Search

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.

Abstract The forward–backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and an inverse strongly monotone operator. In this paper, we present a new convergence analysis of a variable metric forward–backward splitting algorithm with extended relaxation parameters in real Hilbert spaces. We prove that this algorithm is weakly convergent when certain weak conditions are imposed upon the relaxation parameters. Consequently, we recover the forward–backward splitting algorithm with variable step sizes. As an application, we obtain a variable metric forward–backward splitting algorithm for solving the minimization problem of the sum of two convex functions, where one of them is differentiable with a Lipschitz continuous gradient. Furthermore, we discuss the applications of this algorithm to the fundamental of the variational inequalities problem, constrained convex minimization problem, and split feasibility problem. Numerical experimental results on LASSO problem in statistical learning demonstrate the effectiveness of the proposed iterative algorithm.

In this paper, we introduce a two-step inertial primal-dual algorithm (TSIPD) for solving the minimizations of the sum a smooth function with Lipschitzian gradient and two non-smooth convex functions with linear operators. This is a complete splitting approach, in the sense that non-smooth functions are treated separately by their proximity operators. In order to prove the convergence of the TSIPD, we transform the problem into a fixed point equation with good performance, and prove the convergence of the algorithm base on the fixed point theory. This work brings together and significantly extends several classical splitting schemes, like the primal-dual method (PD3O) proposed by Yan, and the recent three-operator splitting scheme proposed by Davis and Yin. The validity of the proposed method is demonstrated on an image denoising problem. Numerical results show that our iterative algorithm (TSIPD) has better performance than the original one (PD3O).

Gene function analysis is challenging for Lilium due to the lack of an efficient method for stable genetic transformation. Virus-induced gene silencing (VIGS) is an attractive tool for determining gene function in plants. This study reported that Tobacco rattle virus (TRV)-based VIGS of a PHYTOENE DESATURASE (PDS) ortholog (LhPDS) can be achieved in Lilium × formolongi seedlings, with a survival rate of 92%, using the inoculation method of rubbing plus injection. Compared with untreated and mock-treated seedlings, the photobleached leaf phenotype of silenced plants significantly correlates with down-regulation of endogenous LhPDS (P ≤ 0.05). In addition, the silencing phenomenon can be observed in the growing points of plants, indicating that systemic viral infection was achieved using the protocol. The results indicate that TRV-based VIGS can be used to characterize gene function in Lilium × formolongi. This work lays the foundation for gene function analysis and molecular breeding in Lilium spp. Keywords: Lilium, photobleaching, seedling, TRV, VIGS, PDS

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.

Lilium lancifolium is one of the most important species of genus Lilium. Besides ornamental value, it also has highly edible and medicinal properties. We investigated the karyotypes of L. lancifolium and four related cultivars. The results indicated that the ploidies of four cultivars varied from diploid to tetraploid. Both ‘Flore Pleno’ and ‘Red Velvet’ were triploid (2n=3x=36), consistenting with the wild species L. lancifolium. ‘Sweet Surrender’ was diploid (2n=2x=24), and ‘Red Life’ was tetraploid. All karyotypes of candidates belonged to 3B type except ‘Flore Pleno’, which belonged to 3A type. Karyotype symmetry analysis revealed that the wild species L. lancifolium had a middle value of A1, A2, and TF%, which meant that the cultivars related to L. lancifolium had different tendencies to symmetry compared to L. lancifolium, but whether they were higher or lower was unclear.

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.

Abstract In this paper, we propose several new iterative algorithms to solve the split feasibility problem in the Hilbert spaces. By virtue of new analytical techniques, we prove that the iterative sequence generated by these iterative procedures converges to the solution of the split feasibility problem which is the best close to a given point. In particular, the minimum-norm solution can be found via our iteration method.

Virus-induced gene silencing (VIGS) is an attractive tool for determining gene function in plants. The present study constitutes the first application of VIGS in S. pseudocapsicum, which has great ornamental and pharmaceutical value, using tobacco rattle virus (TRV) vectors. Two marker genes, PHYTOENE DESATURASE (PDS) and Mg-chelatase H subunit (ChlH), were used to test the VIGS system in S. pseudocapsicum. The photobleaching and yellow-leaf phenotypes of the silenced plants were shown to significantly correlate with the down-regulation of endogenous SpPDS and SpChlH, respectively (P ≤ 0.05). Moreover, the parameters potentially affecting the efficiency of VIGS in S. pseudocapsicum, including the Agrobacterium strain and the inoculation method (leaf syringe-infiltration, sprout vacuum-infiltration and seed vacuum-infiltration), were compared. The optimized VIGS parameters were the leaf syringe-infiltration method, the Agrobacterium strain GV3101 and the growth of agro-inoculated plants at 25°. With these parameters, the silencing efficiency of SpPDS and SpChlH could reach approximately 50% in S. pseudocapsicum. Additionally, the suitability of various reference genes was screened by RT-qPCR using three candidate genes, and the results demonstrated that glyceraldehyde 3-phosphate dehydrogenase (GAPDH) can serve as a suitable reference for assessing the gene expression levels of VIGS systems in S. pseudocapsicum. The proven application of VIGS in S. pseudocapsicum and the characterization of a suitable reference gene in the present work will expedite the functional characterization of novel genes in S. pseudocapsicum.

Aerial bulbils are an important propagative organ, playing an important role in population expansion. However, the detailed gene regulatory patterns and molecular mechanism underlying bulbil formation remain unclear. Triploid Lilium lancifolium, which develops many aerial bulbils on the leaf axils of middle-upper stem, is a useful species for investigating bulbil formation. To investigate the mechanism of bulbil formation in triploid L. lancifolium, we performed histological and transcriptomic analyses using samples of leaf axils located in the upper and lower stem of triploid L. lancifolium during bulbil formation. Histological results indicated that the bulbils of triploid L. lancifolium are derived from axillary meristems that initiate de novo from cells on the adaxial side of the petiole base. Transcriptomic analysis generated ~650 million high-quality reads and 11,871 differentially expressed genes (DEGs). Functional analysis showed that the DEGs were significantly enriched in starch and sucrose metabolism and plant hormone signal transduction. Starch synthesis and accumulation likely promoted the initiation of upper bulbils in triploid L. lancifolium. Hormone-associated pathways exhibited distinct patterns of change in each sample. Auxin likely promoted the initiation of bulbils and then inhibited further bulbil formation. High biosynthesis and low degradation of cytokinin might have led to bulbil formation in the upper leaf axil. The present study achieved a global transcriptomic analysis focused on gene expression changes and pathways' enrichment during upper bulbil formation in triploid L. lancifolium, laying a solid foundation for future molecular studies on bulbil formation.

Quantitative real-time PCR (qRT-PCR) is a reliable and high-throughput technique for gene expression studies, but its accuracy depends on the expression stability of reference genes. To date, several reliable reference gene identifications have been reported in Lilium spp., but none has been obtained for lily tepals at different developmental stages. In this study, ten candidate reference genes were selected and evaluated for their expression stability in Lilium ‘Tiny Padhye’ during the process of bicolor tepal development. The expression stability of these candidates was evaluated by three software programs (geNorm, NormFinder, and BestKeeper) and the comparative ΔCt method, and comprehensive stability rankings were generated by RefFinder. As a result, TIP41-like family gene (TIP41) and actin (ACT) were the best combination of reference genes for tepals at different developmental stages; TIP41 and F-box family gene (F-box) for tepals under shading treatment; ACT, actin11 (ACT11), and elongation factor 1-α (EF1-α) for different tissues; and ACT, TIP41, and ACT11 for all samples. The selected optimal reference genes were further verified by analyzing the expression levels of flavonoid 3′-hydroxylase (LhF3′H) and anthocyanidin 3-O-glucosyltransfersae (LhUFGT) in tepals at different developmental stages. This study provides useful information for gene expression characterization in lilies under different experimental conditions, and can serve as a basis for similar research in other closely related species.

The resolvent is a fundamental concept in studying various operator splitting algorithms. In this paper, we investigate the problem of computing the resolvent of compositions of operators with bounded linear operators. First, we discuss several explicit solutions of this resolvent operator by taking into account additional constraints on the linear operator. Second, we propose a fixed point approach for computing this resolvent operator in a general case. Based on the Krasnoselskii⁻Mann algorithm for finding fixed points of non-expansive operators, we prove the strong convergence of the sequence generated by the proposed algorithm. As a consequence, we obtain an effective iterative algorithm for solving the scaled proximity operator of a convex function composed by a linear operator, which has wide applications in image restoration and image reconstruction problems. Furthermore, we propose and study iterative algorithms for studying the resolvent operator of a finite sum of maximally monotone operators as well as the proximal operator of a finite sum of proper, lower semi-continuous convex functions.

The three-operator splitting algorithm is a new splitting algorithm for finding monotone inclusion problems of the sum of three maximally monotone operators, where one is cocoercive. As the resolvent operator is not available in a closed form in the original three-operator splitting algorithm, in this paper, we introduce an inexact three-operator splitting algorithm to solve this type of monotone inclusion problem. The theoretical convergence properties of the proposed iterative algorithm are studied in general Hilbert spaces under mild conditions on the iterative parameters. As a corollary, we obtain general convergence results of the inexact forward-backward splitting algorithm and the inexact Douglas-Rachford splitting algorithm, which extend the existing results in the literature.

The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.

We discuss convergence theorems of modified Ishikawa and Mann iterative sequences with errors for asymptotically pseudocontractive and asymptotically nonexpansive mappings in Banach spaces, and the boundedness of the domain and range can be dropped, generalizing theorems of Chang.

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.