Gaussian Diffusion Research Articles

A concise continuous time random-walk diffusion model for characterization of non-exponential signal decay in magnetic resonance imaging

Diffusion-weighted magnetic resonance imaging (dMRI) is a method of capturing the signal of water molecules diffusing in heterogeneous materials. Gaussian diffusion is interrupted when water mobility is hampered by obstructions in complex structures, and the dMRI signal decay does not match the single exponential decay in Brownian motion. In this study, a concise continuous time random-walk diffusion model is derived with less parameters than the continuous time random walk (CTRW) model and used to characterize the attenuation signal of brain tissue. The fitting results are compared with the CTRW model and the mono-exponential model reflecting the sub-diffusion and the long tail phenomenon of signal decay. Three sample experiments on rat brain and human brain are chosen to evaluate the validity in explaining the anomalous diffusion of water molecules in biological tissues, particularly in brain tissues in diverse directions, which also extends the applications of the concise continuous time random-walk diffusion model. Furthermore, we note that the concise continuous time random-walk diffusion model has practical advantages over the classical exponential model from the perspective of computational accuracy especially in the case of large b values, and has less parameters and is comparable to the CTRW model.

Fickian yet non-Gaussian diffusion of a quasi-2D colloidal system in an optical speckle field: experiment and simulations

We investigate a quasi-2D suspension of Brownian particles in an optical speckle field produced by holographic manipulation of a laser wavefront. This system was developed to study, in a systematic and controllable way, a distinctive instance of diffusion, called Fickian yet Non Gaussian diffusion (FnGD), observed, during the last decade, for colloidal particles in a variety of complex and biological fluids. Our setup generates an optical speckle field that behaves like a disordered set of optical traps. First, we describe the experimental setup and the dynamics of the particles, focusing on mean square displacements, displacement distributions and kurtosis. Then, we present Brownian Dynamics simulations of point-like particles in a complex energy landscape, mimicking that generated by the optical speckle field. We show that our simulations can capture the salient features of the experimental results, including the emergence of FnGD, also covering times longer than the ones so far achieved in experiments. Some deviations are observed at long time only, with the Gaussian restoring being slower in simulations than in experiments. Overall, the introduced numerical model might be exploited to guide the design of upcoming experiments targeted, for example, to fully monitor the recovery of Gaussianity.

Lévy Flights Diffusion with Drift in Heterogeneous Membranes

The modelling of diffusion in membranes is essential to understanding transport processes through membranes, especially when it comes to improving process efficiency. The purpose of this study is to understand the relationship between membrane structures, external forces, and the characteristic features of diffusive transport. We investigate Cauchy flight diffusion with drift in heterogeneous membrane-like structures. The study focuses on numerical simulation of particle movement across different membrane structures with differently spaced obstacles. Four studied structures are similar to real polymeric membranes filled with inorganic powder, while the next three structures are designed to show which distribution of obstacles can cause changes in transport. The movement of particles driven by Cauchy flights is compared to a Gaussian random walk both with and without additional drift action. We show that effective diffusion in membranes with an external drift depends on the type of the internal mechanism that causes the movement of particles as well as on the properties of the environment. In general, when movement steps are provided by the long-tailed Cauchy distribution and the drift is sufficiently strong, superdiffusion is observed. On the other hand, strong drift can effectively stop Gaussian diffusion.

Multidimensional encoding of restricted and anisotropic diffusion by double rotation of the qvector.

Diffusion NMR and MRI methods building on the classic pulsed gradient spin-echo sequence are sensitive to many aspects of translational motion, including time and frequency dependence ("restriction"), anisotropy, and flow, leading to ambiguities when interpreting experimental data from complex heterogeneous materials such as living biological tissues. While the oscillating gradient technique specifically targets frequency dependence and permits control of the sensitivity to flow, tensor-valued encoding enables investigations of anisotropy in orientationally disordered materials. Here, we propose a simple scheme derived from the "double-rotation" technique in solid-state NMR to generate a family of modulated gradient waveforms allowing for comprehensive exploration of the 2D frequency-anisotropy space and convenient investigation of both restricted and anisotropic diffusion with a single multidimensional acquisition protocol, thereby combining the desirable characteristics of the oscillating gradient and tensor-valued encoding techniques. The method is demonstrated by measuring multicomponent isotropic Gaussian diffusion in simple liquids, anisotropic Gaussian diffusion in a polydomain lyotropic liquid crystal, and restricted diffusion in a yeast cell sediment.

Optimal consumption–investment under partial information in conditionally log-Gaussian models

Certain Merton type consumption−investment problems under partial information are reduced to the ones of full information and within the framework of a complete market model. Then, specializing to conditionally log−Gaussian diffusion models, concrete analysis about the optimal values and optimal strategies is performed by using analytical tools like Feynman−Kac formula, or HJB equations. The explicit solutions to the related forward-backward equations are also given.

Dose Distribution of Radioxenon Due to a Hypothetical Accident of TRIGA Research Reactor in Bangladesh

Radiological dose distribution owing to the deposition of 131m Xe, 133m Xe, 133 Xe, 135m Xe, 135 Xe, and 138 Xe on ground and immersion considering a postulated accident of TRIGA Mark-II research reactor has been assessed. The radiological dose distribution has been carried out in various directions with the help of Gaussian Diffusion Model. Local meteorological data such as average wind speed, frequency, etc. has been collected and evaluated for various directions around the reactor site. For all the dominant directions, the maximum dose values due to 131m Xe, 133m Xe, 133 Xe, 135m Xe, 135 Xe, 138 Xe and the total ( 131m Xe + 133m Xe + 133 Xe + 135m Xe + 135 Xe + 138 Xe) were observed within the limit 3.03E-7–1.23E-4 µSv/h, 1.01E-5–4.09E-3 µSv/h, 0.0003–0.14 µSv/h, 2.29E-5–9.26E-3 µSv/h, 0.002 –1.111 µSv/h, 1.11E-5–4.55E-3 µSv/h, and 0.003–1.269 µSv/h, respectively. Dose distribution was found to be dominant due to immersion and the contribution was 87.55 %. There is shortage of data regarding the release of radioxenon in the atmosphere during nuclear accident especially in the case of TRIGA type research reactor. This paper is the first such detailed study on atmospheric release of radioxenon and its dose distribution for a full power- reactor and the consequences towards the environment and public health. The result can be applied to develop the radiological protective measures and to prepare an emergency response plan for the TRIGA reactor site.

Linear multi-scale modeling of diffusion MRI data: A framework for characterization of oriented structures across length scales.

Diffusion-weighted magnetic resonance imaging (DW-MRI) has evolved to provide increasingly sophisticated investigations of the human brain's structural connectome in vivo. Restriction spectrum imaging (RSI) is a method that reconstructs the orientation distribution of diffusion within tissues over a range of length scales. In its original formulation, RSI represented the signal as consisting of a spectrum of Gaussian diffusion response functions. Recent technological advances have enabled the use of ultra-high b-values on human MRI scanners, providing higher sensitivity to intracellular water diffusion in the living human brain. To capture the complex diffusion time dependence of the signal within restricted water compartments, we expand upon the RSI approach to represent restricted water compartments with non-Gaussian response functions, in an extended analysis framework called linear multi-scale modeling (LMM). The LMM approach is designed to resolve length scale and orientation-specific information with greater specificity to tissue microstructure in the restricted and hindered compartments, while retaining the advantages of the RSI approach in its implementation as a linear inverse problem. Using multi-shell, multi-diffusion time DW-MRI data acquired with a state-of-the-art 3T MRI scanner equipped with 300 mT/m gradients, we demonstrate the ability of the LMM approach to distinguish different anatomical structures in the human brain and the potential to advance mapping of the human connectome through joint estimation of the fiber orientation distributions and compartment size characteristics.

Quenching Behavior of the Solution for the Problems with Sequential Concentrated Sources

This article studies the diffusion problems with a concentrated source which is provided at a sequential time steps in 1 dimensional space. The problems are considered for both Gaussian and fractional diffusion operators. For the fractional diffusion case, Riemann-Liouville operator with fractional order is used to describe the model with diffusion rate slower than normal time scale, which is known as sub diffusive problems. Due to this sub diffusive property, the existence and nonexistence behavior of the solution will be studied. Since the forcing term will experience a concentrated source at a sequence of time steps, the frequency, the time difference and strength of the source may affect the growth rate of the solution. Criteria for these effects which may cause for the quenching behavior of the solution will be given. The existence of the solution is investigated. The monotone behavior in spatial will be given. The quenching behavior of the solution will be studied. The location of the quenching point will be discussed.

QUENCHING BEHAVIOR OF THE SOLUTION FOR THE PROBLEMS WITH SEQUENTIAL CONCENTRATED SOURCES

This article studies the diffusion problems with a concentrated source which is provided at a sequential time steps in 1 dimensional space. The problems are considered for both Gaussian and fractional diffusion operators. For the fractional diffusion case, Riemann-Liouville operator with fractional order is used to describe the model with diffusion rate slower than normal time scale, which is known as sub diffusive problems. Due to this sub diffusive property, the existence and nonexistence behavior of the solution will be studied. Since the forcing term will experience a concentrated source at a sequence of time steps, the frequency, the time difference and strength of the source may affect the growth rate of the solution. Criteria for these effects which may cause for the quenching behavior of the solution will be given. The existence of the solution is investigated. The monotone behavior in spatial will be given. The quenching behavior of the solution will be studied. The location of the quenching point will be discussed.

Health Risk Assessment and Projection of Municipal Solid Waste Disposal in China

Background China’s Municipal solid waste (MSW) is growing rapidly. Incineration and landfill are two main approaches of MSW disposal and both of them emit different types of ambient pollutants and threaten human health. There lacks systematic health risk assessment and projections of MSW incineration and landfill in China. Methods We established the historical MSW incineration and landfill emission inventories from 2015 to 2017 and used the Gaussian Diffusion Model to simulate the spatial distribution of ambient pollutants. We then used Risk Quotients Model to assess the non-carcinogenic and carcinogenic health risks through inhalation exposure. Besides, we set seven possible MSW incineration development scenarios to predict health risk levels in 2035, considering the effect of population growth, incineration rate, waste classification and recycling, and technology progress. Results The results show that non-carcinogenic risk caused by MSW incineration from 2015 to 2017 was lower than landfill at the national level. Both of them were meet the maximum acceptable level (HI ≤ 1). From 2015 to 2017, carcinogenic risks caused by landfill were 9.42 × 10-6, 9.40 × 10-6, 9.37 × 10-6, nine times larger than the maximum acceptable level (CR ≤ 1×10-6). Carcinogenic risks caused by incineration were 5.71 × 10-6, 7.92 × 10-6, 9.44 × 10-6, five to nine times larger than the maximum acceptable level. Projection results show that compared to the baseline scenario, through classification and recycling, changing incinerator furnace, and improving, national health risk levels will be decreased by 24%, 94% and 97%. Conclusions We assessed the health risks caused by MSF disposal and found MSF incineration a relatively low risk alternative disposal approach compared to waste landfill. In the future, local government should reduce MSF disposal health risks by optimizing the selection of incinerators locations, improving the garbage sorting recycling system, and strengthening information disclosure and communications.

Classification of cognitively normal controls, mild cognitive impairment and Alzheimer’s disease using transfer learning approach

Automated classification of dementia stage using imaging will be useful for clinical diagnosis and the classification accuracy will be biased for highly imbalanced samples in each class. Hence, we propose a novel approach using transfer learning-based structural significance (TLSS) for the classification of cognitively normal controls (CN), mild cognitive impairment (MCI) and Alzheimer’s disease (AD) patients based on white matter Gaussian diffusion (tensor) indices and non-Gaussian diffusion (kurtosis) indices. The structural T1-weighted magnetic resonance imaging and diffusion images were taken from ADNI dataset with 44 CN, 84 MCI and 22 AD patients. We estimate the regional Gaussian diffusion indices such as tensor fractional anisotropy (TFA) and mean diffusivity (TMD) as well as non-Gaussian diffusion indices such as kurtosis fractional anisotropy (KFA) and kurtosis mean diffusivity (KMD) in white matter regions. Further, we build transfer learning model using various balanced classifiers with structural expansion reduction (SER) and structure transfer using threshold (STT) and ensemble of majority voting of both SER and STT algorithms. We build two models by training the source model using kurtosis indices, refine the model on target tensor indices and vice versa. Transfer learning model using balanced random forest classifier was able to classify and predict all the groups with an overall accuracy about 0.79 using ensemble of SER and STT forests rather than individual algorithms (SER and STT). Our results conclude that the proposed model using kurtosis indices as source model classified and predicted with accuracies of 0.96, 0.72 and 0.7 in classifying CN vs AD, CN vs MCI and AD vs MCI respectively. To conclude, the proposed approach has improved the classification accuracy and its potential applicability for imbalanced data sample datasets.

Tracking and measuring plumes from sailing ships using an unmanned aerial vehicle

Measuring sailing ship plumes provides comprehensive and real-time emission data. However, accurately tracking and measuring ship plumes still requires research. This study describes a tracking and measurement method of ship plumes using an unmanned aerial vehicle (UAV). A UAV ship exhaust measurement system and monitoring process were developed. Data from an automatic identification system (AIS) was used to improve the Gaussian plume diffusion model to facilitate the initial location of the plume on sailing ships. Based on the real-time gas measurement values obtained by the UAV, the UAV flight method was optimized to accurately track and measure the ship's plume. The Pudong Maritime Safety Administration used this system in 2019 to effectively monitor the plumes of 27 sailing ships as part of maritime law enforcement. Consequently, four cases of excessive fuel sulphur content (FSC) were detected in situ for the first time, indicating that China's maritime authorities can use the technology to supervise and control the FSC of sailing ships.

An automatic method to generate voxel-based absorbed doses from radioactivity distributions for nuclear medicine using generative adversarial networks: a feasibility study.

An approach to autogenerate voxel-based absorbed dose for nuclear medicine is proposed using generative adversarial networks. The method is based on image-to-image transformation and promises to achieve real-time visualization of the absorbed dose and optimization of therapeutic strategies. The activity-density superimposed image is input to generator (G) as a reference image to generate a pseudoabsorbed dose image (DI), which is then mixed with ground truth (GT) DI and recognized by discriminator (D). If the pseudoimage is recognized, the information is fed back, and G regenerates a pseudodose image until D drops to obtain a lifelike DI. As a feasibility study, we used the dose distribution of segmented human anatomy from different sources and activities as training and test datasets. The activity source was assumed to be 1, 2, 3, 4, or 7 subsource blocks. The 3-subsource model was used as the test dataset, and the others were used as the training dataset. The activity distribution in the subsource was assumed to be uniform or heterogeneous (i.e., Gaussian diffusion with sigma 0.0, 0.3, or 0.6). Differences were assessed by Gamma analysis. Results showed that the same or quasi-inhomogeneity model can well predict the dose distribution of different activity-inhomogeneity. Although the 1-source model was trained with very few datasets, it showed an optimal balance between accuracy and training efficiency. There were offsets in the mean absorbed dose between the predicted and GT, but they all showed a higher Gamma-pass-rate (> 93%) and ~ 10% std.

Combined Grey Wolf Optimizer Algorithm and Corrected Gaussian Diffusion Model in Source Term Estimation

It is extremely critical for an emergency response to quickly and accurately use source term estimation (STE) in the event of hazardous gas leakage. To determine the appropriate algorithm, four swarm intelligence optimization (SIO) algorithms including Gray Wolf optimizer (GWO), particle swarm optimization (PSO), genetic algorithm (GA) and ant colony optimization (ACO) are selected to be applied in STE. After calculation, all four algorithms can obtain leak source parameters. Among them, GWO and GA have similar computational efficiency, while ACO is computationally inefficient. Compared with GWO, GA and PSO, ACO requires larger population and more iterations to ensure accuracy of source parameters. Most notably, the convergence factor of GWO is self-adaptive, which is in favor of obtaining accurate results with lower population and iterations. On this basis, combination of GWO and a modified Gaussian diffusion model with surface correction factor is used to estimate the emission source term in this work. The calculation results demonstrate that the corrected Gaussian plume model can improve the accuracy of STE, which is promising for application in emergency warning and safety monitoring.

Data-driven uncertainty quantification in computational human head models

Computational models of the human head are promising tools for estimating the impact-induced response of the brain, and thus play an important role in the prediction of traumatic brain injury. The basic constituents of these models (i.e., model geometry, material properties, and boundary conditions) are often associated with significant uncertainty and variability. As a result, uncertainty quantification (UQ), which involves quantification of the effect of this uncertainty and variability on the simulated response, becomes critical to ensure reliability of model predictions. Modern biofidelic head model simulations are associated with very high computational cost and high-dimensional inputs and outputs, which limits the applicability of traditional UQ methods on these systems. In this study, a two-stage, data-driven manifold learning-based framework is proposed for UQ of computational head models. This framework is demonstrated on a 2D subject-specific head model, where the goal is to quantify uncertainty in the simulated strain fields (i.e., output), given variability in the material properties of different brain substructures (i.e., input). In the first stage, a data-driven method based on multi-dimensional Gaussian kernel-density estimation and diffusion maps is used to generate realizations of the input random vector directly from the available data. Computational simulations of a small number of realizations provide input–output pairs for training data-driven surrogate models in the second stage. The surrogate models employ nonlinear dimensionality reduction using Grassmannian diffusion maps, Gaussian process regression to create a low-cost mapping between the input random vector and the reduced solution space, and geometric harmonics models for mapping between the reduced space and the Grassmann manifold. It is demonstrated that the surrogate models provide highly accurate approximations of the computational model while significantly reducing the computational cost. Monte Carlo simulations of the surrogate models are used for uncertainty propagation. UQ of the strain fields highlights significant spatial variation in model uncertainty, and reveals key differences in uncertainty among commonly used strain-based brain injury predictor variables.

Neurite Exchange Imaging (NEXI): A minimal model of diffusion in gray matter with inter-compartment water exchange

Biophysical models of diffusion in white matter have been center-stage over the past two decades and are essentially based on what is now commonly referred to as the “Standard Model” (SM) of non-exchanging anisotropic compartments with Gaussian diffusion. In this work, we focus on diffusion MRI in gray matter, which requires rethinking basic microstructure modeling blocks. In particular, at least three contributions beyond the SM need to be considered for gray matter: water exchange across the cell membrane – between neurites and the extracellular space; non-Gaussian diffusion along neuronal and glial processes – resulting from structural disorder; and signal contribution from soma. For the first contribution, we propose Neurite Exchange Imaging (NEXI) as an extension of the SM of diffusion, which builds on the anisotropic Kärger model of two exchanging compartments. Using datasets acquired at multiple diffusion weightings (b) and diffusion times (t) in the rat brain in vivo, we investigate the suitability of NEXI to describe the diffusion signal in the gray matter, compared to the other two possible contributions. Our results for the diffusion time window 20–45 ms show minimal diffusivity time-dependence and more pronounced kurtosis decay with time, which is well fit by the exchange model. Moreover, we observe lower signal for longer diffusion times at high b. In light of these observations, we identify exchange as the mechanism that best explains these signal signatures in both low-b and high-b regime, and thereby propose NEXI as the minimal model for gray matter microstructure mapping. We finally highlight multi-b multi-t acquisition protocols as being best suited to estimate NEXI model parameters reliably. Using this approach, we estimate the inter-compartment water exchange time to be 15 – 60 ms in the rat cortex and hippocampus in vivo, which is of the same order or shorter than the diffusion time in typical diffusion MRI acquisitions. This suggests water exchange as an essential component for interpreting diffusion MRI measurements in gray matter.

Impact of intra-axonal kurtosis on fiber orientation densityfunctions estimated with fiber ball imaging.

To determine the impact of an intra-axonal kurtosis on estimates of the fiber orientation density function (fODF) obtained with fiber ball imaging (FBI). Standard FBI assumes Gaussian diffusion within individual axons and estimates the fODF by applying an inverse generalized Funk transform to diffusion MRI data for b-values of 4000 s/mm2 or higher. However, recent work based on numeric simulations shows that diffusion inside axons is non-Gaussian with an intra-axonal kurtosis of ∼ 0.4. Here, the theory underlying FBI is extended to incorporate an intra-axonal kurtosis. This is done to first order in the intra-axonal kurtosis without making assumptions about the details of the diffusion dynamics and to all orders for a specific model based on a gamma distribution of diffusivities. The first order approximation is used to assess the effect of an intra-axonal kurtosis on FBI estimates for the fODF and axonal water fraction. The gamma distribution model is used to test the validity of the approximation. The first order approximation indicates the estimated fODF is altered by a few percent for an intra-axonal kurtosis of 0.4 in comparison to predictions of standard FBI. If one neglects the intra-axonal kurtosis, the angular resolution of the point spread function for the fODF is changed by <1°, whereas the axonal water fraction is overestimated by ∼ 5%. The gamma distribution model shows that the first order approximation is accurate to within a few percent. The intra-axonal kurtosis has a small impact on fODFs estimated with FBI.

Research on Leakage and Diffusion characteristics of Liquid Hydrogen Based on Gaussian Diffusion Model

In order to analyze the diffusion characteristics of the hydrogen cloud during a liquid hydrogen leakage accident, the Matlab calculation program of liquid hydrogen leakage and diffusion was compiled based on the Gaussian diffusion theory, and analyzed the influence of wind speed, pressure, leakage area and other factors on the size of the dangerous area after liquid hydrogen leakage.The calculation results show that: the wind speed accelerates the diffusion, and the higher the wind speed, the stronger the dilution effect on the hydrogen cloud, and the smaller the dangerous area formed; the increase of pressure and leakage port area will increase the leakage of liquid hydrogen, and as a result, the scope of the dangerous area is increased.

Associations between mean apparent propagator MRI and cerebrospinal fluid markers of AD pathology, neurodegeneration, and glial activation, in cognitively unimpaired adults

AbstractBackgroundNumerous studies have reported correlations between diffusion tensor imaging (DTI) metrics and cerebrospinal (CSF) biomarkers of Alzheimer’s disease (AD) pathology. However, the assumption of Gaussian diffusion in DTI limits the ability to characterize white matter (WM) microstructural changes. Mean apparent propagator (MAP) MRI is a model that attempts to overcome this limitation by allowing for the estimation of parameters that convey more precise information about WM microstructure.To investigate MAP MRI’s sensitivity to early WM degeneration associated with preclinical, asymptomatic AD pathology, we examined the relationship between CSF biomarkers and MAP MRI microstructural parameters in 92 cognitively unimpaired adults.Method92 cognitively unimpaired controls from the Wisconsin Registry for Alzheimer’s Prevention and the Wisconsin Alzheimer’s Disease Research Center were imaged with multi‐shell diffusion‐weighted MRI. DTI metrics (FA, MD, RD, AxD) were computed and the MAP MRI model was employed to calculate various microstructural parameters: Return to origin probability (RTOP), return to axis probability (RTAP), return to plane probability (RTPP), mean squared displacement (MSD), Non‐Gaussianity (NG), and q‐space inverse variance (QIV). DTI and MAP parameter values were extracted from the cingulum and correlated to Aβ42, P‐Tau, P‐Tau/Aβ42, YKL‐40, and neurofilament light chain (NFL) levels in lumbar cerebrospinal fluid samples.ResultMAP parameters were moderately and significantly correlated to most CSF measures. RTPP was significantly correlated to all 5 CSF measures, while MSD, NG, and QIV were significantly correlated to 4 of 5 CSF measures. NFL, a known marker for axonal degeneration, was significantly related to 5 of the 6 MAP parameters assessed. Meanwhile, correlations between DTI and CSF measures were weak and non‐significant.ConclusionThese preliminary results highlight the potential of MAP MRI to detect early WM deterioration indicative of preclinical, asymptomatic AD and associated neurodegeneration. MAP metrics extracted from a commonly affected WM tract in AD were more strongly and significantly correlated with CSF measures than DTI metrics were, suggesting that MAP MRI may be more useful than DTI for identifying the earliest WM microstructural changes associated with AD. Future work will incorporate longitudinal data and assess the effects of CSF and molecular imaging markers on MAP age trajectories.

Denoising of Tourist Street Scene Image Based on ROF Model of Second-Order Partial Differential Equation

The noise pollution in tourist street view images is caused by various reasons. A major challenge that researchers have been facing is to find a way to effectively remove noise. Although in the past few decades people have proposed many methods of denoising tourist street scene images, the research on denoising technology of tourist street scene images is still not outdated. There is no doubt that it has become a basic and important research topic in the field of digital image processing. The evolutionary diffusion method based on partial differential equations is helpful to improve the quality of noisy tourist street scene images. This method can process tourist street scene images according to people’s expected diffusion behavior. The adaptive total variation model proposed in this paper is improved on the basis of the total variation model and the Gaussian thermal diffusion model. We analyze the classic variational PDE-based denoising model and get a unified variational PDE energy functional model. We also give a detailed analysis of the diffusion performance of the total variational model and then propose an adaptive total variational diffusion model. By improving the diffusion coefficient and introducing a curvature operator that can distinguish details such as edges, it can effectively denoise the tourist street scene image, and it also has a good effect on avoiding the step effect. Through the improvement of the ROF model, the loyalty term and regular term of the model are parameterized, the adaptive total variation denoising model of this paper is established, and a detailed analysis is carried out. The experimental results show that compared with some traditional denoising models, the model in this paper can effectively suppress the step effect in the denoising process, while protecting the texture details of the edge area of the tourist street scene image. In addition, the model in this paper is superior to traditional denoising models in terms of denoising performance and texture structure protection.