Image denoising methods focus on noise removal with edge and texture preservation as the primary goal. Most deep learning methods are supervised in nature, i.e., they need noisy and clean image data to learn the mapping. On the contrary, deep image prior (DIP) is an unsupervised method. It works on the principle that a structured CNN with enough parameters can be used as the prior of the image. It captures noise with long training, which is a matter of concern. In this work, we try to resolve this problem of DIP. We incorporate the heat equation in DIP, as this equation has smoothing behavior, which is well known in the PDE-based image denoising community. For the validation, we perform the experiments on different images with Gaussian noise and speckle noise of varying levels. Additionally, a theoretical analysis of the mean squared error (MSE) progress over training iterations is presented for a deeper understanding of the training dynamics of both DIP and PI-DIP under these noise conditions. Experiments show that this strategy is not limited to specific noise. With this framework, we do not have to be concerned about the stopping point of DIP optimization, which is a great relief and has a greater impact on unseen image denoising problems.

In this study, we propose a new data-driven algorithm for the Perona-Malik image despeckling problem. The advantage of the proposed algorithm over neural network-based methods is that it does not need any noisy and clean image data pair for training. The proposed algorithm is implemented using a three-dimensional convolution neural network (ConvNet) architecture. We compare its output with results obtained from several existing methods, including the operator splitting RBF collocation method, the finite difference method (FDM), and physics-informed neural networks (PINNs). To evaluate the performance of the proposed algorithm, simulations are carried out using grayscale images that have been artificially corrupted with different levels of speckle noise. Using the peak signal to noise ratio (PSNR) and structural similarity index measure (SSIM) as the evaluation metric, we observed that the proposed algorithm outperforms these existing methods, demonstrating superior image quality with the same numerical scheme and the same discretization. To the best of our knowledge, this work represents the first application of physics-inspired convolutional neural network for PDE-based image despeckling model.

Spiking Neural Networks (SNNs) are poised to lead the next generation of artificial intelligence, offering energy efficiency and performance on par with traditional neural networks. With these advantages, SNNs are finding widespread applications across various domains. One significant area of interest is image generation using deep learning models like Variational Autoencoders (VAE). However, like other deep learning models, SNNs demand substantial training data to achieve desired outcomes, raising concerns about data privacy. Our pioneering contribution is the introduction of a Differentially Private Spiking Variational Autoencoder (DP-SVAE) for image generation and reconstruction. DP-SVAE employs standard Differentially Private Stochastic Gradient Descent (DP-SGD) to ensure privacy preservation. Additionally, we have evaluated the models against various adversarial attacks to highlight the importance of differential privacy. We comprehensively analyze the proposed model through extensive experimentation across publicly available benchmark datasets. This pioneering study marks the first exploration of privacy considerations in SNN-based VAEs and will catalyze further research in this domain.

This article introduces an innovative methodology to unveil the intricacies of white matter fiber pathways in the brain using diffusion MRI. Relying on the rationale that traditional methods observe a significant decrease in signal intensity values in the direction of higher diffusivity, our novel approach strategically selects for diffusion-sensitizing gradient directions (dSGDs, representing the directions along which signals are generated) aligned with reduced signal intensities. By treating these selected directions as maximum diffusivity directions, we generate uniformly distributed gradient directions (GDs) around them, which are subsequently employed in the reconstruction process. This approach addresses the shortcomings of existing methods. It improves upon the uniform gradient directions (UGDs) approach, which suffers from gradient direction redundancy, and the adaptive gradient directions (AGDs) approach, which requires solving the linear system twice per voxel. Proposed method simultaneously addresses both limitations, offering a more efficient and streamlined process. The effectiveness of our proposed methodology is rigorously evaluated through simulations and experiments involving real data, showcasing its superior performance in uncovering the complex white matter fiber pathways in the brain.

This study presents a novel quantum image encryption algorithm, using a 3D chaotic map and controlled qubit-level scrambling operations. The newly proposed 3D-BNM chaotic map effectively reduces the degradation of chaotic dynamics resulting from the finite word length effect. It facilitates the generation of highly unpredictable random sequences and enhances chaotic performance. The system’s efficacy is additionally enhanced by the inclusion of a SHA-256 hash function. Initially, classical plain images are converted into their quantum equivalents using the Novel Enhanced Quantum Representation (NEQR) model. The Generalized Quantum Arnold Transformation (GQAT) is then applied to disrupt the coordinate information of the quantum image. Subsequently, to diffuse the pixel values of the scrambled image, XOR operations are performed using pseudorandom sequences generated by the 3D-BNM chaotic map. Furthermore, to enhance the randomness and reduce the correlation among the pixels in the resulting cipher image, a controlled qubit-level scrambling operation is employed. The encryption process utilizes fundamental quantum gates such as C-NOT and CC-NOT. Both theoretical and numerical simulations validate the effectiveness of the proposed algorithm against various statistical and differential attacks. Moreover, the proposed encryption algorithm operates with low computational complexity.

In this paper, we introduce a fractional-order variant of the Stockwell transform, specifically designed for analyzing signals that can be represented in terms of a graph data structure and integrates the ideas of fractional Stockwell transform and spectral graph theory.The proposed transform is named the 'Spectral Graph Fractional Stockwell Transform' or 'SGFrST' for short.Fundamentally, SGFrST makes use of the graph spectral domain to extract the underlying connection patterns and network structure of complex systems.SGFrST essentially fills the gap between signal processing methods and spectral graph theory by providing a flexible instrument that allows for hitherto unheard-of levels of precision and efficiency when comprehending and interpreting signals on graph-based domains.To begin, we introduce the spectral graph Stockwell transform by modulating the graph wavelet transform.Subsequently, we extend this concept by incorporating the spectral graph wavelet operator alongside the fractional order, resulting in the SGFrST.We derive various mathematical properties associated with the SGFrST, including an inversion mechanism and an inner product theorem.The proposed transform demonstrates effective applicability across a spectrum of graph signal processing scenarios.Basically, this makes it possible to extract useful features from signals that are present on graph structures, which helps with a variety of tasks in domains such as the social sciences, neuroscience, image processing and telecommunications.These tasks include image restoration, anomaly detection, pattern identification, and classification.

This paper focuses on tracing the connectivity of white matter fascicles in the brain. In particular, a generalized order algorithm based on mixture of non-central Wishart distribution model is proposed for this purpose. The proposed algorithm utilizes the generalization of integer order based approach with the mixture of non-central Wishart distribution model. Pseudo super anomalous behavior of water diffusion inside human brain is the prime motivation of the the present study. We have shown results on multiple synthetic simulations with fibers orientations in two and three directions in each voxel as well as experiments on real data. Synthetic simulations were performed with varying noise levels and diffusion weighting gradient i.e. $b-$values. The proposed model performed outstanding especially for distinguishing closely oriented fibers.

This paper introduces an algorithm for reconstructing the brain's white matter fibers (WMFs). In particular, a fractional order mixture of central Wishart (FMoCW) model is proposed to reconstruct the WMFs from diffusion MRI data. The pseudo super diffusive modality of anomalous diffusion is coupled with the mixture of central Wishart (MoCW) model to derive the proposed model. We have shown results on multiple synthetic simulations, including fibers orientations in 2 and 3 directions per voxel and experiments on real datasets of rat optic chiasm and a healthy human brain. In synthetic simulations, a varying Rician distributed noise levels, & sigma; = 0.01 -0.09 is also considered. The proposed model can efficiently distinguish multiple fibers even when the angle of separation between fibers is very small. This model outperformed, giving the least angular error when compared to frac-tional mixture of Gaussian (MoG), MoCW and mixture of non-central Wishart (MoNCW) models.

The friction stir welding (FSW) is a viable welding process for joining the two dissimilar materials owing to its solid-state nature. The process parameters are very crucial in determining if the FSW process is effective. In the present manuscript aims to investigate the effect of process parameters such as rotational speed (RS), where other parameters were kept constant on mechanical characteristics for the dissimilar welded joint (DWJ) of aluminum AA7075 grade with the pure Cu grade. The RS varies at different level i.e., 900, 1200, 1400 RPM. The findings indicate that changes in RS have a considerable impact on mechanical strength, and 1200 RPM was shown to be the ideal RS number for the maximum mechanical strength.

This paper presents a dynamic model-based gearbox fault diagnosis using machine learning. A single-stage spur gear using an eight-degrees-of-freedom (DOF) dynamic model is developed and investigated with four gear tooth conditions, i.e., healthy tooth, 20 % tooth crack, 40 % tooth crack, and 60 % tooth crack. In the developed model, an analytically improved time-varying mesh stiffness (IAM-TVMS) model, which considers the effects of structural coupling of loaded tooth, nonlinear Hertzian contact stiffness, precise transition curve, and misalignment between base and root circle, and an improved tooth crack model, are incorporated to get a reliable system dynamic response. To make the simulated response more realistic, different levels of negative white Gaussian noise (−2dB to −10dB SNR) are added to the simulated signal. The simulated noisy signals are then segmented, and a total of 12 statistical indicators are calculated on each segmented signal to develop the feature matrix. Four different machine learning algorithms are used to classify the faults from the extracted feature matrix, and their performances are compared and discussed. The results show that the KNN classifier outperformed them all, with a classification accuracy of 90.5 %. The finding shows that the proposed method works well in the presence of intense noise and may help in identifying the faults in the system in quick time without expending too much on experimental test setup.

Background: Obtaining the medical history from a patient is a tedious task for doctors as it depends on a lot of factors which are difficult to keep track from a patient's perspective. Doctors have to rely upon technological tools to make a swift and accurate judgment about the patient's health. Introduction: Out of many such tools, there are two special imaging modalities known as X-ray - Computed Tomography (CT) and Magnetic Resonance imaging (MRI) which are of significant importance in the medical world assisting the diagnosis process. Methods: The advancement in signal processing theory and analysis has led to the design and implementation of a large number of image processing and fusion algorithms. Each of these methods has evolved in the terms of their computational efficiency and visual results over the years Results: Various researches have revealed their properties in terms of their efficiency and outreach and it has been concluded that image fusion can be a very suitable process that can help to compensate for the drawbacks. Conclusion: In this manuscript, recent state-of-the-art techniques have been used to fuse these image modalities and established its need and importance in a more intuitive way with the help of a wide range of assessment parameters.

This paper presents a novel algorithm for image denoising using an improved nonlinear diffusion PDE model and a cellular neural network (CeNN) scheme. In particular, the images corrupted with multiplicative (speckle) noise have been considered. The proposed generalized-order nonlinear diffusion (GOND) model is solved through a suitable cellular neural network (CeNN) approach. The CeNN templates act like edge-preserving filters to reduce the multiplicative noise. The present study also gives a convergence analysis of the proposed CeNN based solution scheme. Further, the proposed scheme is numerically validated on synthetic, medical, and real SAR images. The obtained results demonstrate that the proposed algorithm provides a better way to deal with speckle noise and suppresses the staircase effects. To broaden the simulation results, the proposed method is applied to images corrupted with Gaussian, Rayleigh, and gamma noise. The proposed method for SSIM values interpret 0.2dB to 0.4dB better than state-of-the-art methods and comparative results in terms of PSNR in most test cases.

This article introduces a new methodology for reconstructing the white matter fiber pathways of brain in diffusion MRI. Usually, the signal intensity values will be lesser in the direction of higher diffusivity. The proposed approach picks the diffusion sensitivity gradient directions (dSGD), where the signal intensities are diminutive. Considering these as the directions of maximum diffusivity, we generate directions uniformly distributed around the picked dSGD. These newly computed uniformly spaced directions are considered gradient directions used in the reconstruction process. The state-of-art schemes like uniform gradient direction (UGD) have redundancy in the gradient direction, and adaptive gradient direction (AGD) has a constraint of solving linear system twice per voxel. These two limitations are turned down in this study simultaneously. Estimating gradient directions with the proposed scheme is employed in the multi-compartmental mixture models for calculating the fiber orientations. Simulation and experiments on the real data evaluate the feasibility of the proposed method.

This paper proposes a variational approach by minimizing the energy functional to compute the disparity from a given pair of consecutive images. The partial differential equation (PDE) is modeled from the energy function to address the minimization problem. We incorporate a distance regularization term in the PDE model to preserve the boundaries' discontinuities. The proposed PDE is numerically solved by a cellular neural network (CeNN) algorithm. This CeNN based scheme is stable and consistent. The effectiveness of the proposed algorithm is shown by a detailed experimental study along with its superiority over some of the existing algorithms.

The work presents an amalgam of quantum search algorithm (QSA) and quantum secret sharing (QSS). The proposed QSS scheme utilizes Grover's three-particle quantum state. In this scheme, the dealer prepares an encoded state by encoding the classical information as a marked state and shares the states' qubits between three participants. The participants combine their qubits and find the marked state as a measurement result of the three-qubit state. The security analysis shows the scheme is stringent against malicious participants or eavesdroppers. In comparison to the existing schemes, our protocol fairs pretty well and has a high encoding capacity. The simulation analysis is done on the cloud platform IBM-QE thereby showing the practical feasibility of the scheme.

This paper introduces a contour detection scheme to detect object contours in medical images. A new PDE model is designed by including a fractional-order regularization term, making it robust against noise and maintaining the regularity of level set function (LSF) during evolution. A cellular neural network (CeNN) model is used to solve the proposed contour detection PDE. The main advantages of using the CeNN-based approach are that it wipes out the requirement of a reinitialization of level set and can be implemented efficiently on parallel chips. Finally, an experimental study is carried out, which exhibits the feasibility of the proposed approach in contour detection from a set of medical images.

In this present study, the transformation products in micro-alloyed steel have been examined as well as isothermal decomposition of austenite into various phase formation. The rapid cooling from austenitizing temperature 1200°C to 14 different isothermal temperatures between 750 and 100°C with 50°C intervals were carried out by using dilatometric strain dilatometer on thermo-mechanical simulator. The heat treatments were delayed at different times to examine the microstructure evolution at all isothermal temperatures. The transformation kinetics was recorded during isothermal treatments and designed an isothermal transformation diagram, which is verified by microstructural changes. The results show that the initial microstructure which consists of proeutectoid ferrite and pearlite transforms into a combination of proeutectoid ferrite, pearlite, widmanstätten ferrite, upper or lower bainite, or martensite phases. The austenite grain size has been found to be decreased with a decrease in the isothermal holding temperature. The nose temperature was achieved at isothermal temperature 500°C which have been taking the least time for start and end of transformation of phases. It is also worth noticing that the start and end transformation times were observed decreasing with a decrease in the isothermal holding temperatures and after the nose transformation again gradually increased.

This paper proposes a novel and efficient algorithm for defogging of color (RGB) images. The fog in a scene is mostly due to the attenuation and airlight map, which decrease the quality of the image of the scene. To enhance such images from the visual point of view, a fractional-order anisotropic diffusion algorithm with [Formula: see text]-Laplace norm is proposed for removing the fog effect. In particular, a coupling term is added in order to model the inter-channel correlations. The weights used in the coupling term stop the transmission of diffusion with in the edges, thus balances the inter-channel data in the diffusion procedure. Experimental results validate the better performance of the proposed algorithm over some of the existing anisotropic diffusion-based methods. The proposed method is independent of the measure of fog in the images, thus images with different amount of fog can be enhanced.

In the past, several partial differential equations (PDEs) based methods have been widely studied in image denoising. While solving these methods numerically, some parameters need to be chosen manually. This paper proposes a cellular neural network (CNN) based computational scheme for solving the nonlinear diffusion equation modeled for removing additive noise of digital images. The diffusion acts like smoothing on the noisy image, which is taken as an initial condition for the nonlinear PDE. In the proposed scheme, the template matrices of CNN evolve during the iterative diffusion and act as edge-preserving filters on the noisy images. The evolving diffusion ensures convergence of the diffusion process after a specific diffusion time. Therefore, the advantages of such a CNN-based solution scheme are more accurate restoration in terms of image quality with low computation and memory requirements. The experimental results show the effectiveness of the proposed algorithm on different sets of benchmark images degraded with additive noise.