scales as materials, polysaccharide yield as the index, solid-liquid ratio, extraction time and extraction temperature as factors to optimize the extraction process of lily polysaccharide. Then the polysaccharide was purified through removing protein. The physicochemical properties of the polysaccharides were analyzed, and the antioxidant and lipid-lowering abilities were measured in vitro. The results showed that the optimal extraction conditions were the material to liquid ratio 1:20 g/mL, extraction time 20 min, extraction temperature 75℃, and polysaccharide yield was 11.98%. The contents of total sugar, uronic acid and protein of crude polysaccharide were 58.46%, 8.06% and 10.85%, respectively. After deproteinization, the contents of total sugar and uronic acid of polysaccharide were increased to 84.78% and 15.41%, respectively, and the content of protein was reduced to 4.73%. The scavenging rates of 10 mg/mL deproteinized polysaccharide for DPPH and ABTS+ free radicals were 8.75% and 38.59%, respectively, which were lower than those of control VC. The inhibition rate of deproteinized polysaccharide for pancreatic lipase was 85.78%, which was higher than that of the control orlistat, indicating good inhibit pancreatic lipase effect in vitro. These results would provide a basis for further study on the structure-activity relationship and development of potential functional food, and provide theoretical reference for the application of lily.

We study a relaxed inertial forward–backward–half-forward splitting approach with variable step size to solve a monotone inclusion problem involving a maximal monotone operator, a cocoercive operator, and a monotone Lipschitz operator. The convergence of the sequence of iterations generated by the discretisations of a continuous-time dynamical system is established under suitable conditions. Given the challenges associated with computing the resolvent of the composite operator, the proposed method is employed to tackle the composite monotone inclusion problem. Additionally, a convergence analysis is conducted under certain conditions. To demonstrate the effectiveness of the algorithm, numerical experiments are performed on the image deblurring problem.

Lilies (Lilium spp.) are famous bulb flowers worldwide, with high ornamental value. Aphid damage has seriously constrained the development of the lily industry. In this study, the aphid resistance of 16 lily cultivars and 2 wild lily species was characterized in the field and greenhouse. Leaf color parameters, stomatal density and size, thickness of leaf layers, leaf waxy content, and leaf water content were determined to explore the constitutive resistance of lilies. The results show that there was a significant positive correlation between the number of aphids in the field and in the greenhouse (p ≤ 0.05, r = 0.47). This indicated that the level of aphid infestation in both the field and the greenhouse is generally consistent across different types of lily plants. Among these 18 lilies, ‘Palazzo’, ‘Nymph’, ‘Cameleon’ and L. lancifolium were resistant to A. gossypii, while ‘Black Beauty’ and ‘Magnefique’ had poor resistance. The correlation analysis results showed that the number of aphids was negatively correlated with leaf abaxial surface a*, stomatal size, water content, and thickness of leaf palisade tissue and positively correlated with leaf distal axial surface b*, C*, and waxy content. Among them, the correlation between the number of aphids and the thickness of leaf palisade tissue reached a significant level (p ≤ 0.05, r = −0.521). This indicated that the thickness of the palisade tissue of lily leaves might be an important factor influencing the proliferation of aphids. This study not only screened out aphid-resistant lilies but also established a crucial research foundation for the targeted breeding and molecular breeding of lilies with aphid resistance.

In this paper, we propose a novel convex variational model for image restoration with multiplicative noise. To preserve the edges in the restored image, our model incorporates a total variation regularizer. Additionally, we impose an equality constraint on the data fidelity term, which simplifies the model selection process and promotes sparsity in the solution. We adopt the alternating direction method of multipliers (ADMM) method to solve the model efficiently. To validate the effectiveness of our model, we conduct numerical experiments on both real and synthetic noise images, and compare its performance with existing methods. The experimental results demonstrate the superiority of our model in terms of PSNR and visual quality.

A series polysaccharide samples extracted from three edible lilies (Lilium davidii var. willmottiae, Lilium brownii var. viridulum, and Lilium lancifolium) by subcritical water and ultrasound-assisted extraction were systematically compared. The results showed that extraction method was a more important factor than lily species. Subcritical water extracted lily polysaccharides (S-LP) with higher yield, molecular weight, neutral glucose and uronic acid content as well as apparent viscosity. Ultrasound-assisted extracted lily polysaccharides (U-LP) with higher reducing sugars and protein content. Moreover, due to the degradation of glycosidic bonds, ultrasonic extraction was easier to obtain lower molecular weight polysaccharides. In addition, the extraction method significantly affected the monosaccharide proportion of polysaccharides, but had no effect on type. Glucose was the main component in S-LP, and glucose and mannose were the main components in U-LP. The micromorphology of different polysaccharide samples was similar, and the scanning electron microscope (SEM) images showed regular/irregular particle clusters with different particle sizes. Overall, the relationships between extraction methods, lily species and polysaccharide properties were preliminarily elucidated, providing a reference for the targeted extraction of specific lily polysaccharides (LP).

In this paper, a relaxed variable metric primal-dual fixed-point algorithm is proposed for solving the convex optimization problem involving the sum of two convex functions where one is differentiable with the Lipschitz continuous gradient while the other is composed of a linear operator. Based on the preconditioned forward–backward splitting algorithm, the convergence of the proposed algorithm is proved. At the same time, we show that some existing algorithms are special cases of the proposed algorithm. Furthermore, the ergodic convergence and linear convergence rates of the proposed algorithm are established under relaxed parameters. Numerical experiments on the image deblurring problems demonstrate that the proposed algorithm outperforms some existing algorithms in terms of the number of iterations.

The application of cosmetics is indispensable in our current society. In recent years, with an increasing awareness of the long-term health benefits of naturally sourced ingredients, plant-based cosmetic products have gained increasing attention. Lilium belongs to the Liliaceae family, which is one of the main plant families used in cosmetics for skin care treatment. A large number of studies have shown that Lilium plants are rich in components such as phenolic acids, flavonoids, and polysaccharides, with high potential for cosmetic applications. However, the application of lilies in cosmetics has not been systematically reported. This knowledge gap can easily lead to the neglect of its application in cosmetics because lilies are most familiar as ornamental plants. Integrating academic papers and patent publications, we analyzed the potential cosmetic application ingredients in lily, as well as their applications in cosmetics and related efficacy. Patent analysis showed that applications for lily-related cosmetic patents are mainly concentrated in East Asia, including China, Korea, and Japan. The application of lilies involves all aspects of cosmetics, such as sunscreens, facial cleansers, facial masks, conditioners, and so on. Its functions are also rich and diverse, including antiaging, radiation protective, whitening, moisturizing, freckle removal, acne treatment, and hair regeneration promotion. In addition, lilies are compatible with the application of other herbs. Moreover, with a change in people’s consumption concepts and the consideration of long-term health benefits, lily-based food and medicine innovation with health care and beautification effects may be a promising direction.

The aim of this article is to introduce the Douglas–Rachford splitting method with linearization to solve the split feasibility problem (SFP). Our proposed method includes two existing methods in work of Tang et al. and Wang as special cases. The ranges of the parameters in work of Tang et al. are extended from (0,1) to (0,2). Under standard conditions, we prove the weak convergence of proposed algorithms. We also provide two numerical experiments to illustrate the effectiveness of the proposed algorithm by comparing the algorithms in work of Tang et al. and Wang.

This work proposes two different primal-dual splitting algorithms for solving structured monotone inclusion containing a cocoercive operator and the parallel-sum of maximally monotone operators. In particular, the parallel-sum is symmetry. The proposed primal-dual splitting algorithms are derived from two approaches: One is the preconditioned forward–backward splitting algorithm, and the other is the forward–backward–half-forward splitting algorithm. Both algorithms have a simple calculation framework. In particular, the single-valued operators are processed via explicit steps, while the set-valued operators are computed by their resolvents. Numerical experiments on constrained image denoising problems are presented to show the performance of the proposed algorithms.

To overcome the biases in estimating the L1-norm data fidelity term and staircase artifacts of the total variation regularization term, we propose a nonconvex+nonconvex model with box constraints to recover images degraded by blurring and impulse noise. Owing to the data fidelity term and the regularization term being nonconvex, we apply a proximal linearized minimization algorithm to solve the problem. To deal with a subproblem, we utilize the alternating direction multiplier method. The global convergence of the proposed algorithm is established under the assumption that the objective function satisfies the Kurdyka-Lojasiewicz property. We also present numerical results to demonstrate that the proposed nonconvex+nonconvex model outperforms existing models in terms of both numerical accuracy and visual quality. The proposed model also exhibits much better performance than the other methods, especially for piecewise-constant images. [ABSTRACT FROM AUTHOR]

In this paper, we propose a parameterized three-operator splitting algorithm to solve nonconvex minimization problems with the sum of three non-convex functions, where two of them have Lipschitz continuous gradients. We establish the convergence of the proposed algorithm under the KurdykaŁojasiewicz assumption by constructing a suitable energy function with a non-increasing property. As applications, we employ the proposed algorithm to solve low-rank matrix recovery and image inpainting problems. Numerical results demonstrate the efficiency and effectiveness of the proposed algorithm compared to other algorithms. [ABSTRACT FROM AUTHOR]

Inertial methods play a vital role in accelerating the convergence speed of optimization algorithms. We present an inertial forward-backward-half forward splitting algorithm, which mainly finds a zero of the sum of three operators, where two of them are cocoercive operator and monotone-Lipschitz continuous respectively. Meanwhile, the convergence analysis of the proposed algorithm is established under mild conditions. To overcome the difficulty in the calculation for the resolvent of the composite operator, relying on a primal-dual idea, we expand the proposed algorithm to solve the composite inclusion problem involving a linearly composed monotone operator. As an application, we make use of the obtained inertial algorithm to deal with a composite convex optimization problem. We also show extensive numerical experiments on the total variation-based image deblurring problem to demonstrate the efficiency of the proposed algorithm. Specifically, the proposed algorithm not only has a better quality of the deblurring image but also converges more rapidly than the original one. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses articles in the issue on topics including image restoration methods, optimization algorithms, and the integration of traditional and deep learning approaches.

Fenders play an important protective role in ship collisions, but there are few studies related to the collision simulation methods and the protection mechanism of composite fenders. First, aimed at the new composite fender design scheme proposed in this paper and based on the material properties exhibited in the test, low-density foam and hyperelastic models are selected to simulate the inner foam and outer polyurethane of the fender, respectively. Subsequently, for the hull-fender-quay collision problem, a multi-body geometry model is established and a collision simulation method is formed to analyze the fender protection mechanism from the perspective of energy conversion. It is proved that the composite material has a better protection effect on the hull structure than the rubber fender. Finally, the inner foam strength, hull stiffness, outer polyurethane thickness, and tensile strength of composite materials are varied to analyze the protection mechanism of composite materials respectively. The results show that the relative stiffness of the fender and the structure is the main factor affecting the protection performance. The inner foam of the composite fender is the main energy-absorbing structure, absorbing the kinetic energy of the hull through compression deformation to reduce the response of the structure, while the outer polyurethane mainly plays the role of protecting the core.

Unbonded flexible risers are widely applied to transport oil and gas resources from seabed to platform, and composite cylindrical layers are sometimes contained due to design requirements. Based on an 8-layer unbonded flexible riser model, the bending properties of the unbonded flexible risers with composite cylindrical layers are studied. A theoretical method of combining axisymmetric and bending loads acting on unbonded flexible risers is proposed, and a numerical method with detailed geometric characteristics taken into account is established for verification. The influence of two typical composite materials as well as the fibre volume fraction on the bending properties of the unbonded flexible risers is analyzed. The theoretical and the numerical results are in good agreement, which shows that the bending properties of the unbonded flexible risers are greatly affected by the axial Young’s modulus of the composite cylindrical layers, and composite material with larger axial Young’s modulus would greatly enhance the bending stiffness of the unbonded flexible risers, expecially in the full-slipping stage. In addition, the axial tensile stiffness and bending stiffness of full-slipping stage are proportional to the fibre volume fraction of the composite cylindrical layers.