Modified three-term conjugate gradient algorithm and its applications in image restoration

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.

Aim: Image is the most powerful tool to analyze the information. Sometimes the captured image gets affected with blur and noise in the environment, which degrades the quality of the image. Image restoration is a technique in image processing where the degraded image can be restored or recovered to its nearest original image. Materials and Methods: In this research Lucy-Richardson algorithm is used for restoring blurred and noisy images using MATLAB software. And the proposed work is compared with Wiener filter, and the sample size for each group is 30. Results: The performance was compared based on three parameters, Power Signal to Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), Normalized Correlation (NC). High values of PSNR, SSIM and NC indicate the better performance of restoration algorithms. Lucy-Richardson provides a mean PSNR of 10.4086db, mean SSIM of 0.4173%, and NC of 0.7433% and Wiener filter provides a mean PSNR of 6.3979db, SSIM of 0.3016%, NC of 0.3276%. Conclusion: Based on the experimental results and statistical analysis using independent sample T test, image restoration using Lucy-Richardson algorithm significantly performs better than Wiener filter on restoring the degraded image with PSNR (P<0.001) and SSIM (P<0.001).

Some modified Hestenes-Stiefel conjugate gradient algorithms with application in image restoration

This study introduces an improved three-term conjugate gradient (CG) algorithm which fulfills the descent conditions and exhibits good global convergence properties. The development of this new algorithm is based on the findings of recently introduced generalized RMIL CG technique. The algorithm has been modified so that the search direction would always meet the sufficient descent condition no matter the line-search techniques employed. Under some given assumptions, the algorithm’s global convergence result for the general nonconvex functions is established. The numerical efficacy of the suggested three-term CG algorithm is assessed through comparisons with four other CG algorithms. The assessment is performed using an array of unconstrained optimization benchmark functions. The acquired findings indicate that all the considered algorithms exhibit similar performance, particularly the variants of the RMIL method. One algorithm is more robust and slightly faster than the rest. However, it is essential to highlight that the newly developed CG formula outperforms all the other algorithms, including a recently presented three-term PRP algorithm. The study further expanded the proposed method to address an image restoration problem. The computational experiments yielded promising results, proving that the proposed CG algorithm surpasses others. It produces higher-quality output images, requires less CPU time (sec), and achieves higher PSNR values.

This paper addresses the design of an H/sub /spl infin// deconvolution filter and its application to image restoration. The proposed H/sub /spl infin// deconvolution filter has some advantages for image restoration in its capability of handling unknown boundary problems and spatially varying blurs. In this paper, the H/sub /spl infin// filter is compared with the inverse Wiener filter and a regularized restoration method. The experimental results show that the H/sub /spl infin// filter deals with the unknown boundary problem better than the Wiener filter. Compared with the regularization method, it gives a sharper restored image, especially, when the original image contains many details.

Prediction of pleural invasion in lung cancer is crucial in planning appropriate operating procedures and can be assessed using dynamic chest radiography (DCR). However, this assessment is negatively affected by rib shadows in conventional images. The purpose of this study was to develop a deep learning-based bone suppression technique for DCR in various projection directions. Twenty breathing XCAT phantoms with lung tumors and a pair of phantoms consisting only of bone structures were generated. The XCAT phantoms were virtually projected from six directions, resulting in 54000 multidirectional chest X-ray images and were used for training a pix2pix model to estimate bone images from original images. Bone suppression (BS) images were created by subtracting the bone images from the original images and then evaluated based on the peak signal to noise ratio (PSNR), structural similarity index measure (SSIM), and Fréchet Video Distance (FVD). Clinical cases were processed using the trained model as well. Furthermore, lung tumors on the original and BS images were tracked using OpenCV template matching, and the tracking accuracy was compared. The PSNR, SSIM, and FVD were 0.9966, 52.20 and 136.9, respectively. In the visual evaluation, we confirmed the effect of BS without temporal fluctuation of pixel values in both the resulting images of the XCAT phantom and real patients. Furthermore, precise tracking of the targeted tumor was achieved on the resulting BS images even in oblique directions, without any interruption from the rib shadows. These results indicate that our proposed method can effectively reduce bone shadows as well as temporal variations in the effect of bone suppression.

Digital Image Restoration is a technique used to recover original image information from degraded images. Digital images lose information because of factors like noise, blurring and camera misfocus. Image restoration plays a significant role in improving the quality of pictures obtained from unmanned aircrafts, poor quality video tape of a crime scene and blurred satellite images. In this paper we review how the field of image restoration has evolved over the years, and how the techniques of image restoration are making inroads into various applications, thus improving users perception. The article also portrays recent advances and patents in the field of image restoration. Keywords: Image deblurring, image restoration, classical approaches to image restoration, adaptive approaches, median filter, image inpainting, inverse filtering, patents on image restoration applications

Blurring facial images can significantly degrade the performance of face recognition and video surveillance applications. Therefore, an effective image restoration method is essential to address this issue. However, existing methods struggle with varying levels of blur severity, limiting their effectiveness. This study proposes a facial image restoration approach that integrates blur severity classification using a Convolutional Neural Network (CNN) with a U-Net-based deblurring model to overcome these challenges. This method ensures that each blurred image is processed using the most suiTable deblurring model, optimizing the restoration process. The dataset used in this study is Flickr-Faces-HQ (FFHQ), to which a Gaussian blur is applied and categorized into five levels: very low, low, medium, high, and very high. They employ the Peak Signal-to-Noise Ratio (PSNR) and the Structural Similarity Index Measure (SSIM) as quantitative metrics to evaluate the model's performance. Experimental results show that the proposed method consistently outperforms fixed kernel size and multi-kernel size deblurring approaches across all blur severities. Specifically, our method achieves a PSNR of 40.001 dB for very low blur severity and an SSIM of 0.990. For low severity, it attains a PSNR of 31.104 dB and an SSIM of 0.946. For medium severity, the results are 27.995 dB (PSNR) and 0.874 (SSIM). At high severity, our model achieves a PSNR of 28.896 dB and an SSIM of 0.855. Finally, for very high severity, the PSNR drops to 26.566 dB, with an SSIM of 0.812. These results demonstrate the effectiveness of the proposed method in enhancing image clarity across different blur levels while preserving facial details. This research contributes to the development of more adaptive and efficient image restoration techniques, particularly for applications that require high-quality facial images, such as face recognition and video surveillance.

<abstract><p>The conjugate gradient (CG) method is an optimization method, which, in its application, has a fast convergence. Until now, many CG methods have been developed to improve computational performance and have been applied to real-world problems. In this paper, a new hybrid three-term CG method is proposed for solving unconstrained optimization problems. The search direction is a three-term hybrid form of the Hestenes-Stiefel (HS) and the Polak-Ribiére-Polyak (PRP) CG coefficients, and it satisfies the sufficient descent condition. In addition, the global convergence properties of the proposed method will also be proved under the weak Wolfe line search. By using several test functions, numerical results show that the proposed method is most efficient compared to some of the existing methods. In addition, the proposed method is used in practical application problems for image restoration and portfolio selection.</p></abstract>

Denoising computed tomography (CT) medical images is crucial in preserving information and restoring images contaminated with noise. Standard filters have extensively been used for noise removal and fine details’ preservation. During the transmission of medical images, noise degrades the visibility of anatomical structures and subtle abnormalities, making it difficult for radiologists to accurately diagnose and interpret medical conditions. In recent studies, an optimum denoising filter using the wavelet threshold and deep-CNN was used to eliminate Gaussian noise in CT images using the image quality index (IQI) and peak signal-to-noise ratio (PSNR). Although the results were better than those with traditional techniques, the performance resulted in a loss of clarity and fine details’ preservation that rendered the CT images unsuitable. To address these challenges, this paper focuses on eliminating noise in CT scan images corrupted with additive Gaussian blur noise (AGBN) using an ensemble approach that integrates anisotropic Gaussian filter (AGF) and wavelet transform with a deep learning denoising convolutional neural network (DnCNN). First, the noisy image is denoised by AGF and Haar wavelet transform as preprocessing operations to eliminate AGBN. The DnCNN is then combined with AGF and wavelet for post-processing operation to eliminate the rest of the noises. Specifically, we used AGF due to its adaptability to edge orientation and directional information, which prevents blurring along edges for non-uniform noise distribution. Denoised images are evaluated using PSNR, mean squared error (MSE), and the structural similarity index measure (SSIM). Results revealed that the average PSNR value of the proposed ensemble approach is 28.28, and the average computational time is 0.01666 s. The implication is that the MSE between the original and reconstructed images is very low, implying that the image is restored correctly. Since the SSIM values are between 0 and 1.0, 1.0 perfectly matches the reconstructed image with the original image. In addition, the SSIM values at 1.0 or near 1.0 implicitly reveal a remarkable structural similarity between the denoised CT image and the original image. Compared to other techniques, the proposed ensemble approach has demonstrated exceptional performance in maintaining the quality of the image and fine details’ preservation.

At present, the conjugate gradient (CG) method of Hager and Zhang (Hager and Zhang, SIAM Journal on Optimization, 16(2005)) is regarded as one of the most effective CG methods for optimization problems. In order to further study the CG method, we develop the Hager and Zhang's CG method and present two modified CG formulas, where the given formulas possess the value information of not only the gradient but also the function. Moreover, the sufficient descent condition will be holden without any line search. The global convergence is established for nonconvex function under suitable conditions. Numerical results show that the proposed methods are competitive to the normal conjugate gradient method.

As a long-standing task, image restoration aims to recover the latent sharp image from its degraded counterpart. In recent years, owing to the strong ability of self-attention in capturing long-range dependencies, Transformer based methods have achieved promising performance on multifarious image restoration tasks. However, the canonical self-attention leads to quadratic complexity with respect to input size, hindering its further applications in image restoration. In this paper, we propose a Strip Attention Network (SANet) for image restoration to integrate information in a more efficient and effective manner. Specifically, a strip attention unit is proposed to harvest the contextual information for each pixel from its adjacent pixels in the same row or column. By employing this operation in different directions, each location can perceive information from an expanded region. Furthermore, we apply various receptive fields in different feature groups to enhance representation learning. Incorporating these designs into a U-shaped backbone, our SANet performs favorably against state-of-the-art algorithms on several image restoration tasks. The code is available at https://github.com/c-yn/SANet.

Digital images have progressed significantly in many areas but various types of noise still exist in real-world images such as Gaussian noise, Poisson noise, Salt-and-pepper noise so on. Although image denoising plays an important role to remove noise from images by using many techniques to preserve the important feature of an image but faces the problem of computational complexity, over smoothing. To address these limitations proposed paper introduces hybrid image denoising technique that combines the strengths of Wavelet transform and Non-Local Means (NLM) filtering, with enhanced Otsu thresholding. In proposed work, firstly the noisy image is denoised by wavelet-based Otsu thresholding and then NLM is employed to improve the enhance edge preservation of an image by eliminating the further noise. Kodak 24 dataset is used to test the images. Furthermore, we compare the proposed technique to the existing technique based on the performance metrics such as Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and Root Mean Squared Error (RMSE). The Kodak24 dataset is used to evaluate the proposed hybrid denoising method. Experimental results show that the proposed technique outperforms existing approaches in terms of PSNR (34.86), SSIM (0.93) and RMSE (4.61) demonstrating its effectiveness in denoising and preserving structural image quality. Additionally, the FOM and VIF scores indicate the outstanding results of the hybrid strategy: both the FOM and VIF values were the best among all other assessed denoising methods, attained to 0.99 and 0.59, respectively.

Image repair often has errors in filling. An exemplar-based technique has the advantage of filling texture and structure simultaneously, but there exist some problems with this, such as not considering the overall situation of inpainting, the unreasonable calculation of priority, and random selection when there are multiple candidate patches. In view of these situations, this paper proposes a method of screen window propagating where the upper layer guides the lower layer inpainting from the top layer by means of multiple resolution decomposition. Screen window propagating aims to constrain the inpainting of the lower layer and maintain the overall profile. Improving the priority calculation using the upper repair result can lead to getting a better repair order. When there is more than one candidate patch, the structural similarity index measure (SSIM) is used to obtain the best candidate patch. We consider four cases of rotation and inversion when looking for the best exemplar. The experiments show that our method can obtain more satisfactory results than other methods based on subjective and objective indicators, such as peak signal-to-noise ratio (PSNR), SSIM, and feature similarity index measurement. Screen window propagating for image inpainting aims toward image restoration. Whole contours are preserved and the lower layer can utilize more upper layer information. Our method considers information from the whole and its parts.

Image denoising, a classic ill-posed problem, aims to recover a latent image from a noisy measurement. Over the past few decades, a considerable number of denoising methods have been studied extensively. Among these methods, supervised deep convolutional networks have garnered increasing attention, and their superior performance is attributed to their capability to learn realistic image priors from a large amount of paired noisy and clean images. However, if the image to be denoised is significantly different from the training images, it could lead to inferior results, and the networks may even produce hallucinations by using inappropriate image priors to handle an unseen noisy image. Recently, deep image prior (DIP) was proposed, and it overcame this drawback to some extent. The structure of the DIP generator network is capable of capturing the low-level statistics of a natural image using an unsupervised method with no training images other than the image itself. Compared with a supervised denoising model, the unsupervised DIP is more flexible when processing image content that must be denoised. Nevertheless, the denoising performance of DIP is usually inferior to the current supervised learning-based methods using deep convolutional networks, and it is susceptible to the over-fitting problem. To solve these problems, we propose a novel deep generative network with multiple target images and an adaptive termination condition. Specifically, we utilized mainstream denoising methods to generate two clear target images to be used with the original noisy image, enabling better guidance during the convergence process and improving the convergence speed. Moreover, we adopted the noise level estimation (NLE) technique to set a more reasonable adaptive termination condition, which can effectively solve the problem of over-fitting. Extensive experiments demonstrated that, according to the denoising results, the proposed approach significantly outperforms the original DIP method in tests on different databases. Specifically, the average peak signal-to-noise ratio (PSNR) performance of our proposed method on four databases at different noise levels is increased by 1.90 to 4.86 dB compared to the original DIP method. Moreover, our method achieves superior performance against state-of-the-art methods in terms of popular metrics, which include the structural similarity index (SSIM) and feature similarity index measurement (FSIM). Thus, the proposed method lays a good foundation for subsequent image processing tasks, such as target detection and super-resolution.