Diffusion Algorithm Research Articles

Evaluation of Multi-Source High-Resolution Remote Sensing Image Fusion in Aquaculture Areas

Image fusion of satellite sensors can generate a high-resolution multi-spectral image from inputs of a high spatial resolution panchromatic image and a low spatial resolution multi-spectral image for feature extraction and target recognition, such as enclosure seines and floating rafts. However, there is currently no clear and definite method of image fusion for different aquaculture areas distribution extraction from high-resolution satellite images. This study uses three types of high-resolution remote sensing images, GF-1 (Gaofen-1), GF-2 (Gaofen-2), and WV-2 (WorldView-2), covering the raft and enclosure seines aquacultures in the Xiangshan Bay, China, to evaluate panchromatic and multispectral image fusion techniques to determine which is the best. This study applied PCA (principal component analysis), GS (Gram-Schmidt), and NNDiffuse (nearest neighbor diffusion) algorithms to panchromatic and multispectral images fusion of GF-1, GF-2, and WV-2. Two quantitative methods are used to evaluate the fusion effect. The first used seven statistical parameters, including gray mean value, standard deviation, information entropy, average gradient, correlation coefficient, deviation index, and spectral distortion. The second is the CQmax index. Comparing the evaluation results by these seven common statistical indicators with the results of the image fusion evaluation by index CQmax, the results prove that the CQmax index can be applied to the evaluation of image fusion effects in different aquaculture areas. For the floating raft cultured area, the conclusion is consentaneous; NNDiffuse was also optimal for GF-1 and GF-2 data, and PCA was optimal for WV-2 data. For the enclosure seines culture area, the conclusion of quantitative evaluations is not consistent and it shows that there is no definite good method that can be applied to all areas; therefore, careful evaluation and selection of the best applicable image fusion method are required according to the study area and sensor images.

RESEARCH ON STOCHASTIC FUZZY DIFFERENTIAL EQUATIONS IN MULTIPLE BLURRED IMAGE REPAIR MODELS

This paper aims to study the processing and repairing methods of blurred images, promote the development of partial differential equations in the field of image processing, and expand the application of stochastic fuzzy differential equations in the field of image processing and repair. This study starts with a typical blurred image repair method. First, a comparative analysis of several common blurred image repair methods including Wiener filtering restoration, inverse filtering restoration, and Lucy–Richardson (L-R) filtering restoration is performed. Second, based on the linear partial differential equation learning model (LPDE), the concept of fuzzy integral is introduced, and an improved stochastic fuzzy partial differential equation learning model (SFCPDE) is proposed. The effect of the learning model before and after improvement on blurred color image processing is compared and analyzed. Finally, based on the total variation (TV) blurred image repair algorithm, an improved TV blurred image repair algorithm is proposed. The comparison and analysis of the repair effects of several blurred image repair algorithms are performed. The results show that there are obvious differences in the repairing methods with or without noise. Inverse filtering works best when there is no noise. L-R filtering has the disadvantage of amplifying noise. Compared with LDPE, the training speed of SFCPDE is significantly improved, and the training error is less than LDPE. The SFCPDE learning model performs better in the processing of blurred color images. After 10 iterations, the improved TV algorithm is significantly better than the TV algorithm and the CDD algorithm in repairing blurred images. The PSNR value of the TV algorithm and the curvature-driven diffusion (CDD) algorithm after 10 iterations corresponds to about 60% of the PSNR value of the improved algorithm. The algorithms and models of stochastic fuzzy partial differential equations proposed in this paper have great application potential in the processing and repair of multiple blurred images.

Multi-group radiation diffusion convergence in low-density foam experiments

We present an in-depth analysis of a Marshak radiation wave moving through an iron-oxide (Fe2O3) foam using a 1D multigroup diffusive radiation transport model, MDART (Multigroup Diffusion Algorithm for Radiation Transport). We consider the consequences of under-resolving the group structure and address how this could lead to incorrect conclusions in the analysis of general supersonic radiation wave experiments. We also provide an analysis of the types of experimental outcome one may incorrectly link to physical effects but are in fact due to poor simulation practice.

A robust diffusion algorithm using logarithmic hyperbolic cosine cost function for channel estimation in wireless sensor network under impulsive noise environment

In a wireless sensor network (WSN), the performance of the error-squared based adaptive channel estimation algorithm degrades in the presence of impulsive noise. Robust methods are used to minimize the impulsive noise impact at the cost of a slow convergence rate. We propose a robust diffusion adaptive channel estimation algorithm using the logarithmic hyperbolic cosine cost function assuming that the received signal at each node is corrupted by impulsive noise. The sensor nodes experiencing the common channel with the base station are grouped using their initial channel estimates. After grouping, the robust diffusion algorithm is applied in each group to estimate the corresponding channel. The steady-state mean square deviation (MSD) and excess mean square error (EMSE) of the robust algorithm are derived. The algorithm's steady-state and convergence rate performance are simulated for Rayleigh fading channel corrupted by Bernoulli-Gaussian distributed impulsive noise. The simulation results demonstrate that the proposed algorithm gives faster convergence without compromising steady-state performance compared to other robust algorithms.

Fusion of Internal Similarity to Improve the Accuracy of Recommendation Algorithm

Collaborative filtering algorithms (CF) and mass diffusion (MD) algorithms have been successfully applied to recommender systems for years and can solve the problem of information overload. However, both algorithms suffer from data sparsity, and both tend to recommend popular products, which have poor diversity and are not suitable for real life. In this paper, we propose a user internal similarity-based recommendation algorithm (UISRC). UISRC first calculates the item-item similarity matrix and calculates the average similarity between items purchased by each user as the user’s internal similarity. The internal similarity of users is combined to modify the recommendation score to make score predictions and suggestions. Simulation experiments on RYM and Last.FM datasets, the results show that UISRC can obtain better recommendation accuracy and a variety of recommendations than traditional CF and MD algorithms.

Diffusion Particle Filtering on the Special Orthogonal Group Using Lie Algebra Statistics

In this paper, we introduce new distributed diffusion algorithms to track a sequence of hidden random matrices that evolve on the special orthogonal group. The algorithms are based on the Adapt-then-Combine and the Random Exchange methods, and diffuse Gaussian approximations of posterior densities computed in the Lie algebra of the special orthogonal group. Simulation results show that, in scenarios with nonlinear observation functions, the proposed algorithms perform closely to the centralized particle filter estimator and can outperform competing Extended Kalman Filters.

Optimal Diffusion Learning Over Networks—Part I: Single-Task Algorithms

We revisit the theory of distributed networks of cooperative agents under a broader perspective of diffusion adaptation, by exploiting proximity concepts. This leads to two main families of algorithms with enhanced convergence rate and mean-square-error performance. Part I of this work considers mainly single-task scenarios, which are based on formulating optimal learning and fusion steps via an adaptive network penalty function. The main recursions, which we refer to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Adapt-and-Fuse</i> (AAF) diffusion, are reminiscent of a reweighted network regularized algorithm, usually seen in standalone formulations. This is in line with early approaches that promote proximity among agents in cooperative networks. The AAF strategy employs exact fusion in the least-squares sense, and outperforms the exact global least-squares solution that ignores the topology of the network. It also suggests simplified LMS-complexity algorithms, and motivates us to develop a normalized version of the relative variance diffusion algorithm, which also learns combination weights. It is verified that even when agents do not share estimates, but only their uncertainties, the simplified AAF improves accuracy over the NLMS-RV algorithm in the presence of intruders, and becomes more robust to noisy links. In order to cope with the computational burden associated with long parameter vectors and correlated inputs, an overlapped block <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multidelay adaptive frequency-domain</i> (FD) version of each new algorithm is derived. It turns out that for correlated inputs, these FD-LMS versions outperform the exact fullband RLS solutions. In the accompanying Part II of this work, we pursue extensions to the multitask scenario. Extensive simulations illustrate the superiority of the new approaches.

Robust and Sparse Aware Diffusion Adaptive Algorithms for Distributed Estimation

In distributed wireless sensor networks, geographically distributed sensors cooperate wirelessly with each other. While sensing from the environment, the signals from these sensors are often contaminated by noise. Traditional diffusion algorithms for distributed estimation consider this noise to be Gaussian in nature. However, in practice this noise can also be non-Gaussian, which leads to deterioration in performance of traditional adaptive algorithms. Moreover, the parameter vector to be estimated may be sparse in nature. To improve adaptive filter performance for distributed networks, we propose a set of sparsity aware diffusion adaptive filters which are robust to non-Gaussian noises. Extensive simulation study for different Gaussian and non-Gaussian noise environments show the improved estimation ability of the proposed algorithms for modelling highly, moderate and non-sparse distributed systems.

A new anisotropic fourth-order diffusion equation model based on image features for image denoising

&lt;p style='text-indent:20px;'&gt;Image denoising has always been a challenging task. For performing this task, one of the most effective methods is based on variational PDE. Inspired by the LLT model, we first propose a new adaptive LLT model by adding a weighted function, and then we propose a class of fourth-order diffusion equations based on the new functional. Owing to the adaptive function, the new functional is better than the LLT model and other fourth-order models in terms of edge preservation. While generalizing the Euler-Lagrange equation of the new functional, we discuss a new fourth-order diffusion framework for image denoising. Different from those of other fourth-order diffusion models, the new diffusion coefficients depend on the first-order and second-order derivatives, which can preserve edges and smooth images, respectively. Regarding numerical implementations, we first design an explicit scheme for the proposed model. However, fourth-order diffusion equations require strict stability conditions, and the number of iterations needed is considerable. Consequently, we apply the fast explicit diffusion algorithm (FED) to the explicit scheme to reduce the time consumption of the proposed approach. Furthermore, the additive operator splitting (AOS) scheme is applied for the numerical implementation, and it is the most efficient among all of our algorithms. Finally, compared with other models, the new model exhibits superior effectiveness and efficiency.&lt;/p&gt;

Controlling salt crystallization in evaporating thin films of colloidal liquids

Studying crystallization kinetics of mineral salts during desiccation of thin films of the complex colloidal salt matrix is a topic of considerable research interest due to its direct relations to the structures, property of materials, and utmost importance for controlling crystallization and colloidal products design. In this article, the shape and size distribution of macro-structures induced by the crystallization mechanism were systematically investigated using experimental and numerical methods. In the experiments, Sodium Chloride crystallization in starch or Xanthan solutions is considered as a model system. It is found that quantified parameters such as evaporation rate and local viscosity of the medium mainly govern nucleation and propagation of the ramified dendritic patterns leading to several categories of fractal aggregates, such as river patterns, cross-shaped patterns, and finger-like structures. The fractal dimension of the patterns is independent of the salt concentrations but changes with the initial concentration of the thickener. The effect of evaporation rate and the medium viscosity on the dynamics of crystallization for pattern formation was simulated numerically by two modified models based on diffusion-limited aggregation (DLA) and the deposition, diffusion, and aggregation (DDA) algorithms which enable us to successfully reproduce the experimental results. Our experimental results and numerical approaches open avenues for controlling the size and shape of crystals and patterns formed in a complex gel matrix.

Image Processing Method Based on Chaotic Encryption and Wavelet Transform for Planar Design

This paper provides an in-depth study and analysis of image processing for graphic design through chaotic encryption combined with a wavelet transform algorithm. Firstly, the traditional Mallat algorithm is optimized; since the mean value of the transform coefficients generated after the wavelet transform of the image is used as the initial value of the chaotic system to iterate, when the image is modified, then the mean value of the wavelet coefficients will also change, and the final iteration comes out as two different sequences using the property that the chaotic system is extremely sensitive to the initial conditions, so the algorithm has a certain sensitivity to tampering and localization effect. The image of the encrypted graphic design is decrypted by the chaos decryption system, and the final image information of the graphic design is obtained. In terms of the security of the graphic design image itself, the complex dynamical properties of chaos are fully utilized to encrypt it, and the algorithm has a good encryption effect after statistical characteristic analysis, attack complexity, difference analysis, adjacent pixel correlation analysis, and key sensitivity analysis. The plaintext image is decomposed in odd-even sequence using the boosting algorithm to get the sequence with an even index and the sequence with an odd index; then, the diffusion algorithm is applied to the two sequences by the prediction and update algorithm, and this process is repeated many times to get the two ciphertext sequences after scrambling, merging these two sequences, and matrixing them to get the ciphertext image. Finally, the testing of the embedded planar designed image revolves around four aspects, namely, image processing, tamper sensitivity, robustness, and imperceptibility, to examine the designed planar designed image system. In the diffusion manipulation, the key matrix for diffusion is obtained using the threshold processing method of the Local Binary Pattern (LBP) algorithm for the matrices generated by the Logistic Chaos system, which improves the randomness of the algorithm. The experimental results verify the effectiveness and security of the algorithm.

On the use of spectral algorithms for the prediction of short-lived volatile fission product release: Methodology for bounding numerical error

Recent developments on spectral diffusion algorithms, i.e., algorithms which exploit the projection of the solution on the eigenfunctions of the Laplacian operator, demonstrated their effective applicability in fast transient conditions. Nevertheless, the numerical error introduced by these algorithms, together with the uncertainties associated with model parameters, may impact the reliability of the predictions on short-lived volatile fission product release from nuclear fuel. In this work, we provide an upper bound on the numerical error introduced by the presented spectral diffusion algorithm, in both constant and time-varying conditions, depending on the number of modes and on the time discretization. The definition of this upper bound allows introducing a methodology to a priori bound the numerical error on short-lived volatile fission product retention.

Phase-only color rainbow holographic near-eye display.

Color rainbow holography can realize color holographic 3D display without speckle noise under white light illumination. However, traditional color rainbow holograms used for high-resolution static color 3D display or near-eye color display are amplitude-type, resulting in low diffraction efficiency due to the presence of conjugate light. In this Letter, a phase-only color rainbow holographic near-eye display is demonstrated. The calculation of a phase-only color rainbow hologram is realized by combining a band-limited diffraction and a bi-directional error diffusion algorithm with high-frequency blazed gratings coded to control longitudinal dispersion. When the wavelength of illumination light is deviated from the designated wavelength of the hologram, only a certain wavefront aberration is caused, but there is no conjugate light. The phase-only color rainbow holographic near-eye display of both a 2D color image and a 3D scene are implemented by optical experiments. It has potential applications in head-mounted 3D augmented reality displays without vergence-accommodation conflict.

A Distributed Two-Stage Economic Dispatch for Virtual Power Plant Based on An Improved Exact Diffusion Algorithm

To manage a large scale of distributed energy resources (DERs) dispersed geographically and reduce the impact of DER uncertainties, this paper proposes a distributed two-stage economic dispatch for virtual power plant (VPP) to track a specified VPP schedule curve. In the look-ahead stage, a distributed economic dispatch strategy is proposed to optimally allocate the scheduled power among DERs. In the real-time stage, a distributed VPP schedule curve tracking problem is modeled to balance the fluctuation of wind farms and/or PV stations. The two-stage distributed optimization problems are solved by an improved exact diffusion algorithm which is proved to be robust to local communication failure. Case studies validate the performance of the algorithm proposed.

A diffusion-based method for removing background stars from astronomical images

Image processing techniques for background star removal from astronomical images have important applications such as streak detection and star/galaxy differentiation in galaxy morphology classification. Previous star removal methods relied on frame differencing and so required multiple images. In this work we present a new diffusion-based method that can remove stars and noise at the same time, using only a single image. The method measures a parameter called the local asymmetry around each pixel to identify stars and remove them with varying diffusion strength according to the measured parameter. To optimise the balance between signal preservation and star removal, it further incorporates a local stopping function that can adaptively turn the diffusion process on and off by monitoring the image residues. In order to test the method, we constructed a synthetic image that mimics astronomical images of interest and compared the processed images to the ground truth through the measurement of a range of metrics such as mean average error, root mean squared error, peak signal-to-noise ratio and structural similarity index. The results showed clear improvements in all the metrics compared to previous diffusion algorithms. Finally, we applied our method to a dataset of natural images and confirmed its effectiveness at preserving a wide variety of astronomical objects.

Diffusion Bayesian Subband Adaptive Filters for Distributed Estimation Over Sensor Networks

Sensor networks are an indispensable part of the Internet of Things (IoT), where sensors perform data acquisition and information processing tasks to obtain the parameters of interest so that IoT-based monitoring, diagnosis and other systems respond quickly to the changing conditions, instantaneous faults, etc. Distributed estimation algorithms are usually employed to estimate the parameters of interest in these IoT-based applications. However, when sensor networks have highly correlated input signals and nonstationary behavior in which the parameters of interest are time-varying, conventional distributed estimation algorithms suffer from severely degraded learning performance due to the large eigenvalue spread in the covariance matrix of the input signals and the random perturbation of the parameters of interest. To address these problems, this paper proposes two diffusion Bayesian subband adaptive filter (DBSAF) algorithms from a Bayesian learning perspective. As the highly-correlated input signal is whitened in a multiband structure and an estimate of the uncertainty in the parameters of interest is obtained by performing Bayesian inference, the proposed DBSAF algorithms are able to achieve better learning performance in comparison with the competing diffusion algorithms. The transient and steady-state mean square error performance of the proposed DBSAF algorithms are analyzed, and are verified by numerical simulations. A lower bound on the time-varying step-size is derived to maintain the optimal steady-state performance in nonstationary scenarios. A new method for the estimation of the noise variance is also proposed. Numerical simulations demonstrate the excellent learning performance of the proposed algorithms in comparison with benchmark algorithms.

Identification of Novel Choroidal Neovascularization-Related Genes Using Laplacian Heat Diffusion Algorithm.

Choroidal neovascularization (CNV) is a type of eye disease that can cause vision loss. In recent years, many studies have attempted to investigate the major pathological processes and molecular pathogenic mechanisms of CNV. Because many diseases are related to genes, the genes associated with CNV need to be identified. In this study, we proposed a network-based approach for identifying novel CNV-associated genes. To execute such method, we first employed a protein-protein interaction network reported in STRING. Then, we applied a network diffusion algorithm, Laplacian heat diffusion, on this network by selecting validated CNV-related genes as the seed nodes. As a result, some novel genes that had unknown but strong relationships with validated genes were identified. Furthermore, we used a screening procedure to extract the most essential genes. Eleven latent CNV-related genes were finally obtained. Extensive analyses were performed to confirm that these genes are novel CNV-related genes.

Aeroacoustic prediction for cooling fan using convolution quadrature boundary element method.

A computational method to predict the aeroacoustic sound produced by the interaction between fluid and moving body is developed, then applied to the problem of aerodynamic noise radiation from an engine cooling fan. The flow field is computed using the viscous vortex method with a simplified diffusion algorithm, followed by a noise sources extraction within the turbulent region, based on the vortex sound model. Then, the sound field is determined using a Convolution Quadrature Boundary Element Method, accounting for the scattering effect from solid surface. With the help of Convolution Quadrature Method, time-stepping Boundary Element procedure can be established circumventing the requisite for time-dependent fundamental solution. Fast Multipole Method is also adopted to improve computational efficiency. It is found that the results of flow field calculation are close to those obtained from measurement. The predicted noise levels at the microphone position are in qualitative agreement with the measured. The comparison of computation time also shows that the proposed method can effectively predict the fluid-blade interaction noise.

A systematic comparison of data- and knowledge-driven approaches to disease subtype discovery.

Typical clustering analysis for large-scale genomics data combines two unsupervised learning techniques: dimensionality reduction and clustering (DR-CL) methods. It has been demonstrated that transforming gene expression to pathway-level information can improve the robustness and interpretability of disease grouping results. This approach, referred to as biological knowledge-driven clustering (BK-CL) approach, is often neglected, due to a lack of tools enabling systematic comparisons with more established DR-based methods. Moreover, classic clustering metrics based on group separability tend to favor the DR-CL paradigm, which may increase the risk of identifying less actionable disease subtypes that have ambiguous biological and clinical explanations. Hence, there is a need for developing metrics that assess biological and clinical relevance. To facilitate the systematic analysis of BK-CL methods, we propose a computational protocol for quantitative analysis of clustering results derived from both DR-CL and BK-CL methods. Moreover, we propose a new BK-CL method that combines prior knowledge of disease relevant genes, network diffusion algorithms and gene set enrichment analysis to generate robust pathway-level information. Benchmarking studies were conducted to compare the grouping results from different DR-CL and BK-CL approaches with respect to standard clustering evaluation metrics, concordance with known subtypes, association with clinical outcomes and disease modules in co-expression networks of genes. No single approach dominated every metric, showing the importance multi-objective evaluation in clustering analysis. However, we demonstrated that, on gene expression data sets derived from TCGA samples, the BK-CL approach can find groupings that provide significant prognostic value in both breast and prostate cancers.

Recommendation with Diversity: Mass Diffusion Model Based on Trust Network and Object Reputation

The traditional mass diffusion recommendation algorithm only relies on the user’s object collection relationship, resulting in poor recommendation performance for users with small purchases (i.e., small-degree user), and it is difficult to balance the accuracy and diversity of the recommendation system. This paper introduces the trust relationship into the resource allocation process of the traditional mass diffusion algorithm and proposes the Dual Wing Mass Diffusion model (DWMD), which constructs a dual wing graph based on trust relationships and object collection relationships. Implicit trust is mined according to the network structure of the trust relationship and integrated into the resource allocation process, and then merging the positive effects of object reputation on a recommendation through tunable scaling parameters. The user controls the tunable scaling parameter to achieve the best recommendation performance. The experimental results show that the DWMD method significantly improves diversity and novelty while ensuring high accuracy and effectively improves the accuracy and diversity balance. The improved recommendation performance for small-degree users proves that the trust relationship can effectively alleviate the generalized cold start problem of the recommendation algorithm for users who collect a small number of objects.