Image Restoration Applications Research Articles

A family of spectral conjugate gradient methods with strong convergence and its applications in image restoration and machine learning

In this paper, we propose a family of spectral conjugate gradient methods for solving unconstrained optimization problems. Specifically, we provide two classes of bounded spectral parameters to be chosen, design a new truncation scheme of the non-negative conjugate parameter and set a restart procedure in our search direction. Independently of the specific spectral parameter, conjugate parameter and line search criterion, we prove that our proposed family satisfies the sufficient descent condition. We also prove its strong convergence under mild assumptions and the weak Wolfe line search. Numerical comparisons with other methods demonstrate the outstanding performances of our algorithm for solving medium–large-scale unconstrained optimization, image restoration and machine learning problems.

Solving a system of complex matrix equations using a gradient-based method and its application in image restoration

Solving a system of complex matrix equations using a gradient-based method and its application in image restoration

A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration

A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration

Application of Image Restoration and Object Detection Techniques in Fruit-Picking Robots

This paper focuses on the problem that existing apple picking robots are unable to accurately recognize targets in complex and unstructured orchard environments. The target detection algorithm of the robot is optimized based on YOLOv5 and ResNet neural network model. First, considering the low resolution of the robot's own binocular camera, this paper adopts the RealSR model to process the image with super-resolution. Then, the YOLOv5 model is chosen as the optimized target detection algorithm, which can obtain the number, location, ripeness and quality information of apples in the image through training. Secondly, by comparing the VGG and ResNet models, which are widely used in the field of image classification, the ResNet model is finally chosen as the main body for recognizing and classifying different fruits, and its correct rate can reach more than 97%.

A three-term conjugate gradient descent method with some applications

The stationary point of optimization problems can be obtained via conjugate gradient (CG) methods without the second derivative. Many researchers have used this method to solve applications in various fields, such as neural networks and image restoration. In this study, we construct a three-term CG method that fulfills convergence analysis and a descent property. Next, in the second term, we employ a Hestenses-Stiefel CG formula with some restrictions to be positive. The third term includes a negative gradient used as a search direction multiplied by an accelerating expression. We also provide some numerical results collected using a strong Wolfe line search with different sigma values over 166 optimization functions from the CUTEr library. The result shows the proposed approach is far more efficient than alternative prevalent CG methods regarding central processing unit (CPU) time, number of iterations, number of function evaluations, and gradient evaluations. Moreover, we present some applications for the proposed three-term search direction in image restoration, and we compare the results with well-known CG methods with respect to the number of iterations, CPU time, as well as root-mean-square error (RMSE). Finally, we present three applications in regression analysis, image restoration, and electrical engineering.

Modification of a conjugate gradient approach for convex constrained nonlinear monotone equations with applications in signal recovery and image restoration

Conjugate gradient (CG )methods have received widespread use in recent years for recovering damaged signals in compressive sensing. This study attempts to create a CG method that is more effective than the recent existing scheme for recovering disrupted signals. The newly created method is a modification of the method proposed by Halilu et al. (2021). Because the authors’ CG parameter can be undefined while solving general functions. As a result, to accomplish the desired result, a new CG method combined with the projection scheme of Solodov and Svaiter (1999) is presented. In addition, under mild conditions, the proposed method converges globally. Numerical experiments conducted with recent methods show the effectiveness of the proposed method. Furthermore, the proposed method is applied efficiently to address the signal recovery and image restoration problems, yielding a better result than some existing methods in the literature.

Some Conditions and Perturbation Theorem of Irregular Wavelet/Gabor Frames in Sobolev Space

Due to its potential applications in image restoration and deep convolutional neural networks, the study of irregular frames has interested some researchers. This paper addresses irregular wavelet systems (IWSs) and irregular Gabor systems (IGSs) in Sobolev space HsR. We obtain the sufficient and necessary conditions for IWS and IGS to be frames. By applying these conditions, we also derive the characterizations of IWS and IGS to be frames. Finally, we discuss the perturbation theorem of irregular wavelet frames (IWFs) and irregular Gabor frames (IGFs). We also provided some examples to support our results.

Estimation of modified Zernike coefficients from turbulence-degraded multispectral imagery using deep learning

We investigate how wavelength diversity affects the performance of a deep-learning model that predicts the modified Zernike coefficients of turbulence-induced wavefront error from multispectral images. The ability to perform accurate predictions of the coefficients from images collected in turbulent conditions has potential applications in image restoration. The source images for this work were a point object and extended objects taken from a character-based dataset, and a wavelength-dependent simulation was developed that applies the effects of isoplanatic atmospheric turbulence to the images. The simulation utilizes a phase screen resampling technique to emulate the simultaneous collection of each band of a multispectral image through the same turbulence realization. Simulated image data were generated for the point and extended objects at various turbulence levels, and a deep neural network architecture based on AlexNet was used to predict the modified Zernike coefficients. Mean squared error results demonstrate a significant improvement in predicting modified Zernike coefficients for both the point object and extended objects as the number of spectral bands is increased. However, the improvement with the number of bands was limited when using extended objects with additive noise.

An accelerated conjugate gradient method with adaptive two-parameter with applications in image restoration

An accelerated conjugate gradient method with adaptive two-parameter with applications in image restoration

Application of Generative Adversarial Network in Image Color Correction

The popularity of electronic products has increased with the development of technology. Electronic devices allow people to obtain information through the transmission of images. However, color distortion can occur during the transmission process, which may hinder the usefulness of the images. To this end, a deep residual network and a deep convolutional network were used to define the generator and discriminator. Then, self-attention-enhanced convolution was applied to the generator network to construct an image resolution correction model based on coupled generative adversarial networks. On this basis, a generative network model integrating multi-scale features and contextual attention mechanism was constructed to achieve image restoration. Finally, performance and image restoration application tests were conducted on the constructed model. The test showed that when the coupled generative adversarial network was tested on the Set5 dataset, the image peak signal-to-noise ratio and image structure similarity values were 31.2575 and 0.8173. On the Set14 dataset, they were 30.8521 and 0.8079, respectively. The multi-scale feature-fusion algorithm was tested on the BSDS100 dataset with an image peak signal-to-noise ratio of 30.2541 and an image structure similarity value of 0.8352. Based on the data presented, it can be concluded that the image correction model constructed in this study has a strong image restoration ability. The reconstructed image has the highest similarity with the real high-resolution image and a low distortion rate. It can achieve the task of repairing problems such as color distortion during image transmission. In addition, this study can provide technical support for similar information correction and restoration work.

Semi-Proximal ADMM for Primal and Dual Robust Low-Rank Matrix Restoration from Corrupted Observations

The matrix nuclear norm minimization problem has been extensively researched in recent years due to its widespread applications in control design, signal and image restoration, machine learning, big data problems, and more. One popular model is nuclear norm minimization with the l2-norm fidelity term, but it is only effective for those problems with Gaussian noise. A nuclear norm minimization problem with the l1-norm fidelity term has been studied in this paper, which can deal with the problems with not only non-Gaussian noise but also Gaussian noise or their mixture. Moreover, it also keeps the efficiency for the noiseless case. Given the nonsmooth proposed model, we transform it into a separated form by introducing an auxiliary variable and solve it by the semi-proximal alternating direction method of multipliers (sPADMM). Furthermore, we first attempt to solve its dual problem by sPADMM. Then, the convergence guarantees for the aforementioned algorithms are given. Finally, some numerical studies are dedicated to show the robustness of the proposed model and the effectiveness of the presented algorithms.

A new hybrid conjugate gradient method close to the memoryless BFGS quasi-Newton method and its application in image restoration and machine learning

<p>A new hybrid conjugate gradient algorithm for solving the unconstrained optimization problem was presented. The algorithm could be considered as a modification of the memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method. Based on a normalized gradient difference, we introduced a new combining conjugate gradient direction close to the direction of the memoryless BFGS quasi-Newton direction. It was shown that the search direction satisfied the sufficient descent property independent of the line search. For general nonlinear functions, the global convergence of the algorithm was proved under standard assumptions. Numerical experiments indicated a potential performance of the new algorithm, especially for solving the large-scale problems. In addition, the proposed method was used in practical application problems for image restoration and machine learning.</p>

A new three-term conjugate gradient method for unconstrained optimisation and its applications in image restoration

A new three-term conjugate gradient method for unconstrained optimisation and its applications in image restoration

Color restoration of images through high order zeroing neural networks

One of the fundamental tasks in pattern recognition is color image restoration. Every color image has three channels in the RGB color space, in contrast to grayscale images. The restoration of color images is typically far more challenging than that of grayscale images because of the internal relationships among the three channels. Given that the color image restoration can be represented as a dynamic problem with quaternion matrices, a new high order zeroing neural network (HZNN) model is developed to tackle this issue. Specifically, the time-varying quaternion matrix linear equations can be solved using the HZNN design, which is a member of the family of zeroing neural network (ZNN) models that correlate to hyperpower iterative techniques. In a realistic color image restoration application, the HZNN design outperforms the ZNN design, although both approaches work amazingly well.

A class of CG algorithms overcoming jamming of the iterative solving process and its application in image restoration

Intending to improve the numerical performance of the classic Fletcher–Reeves conjugate gradient method, Jiang and Jian embedded a shrinkage multiplier on the Fletcher–Reeves parameter which enhances its computational merits. As a matter of fact, we show that when the iterations jam, the line search turns to be approximately exact and so, search direction of the Jiang–Jian method automatically approaches the steepest descent direction which may lead to overcoming undesirable jamming effect of the classic Fletcher–Reeves method. A more detailed analysis of the numerical behavior of the Fletcher–Reeves method under the jamming phenomenon is presented as well. Then, on account of the advantages of the Jiang–Jian method, a conjugate gradient parameter is devised. Additionally, a descent spectral version of the proposed method is developed which fulfills the sufficient descent property regardless of the line search technique. Convergence of the proposed methods is addressed under classical suppositions. To gain support for our theoretical arguments, the computational merits of the given algorithms on a set of CUTEr test functions and the image restoration problem are depicted.

Low-Rankness Guided Group Sparse Representation for Image Restoration.

As a spotlighted nonlocal image representation model, group sparse representation (GSR) has demonstrated a great potential in diverse image restoration tasks. Most of the existing GSR-based image restoration approaches exploit the nonlocal self-similarity (NSS) prior by clustering similar patches into groups and imposing sparsity to each group coefficient, which can effectively preserve image texture information. However, these methods have imposed only plain sparsity over each individual patch of the group, while neglecting other beneficial image properties, e.g., low-rankness (LR), leads to degraded image restoration results. In this article, we propose a novel low-rankness guided group sparse representation (LGSR) model for highly effective image restoration applications. The proposed LGSR jointly utilizes the sparsity and LR priors of each group of similar patches under a unified framework. The two priors serve as the complementary priors in LGSR for effectively preserving the texture and structure information of natural images. Moreover, we apply an alternating minimization algorithm with an adaptively adjusted parameter scheme to solve the proposed LGSR-based image restoration problem. Extensive experiments are conducted to demonstrate that the proposed LGSR achieves superior results compared with many popular or state-of-the-art algorithms in various image restoration tasks, including denoising, inpainting, and compressive sensing (CS).

A projection-based derivative free DFP approach for solving system of nonlinear convex constrained monotone equations with image restoration applications

A projection-based derivative free DFP approach for solving system of nonlinear convex constrained monotone equations with image restoration applications

Investigation of Optimal Image Inpainting Techniques for Image Reconstruction and Image Restoration Applications

People in today's society take a lot of pictures with their smartphones and also make an effort to keep their old photographs safe, but with time, those photographs deteriorate. Image inpainting is the art of reconstructing damaged or missing parts of an image. Repairing scratches in photographs or film negatives, or adding or removing elements like stamped dates or "red-eye," are all possible through inpainting. In order to restore the image many techniques have been developed, significant techniques include exemplar based inpainting, coherent based inpainting and method for correction of non-uniform illumination. The four main applications of these image inpainting techniques are scratch removal, text removal, object removal and image restoration. However, all the four image inpainting applications cannot be implemented using a single technique. According to the literature, there has been relatively less work done in the field of image inpainting applications. Investigation has been carried out to find the suitability of these three techniques for the four above mentioned image inpainting applications based on two performance metrics.

A Family of Developed Hybrid Four-Term Conjugate Gradient Algorithms for Unconstrained Optimization with Applications in Image Restoration

The most important advantage of conjugate gradient methods (CGs) is that these methods have low memory requirements and convergence speed. This paper contains two main parts that deal with two application problems, as follows. In the first part, three new parameters of the CG methods are designed and then combined by employing a convex combination. The search direction is a four-term hybrid form for modified classical CG methods with some newly proposed parameters. The result of this hybridization is the acquisition of a newly developed hybrid CGCG method containing four terms. The proposed CGCG has sufficient descent properties. The convergence analysis of the proposed method is considered under some reasonable conditions. A numerical investigation is carried out for an unconstrained optimization problem. The comparison between the newly suggested algorithm (CGCG) and five other classical CG algorithms shows that the new method is competitive with and in all statuses superior to the five methods in terms of efficiency reliability and effectiveness in solving large-scale, unconstrained optimization problems. The second main part of this paper discusses the image restoration problem. By using the adaptive median filter method, the noise in an image is detected, and then the corrupted pixels of the image are restored by using a new family of modified hybrid CG methods. This new family has four terms: the first is the negative gradient; the second one consists of either the HS-CG method or the HZ-CG method; and the third and fourth terms are taken from our proposed CGCG method. Additionally, a change in the size of the filter window plays a key role in improving the performance of this family of CG methods, according to the noise level. Four famous images (test problems) are used to examine the performance of the new family of modified hybrid CG methods. The outstanding clearness of the restored images indicates that the new family of modified hybrid CG methods has reliable efficiency and effectiveness in dealing with image restoration problems.

Asymptotic Behavior of Some Parabolic Equations and Application in Image Restoration

In this paper, we consider some nonlinear parabolic problem involving the well known p-laplacian and some operator having exponential growth with respect to the gradient. We start by dealing the asymptotic behavior for some evolution equation then we give some numerical results with an application in image processing.