PDE-Based Image Processing

This research presents a development of the affine projection algorithm (APA) in voice communication applications. A method of controlling the parameters of the APA is devised to improve the performance in cancelling various types of ambient noise that could possibly corrupt speech signals in voice communication systems. Indicators are used to identify the type of noise accompanying the target signal. Then the corrupted signal is processed in a noise a cancellation setup in such a way that three parameters of algorithm are changed according to the nature of the noise. The spreading of elements in the covariance matrix of the noise is used as an indicator for the type of noise so that the projection order, step-size and filter length are changed at the same time. This way the performance of the canceller is improved rendering lower estimation error with a moderate computational power. The method was tested under various types of noise and showed better convergence performance than the original APA as well as other commonly used algorithms in noise cancellation systems. The MSE of the proposed VPAPA method drops to -65 dB in steady state compared to -20 dB using NLMS and just below -30 dB using standard APA with projection order of 8, while the powerful RLS reaches around -60dB under the same environment. The method can be useful for clearer voice communication in variable environmental noise.

The contribution of type and levels of community noises to the perception of loudness, noisiness, and annoyance is being explored in ongoing research projects. Particular attention has been given to the relationship between scaling method and the conclusions it is possible to draw from the data, especially with regard to observers' abilities to differentiate noises according to the above attributes. Procedures for calibrating and possibly standardizing the perceptual scales have been attempted with preliminary success. Various types of noises have been investigated: aircraft noise under different flying conditions, traffic noise, and a number of other community noises. Besides specific scaling problems, the investigations have addressed the specific problems of observers' abilities to differentiate among noises that are combined in a complex setting as well as their ability to integrate various noises into a unitary perception of loudness and annoyance. Since the experimental setups reflect real‐life situations, the answers to these latter questions are relevant to understanding the responses of the individual who is exposed to combinations of noises in his or her community.The contribution of type and levels of community noises to the perception of loudness, noisiness, and annoyance is being explored in ongoing research projects. Particular attention has been given to the relationship between scaling method and the conclusions it is possible to draw from the data, especially with regard to observers' abilities to differentiate noises according to the above attributes. Procedures for calibrating and possibly standardizing the perceptual scales have been attempted with preliminary success. Various types of noises have been investigated: aircraft noise under different flying conditions, traffic noise, and a number of other community noises. Besides specific scaling problems, the investigations have addressed the specific problems of observers' abilities to differentiate among noises that are combined in a complex setting as well as their ability to integrate various noises into a unitary perception of loudness and annoyance. Since the experimental setups reflect real‐life situ...

Image restoration refers to the recovery of an underlying image from an observation that has been corrupted by various types of noise. In a digital forensic software, such image restoration process should be noise-tolerant, robust, fast, and scalable. In this paper, we apply implicative fuzzy association memory structure in colored facial image restoration with enhanced similarity measure involved in output computarion. The efficacy if the proposed fuzzy associative memory model is verified by the experiment in that it was 95% successful (with zero mean square error) out of 20 tested images.

Nowadays, voice interaction is increasingly applied to smart home appliances. There are various types of noises in our real lives, which requires speech enhancement technology to deal with multiple noisy speech scenarios and to process them in real-time. Traditional technologies of speech noise reduction require estimating the noise power spectrum first, then estimating the spectrogram gain value of noise reduction, such as minima controlled recursive averaging (MCRA), which can only deal with stationary environmental noises but cannot estimate noises with serious fluctuations of the power spectrum within quite limited durations. A highly complicated deep-learning model can estimate the power spectrum of various types of noise, but it cannot meet the requirement of real-time processing due to the large number of parameters of these general models. In this paper, we proposed a method combining deep-learning technologies with traditional signal processing techniques to estimate the power spectrum of various types of noises by designing a new model with fewer parameters, tiny deep convolutional recurrent network (TDCRN), and computing the speech gain value with the power spectrum. The result of our experiment indicates that, compared with the traditional technology and complicated deep-learning model, the proposed method, with only 0.29M parameters, increases the PESQ by more than 0.6, the STOI by more than 0.2 and the wake-up rate by more than 6%.

Digital image quality is crucial for reliable analysis in applications such as medical imaging, satellite remote sensing, and video surveillance. However, traditional denoising methods struggle to balance noise removal with detail preservation and lack adaptability to various types of noise. We propose a novel three-module architecture for image denoising, comprising a generator, a dual-path-UNet-based denoiser, and a discriminator. The generator creates synthetic noise patterns to augment training data, while the dual-path-UNet denoiser uses multiple receptive field modules to preserve fine details and dense feature fusion to maintain global structural integrity. The discriminator provides adversarial feedback to enhance denoising performance. This dual-path adversarial training mechanism addresses the limitations of traditional methods by simultaneously capturing both local details and global structures. Experiments on the SIDD, DND, and PolyU datasets demonstrate superior performance. We compare our architecture with the latest state-of-the-art GAN variants through comprehensive qualitative and quantitative evaluations. These results confirm the effectiveness of noise removal with minimal loss of critical image details. The proposed architecture enhances image denoising capabilities in complex noise scenarios, providing a robust solution for applications that require high image fidelity. By enhancing adaptability to various types of noise while maintaining structural integrity, this method provides a versatile tool for image processing tasks that require preserving detail.

A novel adaptive spatial and transform based approach by fusing Bilateral Filter (BF), Joint Bilateral Filter (JBF) and Wavelet Thresholding (WT) is proposed for image restoration. The Bilateral and Joint Bilateral filter can perform as an edge-preserving smoothing operator and have better behavior near the edges. In the first stage, the noisy image is passed through bilateral filter and some amount of noise is reduced but the image becomes blurred, hence wavelet thresholding is applied first with Bayes Shrinkage (BS) rule and then with Modified Bayes Shrinkage (MBS) rule in the second stage. In the third stage, the wavelet thresholding output is used as a reference image for the joint bilateral filter to preserve and enhance the edges effectively. The main aim is to achieve a cleaner version of the noisy image without blurring important features like edges, curves, and textures. The filter-performances are usually compared in terms of peak-signal-to-noise ratio (PSNR) and visual quality sense. Experimental results show that the proposed image denoising method is competitive when compared to other methods in suppressing various types of noise.

A critical challenge in image restoration is the presence of various types of noise. Meanwhile, noise detection is a crucial step in mixed noise removal. This paper tackles the challenge of restoring images corrupted by a mixture of additive Gaussian and multiplicative Gamma noise. In the proposed method, we integrate the noise detection process into a variational model using a dual formulation of a maximum a posteriori (MAP) estimator. The variational model consists of a novel adaptive fidelity term and a plugin-and-play regularization term. The fidelity term contains an adaptive weight that can automatically detect the noise types, levels, and pollution ways for each pixel. There is flexibility in choosing a plugin-and-play regularization term. For example, we can use a model-based regularizer or a deep learning-based regularizer. In addition, we present a splitting algorithm to minimize the proposed cost functional. This splitting technique enables us to transfer a mixed noise removing problem to several subproblems, including noise removal and detection. The noise detection process can be iteratively estimated by the proposed algorithm itself. Therefore, in the numerical experiments, the proposed model outperforms the existing Rudin-Osher-Fatemi (ROF), Aubert-Aujol (AA), BM3D, and deep learning-based single type denoiser. Experimental results show that the proposed model can remove noise more efficiently and better preserve details in images. Compared to the existing best-performing single type denoiser, on average, the improvements of PSNR values range from 0.33 dB to 0.81 dB under noise mixture ratios α = 0.4, 0.6.

Image processing is one of the rapidly growing technologies with operations that can be applied to image data which may be in the form of a 2D, 3D or 4D signals. It has created tremendous opportunities for mathematical modeling, analysis, and computation. A novel approach in image processing has been developed, known as PDE (Partial Differential Equations) based image processing. The PDE approach is very promising for solving many problems in image processing because it provides new and more intuitive mathematical models, gives better approximations to the Euclidean geometry of the problem, and is supported by efficient discrete numerical algorithms based on difference approximations. In this paper, we have discussed how Euler Lagrange Equation plays a significant role in solving PDE based image processing problems. The typical image processing problems such as denoising and inpainting can be solved using EL equation. The ROF and Tikhnov models of denoising and Total Variation based inpainting has been implemented and a comparative study is done with the conventional methods. We have considered various well-known objective quality evaluation metrics used in image processing in this comparison. The results show that PDE based image processing techniques outperforms the conventional approaches.

Image restoration remains a challenging task in image processing. Numerous methods tackle this problem, often solved by minimizing a non-smooth penalized co-log-likelihood function. Although the solution is easily interpretable with theoretic guarantees, its estimation relies on an optimization process that can take time. Considering the research effort in deep learning for image classification and segmentation, this class of methods offers a serious alternative to perform image restoration but stays challenging to solve inverse problems. In this work, we design a deep network, named DeepPDNet, built from primal-dual proximal iterations associated with the minimization of a standard penalized likelihood with an analysis prior, allowing us to take advantage of both worlds. We reformulate a specific instance of the Condat-Vu primal-dual hybrid gradient (PDHG) algorithm as a deep network with fixed layers. The learned parameters are both the PDHG algorithm step-sizes and the analysis linear operator involved in the penalization (including the regularization parameter). These parameters are allowed to vary from a layer to another one. Two different learning strategies: "Full learning" and "Partial learning" are proposed, the first one is the most efficient numerically while the second one relies on standard constraints ensuring convergence in the standard PDHG iterations. Moreover, global and local sparse analysis prior are studied to seek a better feature representation. We apply the proposed methods to image restoration on the MNIST and BSD68 datasets and to single image super-resolution on the BSD100 and SET14 datasets. Extensive results show that the proposed DeepPDNet demonstrates excellent performance on the MNIST and the more complex BSD68, BSD100, and SET14 datasets for image restoration and single image super-resolution task.

Partial differential equation(PDE) plays an important role in the field of image segmentation in biological detection. According to the analysis of some problems existing in the process of current biological detection image segmentation, this research set up a kind of image analysis and processing of biological detection algorithm based on PDE.Through the analysis of PDE in image processing and application situation of development methods, this study constructed a biological detection image segmentation application model based on PDE. The results show that the PDE is a mathematical operation as the foundation, and with an open framework for development mode. PDE is a biological detection very effective image segmentation analysis tool that can solve the image topology in biology of high complexity and noise problems.

This paper investigates the influence of the signal to noise ratio (SNR) and the type of a noise on the performance of two adaptive novelty detection methods. The evaluated methods are Learning Entropy (LE) and Error and Learning Based Novelty Detection (ELBND). The methods are compared in empirical way in classification framework. A classification based only on the error of the adaptive model was used as a reference. The research in this field is important, because a noise is present in every measured data and can drastically influence the result of tasks like the novelty detection. Moreover, various types of noise can influence the novelty detection in different ways, therefore the optimal method of adaptive novelty detection can be hard to choose. This assumption is supported by experimental results in this study.

Virtual reality (VR) presents objects or simulated scenes to reproduce situations in a way similar to the real thing. In medicine, processing and 3D reconstruction of medical images is an important step in VR. We propose a methodology for processing medical images, to segment organs, reconstruct structures in 3D and represent structures in a VR environment, in order to provide the specialist with an alternative tool for the analysis of medical images. We present a method of image segmentation based on area differentiation and other image processing techniques; the 3D reconstruction was by the 'isosurface' method. Different studies show the benefits of VR applied to clinical practice, adding its uses as an educational tool. A VR environment was created to be visualized with glasses for this purpose, this can be an alternative tool in the identification and visualization of COVID-19 affected lungs through medical image processing and subsequent 3D reconstruction.

In the past decade it has been demonstrated that the use of fractional order derivatives or integrals can be modelled more accurately than the integer order derivatives or integrals. These fractional systems are easy to solve due to availability of many methods. Further the adaptiveness in the fractional order provide an additional degree of freedom in optimization of performance. In many fields of image processing the fractional order-based methods have been extensively used. These fields include Image enhancements, image de-noising, image segmentation, image compression, image restoration etc. Totally it is a well proved fundamental mathematical tool in image processing.

Topological derivative: A tool for image processing

The goal of this book was to introduce the reader to the recent advances in the field of uncertainty quantification and error propagation for computer vision, image processing, and image analysis that are based on partial differential equations (PDEs). Our original motivation was the observation that more and more often, measured data in the form of images are being used as part of the simulation pipeline, and that error propagation and uncertainty quantification—starting from images but then moving through the pipeline—are important to understanding the ending result of this scientific or engineering process. To analyze the image processing pipeline, we have presented concepts that enable error propagation to be formulated with a set of basic operations: the idea of stochastic images and corresponding (numerical PDE) operations on those images. From this perspective, one approach commonly used within the engineering literature is to employ Monte Carlo sampling techniques to attempt to quantify the impact of errors and variability on an engineering pipeline. Within the uncertainty quantification world, alternative approaches such as the class of generalized polynomial chaos (gPC) methods, which make assumptions about the ability to approximate the process of interest through polynomial approximations, have gained traction as a way of accelerating the convergence of the error and uncertainty quantification process in a computationally tractable way. In this book, we have shown the results of our exploration of the use of the gPC methodology for image processing and computer vision problems. We have relied on the fact that all the prerequisites of the gPC framework (e.g., finite variance, smoothness in the stochastic space, etc.) are intrinsically satisfied in the image processing context. In particular, we have shown how the generalized polynomial chaos (gPC) approach and its corresponding rules for computation (e.g., sums, products, projections on the gPC space, etc.) lead to straightforward generalizations to image processing and computer vision techniques. We have shown that the gPC methodology, when combined with image processing and computer vision techniques, provides a powerful approach to error propagation and uncertainty quantification, and to accessing system sensitivity.