Triple-output phase unwrapping network with a physical prior in fringe projection profilometry.

Deep learning has been attracting more and more attention in the phase unwrapping of fringe projection profilometry (FPP) in recent years. In order to improve the accuracy of the deep-learning-based unwrapped phase methods from a single fringe pattern, this paper proposes a single-input triple-output neural network structure with a physical prior. In the proposed network, a single-input triple-output network structure is developed to convert the input fringe pattern into three intermediate outputs: the wrapped phase, the fringe order, the coarse unwrapped phase, and the final output high-precision unwrapped phase from the three outputs. Moreover, a new, to the best of our knowledge, loss function is designed to improve the performance of the model using a physical prior about these three outputs in FPP. Numerous experiments demonstrated that the proposed network is able to improve the accuracy of the unwrapped phase, which can also be extended to other deep learning phase unwrapping models.

Polysaccharides from apple pomace exhibit anti-fatigue activity through increasing glycogen content.

The polysaccharides were isolated from apple pomace by hot-water extraction, and their anti-fatigue activity was evaluated in C2C12 muscle myoblasts and male Kunming mice. The purified polysaccharides from apple pomace (PAP) have a molecular weight of 1.74 × 105 Da and were composed of mannose, rhamnose, glucose, galactose and arabinose. In C2C12 myoblasts, PAP showed no cytotoxicity in the concentrations of 0-300 µg/ml. PAP treatment increased the glycogen content, while the ATP content was not affected in C2C12 myoblasts. Further investigation found that the activity and gene expression of glycogen synthase, rather than glycogen phosphorylase, were upregulated by PAP treatment. The studies in vivo showed that PAP treatment did not affect the food intake and weight again in mice. Importantly, PAP prolonged the exhaustive swimming time, increased hepatic and skeletal muscle glycogen levels, and effectively inhibited the accumulation of blood lactic and blood urea nitrogen in mice. Taken together, the results suggested that PAP exhibit anti-fatigue activity in vitro and in vivo through increasing glycogen content.

Microglial mTOR is Neuronal Protective and Antiepileptogenic in the Pilocarpine Model of Temporal Lobe Epilepsy.

Excessive activation of mammalian target of rapamycin (mTOR) signaling is epileptogenic in genetic epilepsy. However, the exact role of microglial mTOR in acquired epilepsy remains to be clarified. In the present study, we found that mTOR is strongly activated in microglia following excitatory injury elicited by status epilepticus. To determine the role of microglial mTOR signaling in excitatory injury and epileptogenesis, we generated mice with restrictive deletion of mTOR in microglia. Both male and female mice were used in the present study. We found that mTOR-deficient microglia lost their typical proliferative and inflammatory responses to excitatory injury, whereas the proliferation of astrocytes was preserved. In addition, mTOR-deficient microglia did not effectively engulf injured/dying neurons. More importantly, microglial mTOR-deficient mice displayed increased neuronal loss and developed more severe spontaneous seizures. These findings suggest that microglial mTOR plays a protective role in mitigating neuronal loss and attenuating epileptogenesis in the excitatory injury model of epilepsy.SIGNIFICANCE STATEMENT The mammalian target of rapamycin (mTOR) pathway is strongly implicated in epilepsy. However, the effect of mTOR inhibitors in preclinical models of acquired epilepsy is inconsistent. The broad presence of mTOR signaling in various brain cells could prevent mTOR inhibitors from achieving a net therapeutic effect. This conundrum has spurred further investigation of the cell type-specific effects of mTOR signaling in the CNS. We found that activation of microglial mTOR is antiepileptogenic. Thus, microglial mTOR activation represents a novel antiepileptogenic route that appears to parallel the proepileptogenic route of neuronal mTOR activation. This may explain why the net effect of mTOR inhibitors is paradoxical in the acquired models of epilepsy. Our findings could better guide the use of mTOR inhibitors in preventing acquired epilepsy.

IFN-γ and IL-17A regulate intestinal crypt production of CXCL10 in the healthy and inflamed colon.

During intestinal inflammation, immature cells within the intestinal crypt are called upon to replenish lost epithelial cell populations, promote tissue regeneration, and restore barrier integrity. Inflammatory mediators including TH1/TH17-associated cytokines influence tissue health and regenerative processes, yet how these cytokines directly influence the colon crypt epithelium and whether the crypt remains responsive to these cytokines during active damage and repair, remain unclear. Here, using laser-capture microdissection and primary colon organoid culture, we show that the cytokine milieu regulates the ability of the colonic crypt epithelium to participate in proinflammatory signaling. IFN-γ induces the TH1-recruiting, proinflammatory chemokine CXCL10/IP10 in primary murine intestinal crypt epithelium. CXCL10 was also induced in colonic organoids derived from mice with active, experimentally induced colitis, suggesting that the crypt can actively secrete CXCL10 in select cytokine environments during colitis. Colon expression of cxcl10 further increased during infectious and noninfectious colitis in Il17a-/- mice, demonstrating that IL-17A exerts a negative effect on CXCL10 in vivo. Furthermore, IL-17A directly antagonized CXCL10 production in ex vivo organoid cultures derived from healthy murine colons. Interestingly, direct antagonism of CXCL10 was not observed in organoids derived from colitic mouse colons bearing active lesions. These data, highlighting the complex interplay between the cytokine milieu and crypt epithelia, demonstrate proinflammatory chemokines can be induced within the colonic crypt and suggest the crypt remains responsive to cytokine modulation during inflammation.NEW & NOTEWORTHY Upon damage, the intestinal epithelium regenerates to restore barrier function. Here we observe that the local colonic cytokine milieu controls the production of procolitic chemokines within the crypt base and colon crypts remain responsive to cytokines during inflammation. IFN-γ promotes, while IL-17 antagonizes, CXCL10 production in healthy colonic crypts, while responses to cytokines differ in inflamed colon epithelium. These data reveal novel insight into colon crypt responses and inflammation-relevant alterations in signaling.

Label enhanced and patch based deep learning for phase retrieval from single frame fringe pattern in fringe projection 3D measurement.

We propose a label enhanced and patch based deep learning phase retrieval approach which can achieve fast and accurate phase retrieval using only several fringe patterns as training dataset. To the best of our knowledge, it is the first time that the advantages of the label enhancement and patch strategy for deep learning based phase retrieval are demonstrated in fringe projection. In the proposed method, the enhanced labeled data in training dataset is designed to learn the mapping between the input fringe pattern and the output enhanced fringe part of the deep neural network (DNN). Moreover, the training data is cropped into small overlapped patches to expand the training samples for the DNN. The performance of the proposed approach is verified by experimental projection fringe patterns with applications in dynamic fringe projection 3D measurement.

A Multi-View Stereo Measurement System Based on a Laser Scanner for Fine Workpieces.

A new solution to the high-quality 3D reverse modeling problem of complex surfaces for fine workpieces is presented using a laser line-scanning sensor. Due to registration errors, measurement errors, deformations, etc., a fast and accurate method is important in machine vision measurement. This paper builds a convenient and economic multi-view stereo (MVS) measurement system based on a linear stage and a rotary stage to reconstruct the measured object surface completely and accurately. In the proposed technique, the linear stage is used to generate the trigger signal and synchronize the laser sensor scanning; the rotary stage is used to rotate the object and obtain multi-view point cloud data, and then the multi-view point cloud data are registered and integrated into a 3D model. The measurement results show a measurement accuracy of 0.075 mm for a 360° reconstruction in 34 s, and some evaluation experiments were carried out to demonstrate the validity and practicability of the proposed technique.

Information-weighted constrained regularization for particle size distribution recovery in multiangle dynamic light scattering.

In particle size measurement with dynamic light scattering (DLS), it is difficult to get an accurate recovery of a bimodal particle size distribution (PSD) with a peak position ratio less than ~2:1, especially when large particles (>350nm) are present. This is due to the inherent noise in the autocorrelation function (ACF) data and the scarce utilization of PSD information during the inversion process. In this paper, the PSD information distribution in the ACF data is investigated. It was found that the initial decay section of the ACF contains more information, especially for a bimodal PSD. Based on this, an information-weighted constrained regularization (IWCR) method is proposed in this paper and applied in multiangle DLS analysis for bimodal PSD recovery. By using larger (or smaller) coefficients for weighting the ACF data, more (or less) weight can then be given to the initial part of the ACF. In this way, the IWCR method can enhance utilization of the PSD information in the ACF data, and effectively weaken the effect of noise at large delay time on PSD recovery. Using this method, bimodal PSDs (with nominal diameters of 400:608 nm, 448:608 nm, 500:600 nm) were recovered successfully from simulated data and it appears that the IWCR method can improve the recovery resolution for closely spaced bimodal particles. Results of the PSD recovery from experimental DLS data confirm the performance of this method.

Assessment of Fringe Pattern Decomposition with a Cross-Correlation Index for Phase Retrieval in Fringe Projection 3D Measurements.

Phase retrieval from single frame projection fringe patterns, a fundamental and challenging problem in fringe projection measurement, attracts wide attention and various new methods have emerged to address this challenge. Many phase retrieval methods are based on the decomposition of fringe patterns into a background part and a fringe part, and then the phase is obtained from the decomposed fringe part. However, the decomposition results are subject to the selection of model parameters, which is usually performed manually by trial and error due to the lack of decomposition assessment rules under a no ground truth data situation. In this paper, we propose a cross-correlation index to assess the decomposition and phase retrieval results without the need of ground truth data. The feasibility of the proposed metric is verified by simulated and real fringe patterns with the well-known Fourier transform method and recently proposed Shearlet transform method. This work contributes to the automatic phase retrieval and three-dimensional (3D) measurement with less human intervention, and can be potentially employed in other fields such as phase retrieval in digital holography.

Structured-Light Based 3D Reconstruction System for Cultural Relic Packaging.

The non-contact three-dimensional measurement and reconstruction techniques have played a significant role in the packaging and transportation of precious cultural relics. This paper develops a structured light based three-dimensional measurement system, with a low-cost for cultural relics packaging. The structured light based system performs rapid measurements and generates 3D point cloud data, which is then denoised, registered and merged to achieve accurate 3D reconstruction for cultural relics. The multi-frequency heterodyne method and the method in this paper are compared. It is shown that the relative accuracy of the proposed low-cost system can reach a level of 1/1000. The high efficiency of the system is demonstrated through experimental results.

Detection of Micro-Defects on Metal Screw Surfaces Based on Deep Convolutional Neural Networks.

This paper proposes a deep convolutional neural network (CNN) -based technique for the detection of micro defects on metal screw surfaces. The defects we consider include surface damage, surface dirt, and stripped screws. Images of metal screws with different types of defects are collected using industrial cameras, which are then employed to train the designed deep CNN. To enable efficient detection, we first locate screw surfaces in the pictures captured by the cameras, so that the images of screw surfaces can be extracted, which are then input to the CNN-based defect detector. Experiment results show that the proposed technique can achieve a detection accuracy of 98%; the average detection time per picture is 1.2 s. Comparisons with traditional machine vision techniques, e.g., template matching-based techniques, demonstrate the superiority of the proposed deep CNN-based one.

Reduced sodium/proton exchanger NHE3 activity causes congenital sodium diarrhea.

Congenital sodium diarrhea (CSD) refers to an intractable diarrhea of intrauterine onset with high fecal sodium loss. CSD is clinically and genetically heterogeneous. Syndromic CSD is caused by SPINT2 mutations. While we recently described four cases of the non-syndromic form of CSD that were caused by dominant activating mutations in intestinal receptor guanylate cyclase C (GC-C), the genetic cause for the majority of CSD is still unknown. Therefore, we aimed to determine the genetic cause for non-GC-C non-syndromic CSD in 18 patients from 16 unrelated families applying whole-exome sequencing and/or chromosomal microarray analyses and/or direct Sanger sequencing. SLC9A3 missense, splicing and truncation mutations, including an instance of uniparental disomy, and whole-gene deletion were identified in nine patients from eight families with CSD. Two of these nine patients developed inflammatory bowel disease (IBD) at 4 and 16 years of age. SLC9A3 encodes Na(+)/H(+) antiporter 3 (NHE3), which is the major intestinal brush-border Na(+)/H(+) exchanger. All mutations were in the NHE3 N-terminal transport domain, and all missense mutations were in the putative membrane-spanning domains. Identified SLC9A3 missense mutations were functionally characterized in plasma membrane NHE null fibroblasts. SLC9A3 missense mutations compromised NHE3 activity by reducing basal surface expression and/or loss of basal transport function of NHE3 molecules, whereas acute regulation was normal. This study identifies recessive mutations in NHE3, a downstream target of GC-C, as a cause of CSD and implies primary basal NHE3 malfunction as a predisposition for IBD in a subset of patients.

A common NHE3 single-nucleotide polymorphism has normal function and sensitivity to regulatory ligands.

Na+/H+ exchanger NHE3 mediates the majority of intestinal and renal electroneutral sodium absorption. Dysfunction of NHE3 is associated with a variety of diarrheal diseases. We previously reported that the NHE3 gene (SLC9A3) has more than 400 single-nucleotide polymorphisms (SNPs) but few nonsynonymous polymorphisms. Among the latter, one polymorphism (rs2247114-G>A), which causes a substitution from arginine to cysteine at amino acid position 799 (p.R799C), is common in Asian populations. To improve our understanding of the population distribution and potential clinical significance of the NHE3-799C variant, we investigated the frequency of this polymorphism in different ethnic groups using bioinformatics analyses and in a cohort of Japanese patients with cardiovascular or renal disease. We also characterized the function of human NHE3-799C and its sensitivity to regulatory ligands in an in vitro model. NHE3-799C had an allele frequency of 29.5-57.6% in Asian populations, 11.1-23.6% in European populations, and 10.2-22.7% in African populations. PS120/FLAG-NHERF2 fibroblasts stably expressing NHE3-799C had lower total protein expression but a higher percentage of surface expression than those expressing NHE3-799R. NHE3-799C had similar basal activity to NHE3-799R and was similarly stimulated or inhibited, by serum or forskolin, respectively. Tenapanor, a small-molecule NHE3 inhibitor, dose-dependently inhibited NHE3-799R and NHE3-799C activities. The IC50 values of tenapanor for NHE3-799C and NHE3-799R were significantly different, but both were in the nanomolar range. These results suggest that NHE3-799C is a common variant enriched in Asian populations, is not associated with compromised function or abnormal regulation, and is unlikely to contribute to clinical disease.NEW & NOTEWORTHY This study reports results on the functional significance of human NHE3-799C under basal conditions and in response to regulatory ligands, including a novel NHE3 inhibitor called tenapanor. We demonstrate that NHE3-799C is a common variant of NHE3 that is enriched in Asian populations; however, in contrast to our previous studies using rabbit NHE3, its presence seems to have limited clinical significance in humans and is not associated with compromised function or abnormal transport regulation.

Lp-norm-residual constrained regularization model for estimation of particle size distribution in dynamic light scattering.

In particle size measurement using dynamic light scattering (DLS), noise makes the estimation of the particle size distribution (PSD) from the autocorrelation function data unreliable, and a regularization technique is usually required to estimate a reasonable PSD. In this paper, we propose an Lp-norm-residual constrained regularization model for the estimation of the PSD from DLS data based on the Lp norm of the fitting residual. Our model is a generalization of the existing, commonly used L2-norm-residual-based regularization methods such as CONTIN and constrained Tikhonov regularization. The estimation of PSDs by the proposed model, using different Lp norms of the fitting residual for p=1, 2, 10, and ∞, is studied and their performance is determined using simulated and experimental data. Results show that our proposed model with p=1 is less sensitive to noise and improves stability and accuracy in the estimation of PSDs for unimodal and bimodal systems. The model with p=1 is particularly applicable to the noisy or bimodal PSD cases.

Rapamycin Inhibition of mTOR Reduces Levels of the Na+/H+ Exchanger 3 in Intestines of Mice and Humans, Leading to Diarrhea.

BACKGROUND & AIMS: The immunosuppressant rapamycin frequently causes noninfectious diarrhea in organ transplant recipients. We investigated the mechanisms of this process. METHODS: We performed a retrospective analysis of renal transplant recipients treated with rapamycin from 2003 through 2010 at Albany Medical College, collecting data on serum levels of rapamycin. Levels of the Na+/H+ exchanger 3 (NHE3) were measured in human ileal biopsy specimens from patients who did and did not receive rapamycin (controls), in ileum tissues from rats or mice given rapamycin, and in mice with intestine-specific disruption of mammalian target of rapamycin (Mtor) (mTOR(f/f):Villin-cre mice) or Atg7 (Atg7(flox/flox); Villin-Cre). Exchange activity and intestinal water absorption were measured using a pH-sensitive dye and small intestine perfusion, respectively. RESULTS: Episodes of noninfectious diarrhea occurred in organ recipients after increases in serum levels of rapamycin. The expression of NHE3 was reduced in the ileal brush border of patients with diarrhea. In rats and mice, continuous administration of low doses of rapamycin reduced levels of NHE3 in intestinal tissues; this effect was not observed in mice with intestinal deletion of ATG7, indicating that autophagy is required for the reduction. Administration of single high doses of rapamycin to mice, to model the spikes in rapamycin levels that occur in patients with severe diarrheal episodes, resulted in reduced phosphorylation of S6 and AKT in ileal tissues, indicating inhibition of the mTOR complex (mTORC1 and mTORC2). The intestines of mice with intestine-specific deletion of mTOR were dilated and contained large amounts of liquid stools; they also had reduced levels of total NHE3 and NHERF1 compared with control mice. We observed a significant reduction in Na(+)/H(+) exchange activity in ileum tissues from these mice. CONCLUSIONS: Rapamycin inhibition of mTOR reduces levels of NHE3 and Na(+)/H(+) exchange activity in intestinal tissues of patients and rodents. This process appears to require the autophagic activity mediated by ATG7. Loss of mTOR regulation of NHE3 could mediate the development of diarrhea in patients undergoing rapamycin therapy.

Nonsynonymous single nucleotide polymorphisms of NHE3 differentially decrease NHE3 transporter activity.

Genetic determinants appear to play a role in susceptibility to chronic diarrhea, but the genetic abnormalities involved have only been identified in a few conditions. The Na⁺/H⁺ exchanger 3 (NHE3) accounts for a large fraction of physiologic intestinal Na⁺ absorption. It is highly regulated through effects on its intracellular COOH-terminal regulatory domain. The impact of genetic variation in the NHE3 gene, such as single nucleotide polymorphisms (SNPs), on transporter activity remains unexplored. From a total of 458 SNPs identified in the entire NHE3 gene, we identified three nonsynonymous mutations (R474Q, V567M, and R799C), which were all in the protein's intracellular COOH-terminal domain. Here we evaluated whether these SNPs affect NHE3 activity by expressing them in a mammalian cell line that is null for all plasma membrane NHEs. These variants significantly reduced basal NHE3 transporter activity through a reduction in intrinsic NHE3 function in variant R474Q, abnormal trafficking in variant V567M, or defects in both intrinsic NHE3 function and trafficking in variant R799C. In addition, variants NHE3 R474Q and R799C failed to respond to acute dexamethasone stimulation, suggesting cells with these mutant proteins might be defective in NHE3 function during postprandial stimulation and perhaps under stressful conditions. Finally, variant R474Q was shown to exhibit an aberrant interaction with calcineurin B homologous protein (CHP), an NHE3 regulatory protein required for basal NHE3 activity. Taken together, these results demonstrate decreased transport activity in three SNPs of NHE3 and provide mechanistic insight into how these SNPs impact NHE3 function.

Seizure-dependent mTOR activation in 5-HT neurons promotes autism-like behaviors in mice.

Epilepsy and autism spectrum disorder (ASD) are common comorbidities of one another. Despite the prevalent correlation between the two disorders, few studies have been able to elucidate a mechanistic link. We demonstrate that forebrain specific Tsc1 deletion in mice causes epilepsy and autism-like behaviors, concomitant with disruption of 5-HT neurotransmission. We find that epileptiform activity propagates to the raphe nuclei, resulting in seizure-dependent hyperactivation of mTOR in 5-HT neurons. To dissect whether mTOR hyperactivity in 5-HT neurons alone was sufficient to recapitulate an autism-like phenotype we utilized Tsc1flox/flox;Slc6a4-cre mice, in which mTOR is restrictively hyperactivated in 5-HT neurons. Tsc1flox/flox;Slc6a4-cre mice displayed alterations of the 5-HT system and autism-like behaviors, without causing epilepsy. Rapamycin treatment in these mice was sufficient to rescue the phenotype. We conclude that the spread of seizure activity to the brainstem is capable of promoting hyperactivation of mTOR in the raphe nuclei, which in turn promotes autism-like behaviors. Thus our study provides a novel mechanism describing how epilepsy can contribute to the development of autism-like behaviors, suggesting new therapeutic strategies for autism.

Impaired autophagy in neurons after disinhibition of mammalian target of rapamycin and its contribution to epileptogenesis.

Certain mutations within the mammalian target of rapamycin (mTOR) pathway, most notably those affecting the tuberous sclerosis complex (TSC), lead to aberrant activation of mTOR and result in a high incidence of epilepsy in humans and animal models. Although hyperactivation of mTOR has been strongly linked to the development of epilepsy and, conversely, inhibition of mTOR by rapamycin treatment is protective against seizures in several models, the downstream epileptic mechanisms have remained elusive. Autophagy, a catabolic process that plays a vital role in cellular homeostasis by mediating the turnover of cytoplasmic constituents, is negatively regulated by mTOR. Here we demonstrate that autophagy is suppressed in brain tissues of forebrain-specific conditional TSC1 and phosphatase and tensin homlog knock-out mice, both of which display aberrant mTOR activation and seizures. In addition, we also discovered that autophagy is suppressed in the brains of human TSC patients. Moreover, conditional deletion of Atg7, an essential regulator of autophagy, in mouse forebrain neurons is sufficient to promote development of spontaneous seizures. Thus, our study suggests that impaired autophagy contributes to epileptogenesis, which may be of interest as a potential therapeutic target for epilepsy treatment and/or prevention.

Leucine stimulates insulin secretion via down-regulation of surface expression of adrenergic α2A receptor through the mTOR (mammalian target of rapamycin) pathway: implication in new-onset diabetes in renal transplantation.

The amino acid leucine is a potent secretagogue, capable of inducing insulin secretion. It also plays an important role in the regulation of mTOR activity, therefore, providing impetus to investigate if a leucine-sensing mechanism in the mTOR pathway is involved in insulin secretion. We found that leucine-induced insulin secretion was inhibited by both the mTOR inhibitor rapamycin as well as the adrenergic α2 receptor agonist clonidine. We also demonstrated that leucine down-regulated the surface expression of adrenergic α2A receptor via activation of the mTOR pathway. The leucine stimulatory effect on insulin secretion was attenuated in diabetic Goto-Kakizaki rats that overexpress adrenergic α2A receptors, confirming the role of leucine in insulin secretion. Thus, our data demonstrate that leucine regulates insulin secretion by modulating adrenergic α2 receptors through the mTOR pathway. The role of the mTOR pathway in metabolic homeostasis led us to a second important finding in this study; retrospective analysis of clinical data showed that co-administration of rapamycin and clonidine was associated with an increased incidence of new-onset diabetes in renal transplantation patients over those receiving rapamycin alone. We believe that inhibition of mTOR by rapamycin along with activation of adrenergic α2 receptors by clonidine represents a double-hit to pancreatic islets that synergistically disturbs glucose homeostasis. This new insight may have important implications for the clinical management of renal transplant patients.

Variational image decomposition for automatic background and noise removal of fringe patterns.

In optical metrology, state of the art algorithms for background and noise removal of fringe patterns are based on space-frequency analysis. In this Letter, an approach based on variational image decomposition is proposed to remove background and noise from a fringe pattern simultaneously. In the proposed method, a fringe image is directly decomposed into three components: a first one containing background, a second one fringes, and a third one noise, which are described in different function spaces and are solved by minimization of the functional. A simple technical process involved in the minimization algorithm improves the convergence performance. The proposed approach is verified with the simulated and experimental fringe patterns.

Application of two oriented partial differential equation filtering models on speckle fringes with poor quality and their numerically fast algorithms.

In this paper, we are concerned with denoising in experimentally obtained electronic speckle pattern interferometry (ESPI) speckle fringe patterns with poor quality. We extend the application of two existing oriented partial differential equation (PDE) filters, including the second-order single oriented PDE filter and the double oriented PDE filter, to two experimentally obtained ESPI speckle fringe patterns with very poor quality, and compare them with other efficient filtering methods, including the adaptive weighted filter, the improved nonlinear complex diffusion PDE, and the windowed Fourier transform method. All of the five filters have been illustrated to be efficient denoising methods through previous comparative analyses in published papers. The experimental results have demonstrated that the two oriented PDE models are applicable to low-quality ESPI speckle fringe patterns. Then for solving the main shortcoming of the two oriented PDE models, we develop the numerically fast algorithms based on Gauss-Seidel strategy for the two oriented PDE models. The proposed numerical algorithms are capable of accelerating the convergence greatly, and perform significantly better in terms of computational efficiency. Our numerically fast algorithms are extended automatically to some other PDE filtering models.