A rapid hybrid algorithm for image restoration combining parametric Wiener filtering and wave atom transform

This paper introduces an expectation-maximization (EM) algorithm for image restoration (deconvolution) based on a penalized likelihood formulated in the wavelet domain. Regularization is achieved by promoting a reconstruction with low-complexity, expressed in the wavelet coefficients, taking advantage of the well known sparsity of wavelet representations. Previous works have investigated wavelet-based restoration but, except for certain special cases, the resulting criteria are solved approximately or require demanding optimization methods. The EM algorithm herein proposed combines the efficient image representation offered by the discrete wavelet transform (DWT) with the diagonalization of the convolution operator obtained in the Fourier domain. Thus, it is a general-purpose approach to wavelet-based image restoration with computational complexity comparable to that of standard wavelet denoising schemes or of frequency domain deconvolution methods. The algorithm alternates between an E-step based on the fast Fourier transform (FFT) and a DWT-based M-step, resulting in an efficient iterative process requiring O(N log N) operations per iteration. The convergence behavior of the algorithm is investigated, and it is shown that under mild conditions the algorithm converges to a globally optimal restoration. Moreover, our new approach performs competitively with, in some cases better than, the best existing methods in benchmark tests.

Wiener filter is widely used for image denoising and restoration. It is alternatively known as the minimum mean square error filter or the least square error filter, since the objective function used in Wiener filter is an age-old benchmark called the Mean Square Error (MSE). Wiener filter tries to approximate the degraded image so that its objective function is optimized. Although MSE is considered to be a robust measurement metric to assess the closeness between two images, recent studies show that MSE can sometimes be misleading whereas the Structural Similarity (SSIM) can be an acceptable alternative. In spite of having this misleading natured objective function, Wiener filter is being heavily used as a fundamental component in many image denoising and restoration algorithms such as in current state-of-the-art of image denoising- BM3D. In this study, we explored the problem with the objective function of Wiener filter. We then improved the Wiener filter by optimizing it for SSIM. Our proposed method is tested using the standard performance evaluation methods. Experimental results show that the proposed SSIM optimized Wiener filter can achieve significantly better denoising (and restoration) as compared to its original MSE optimized counterpart. Finally, we discussed the potentials of using our improved Wiener filter inside BM3D in order to eventually improve BM3D’s denoising performance.

The expectation-maximization (EM) algorithm for maximum-likelihood image recovery is guaranteed to converge, but it converges slowly. Its ordered-subset version (OS-EM) is used widely in tomographic image reconstruction because of its order-of-magnitude acceleration compared with the EM algorithm, but it does not guarantee convergence. Recently the ordered-subset, separable-paraboloidal-surrogate (OS-SPS) algorithm with relaxation has been shown to converge to the optimal point while providing fast convergence. We adapt the relaxed OS-SPS algorithm to the problem of image restoration. Because data acquisition in image restoration is different from that in tomography, we employ a different strategy for choosing subsets, using pixel locations rather than projection angles. Simulation results show that the relaxed OS-SPS algorithm can provide an order-of-magnitude acceleration over the EM algorithm for image restoration. This new algorithm now provides the speed and guaranteed convergence necessary for efficient image restoration.

To improve data transmission efficiency, image compression is a commonly used method with the disadvantage of accompanying image distortion. There are many image restoration (IR) algorithms, and one of the most advanced algorithms is the generative adversarial network (GAN)-based method with a high correlation to the human visual system (HVS). To evaluate the performance of GAN-based IR algorithms, we proposed an ensemble image quality assessment (IQA) called ATDIQA (Auxiliary Transformer with DISTS IQA) to give weights on multiscale features global self-attention transformers and local features of convolutional neural network (CNN) IQA of DISTS. The result not only performed better on the perceptual image processing algorithms (PIPAL) dataset with images by GAN IR algorithms but also has good model generalization over LIVE and TID2013 as traditional distorted image datasets. The ATDIQA ensemble successfully demonstrates its performance with a high correlation with the human judgment score of distorted images.

The expectation-maximization (EM) algorithm for maximum-likelihood image recovery converges very slowly. Thus, the ordered subsets EM (OS-EM) algorithm has been widely used in image reconstruction for tomography due to an order-of-magnitude acceleration over the EM algorithm. However, OS-EM is not guaranteed to converge. The recently proposed ordered subsets, separable paraboloidal surrogates (OS-SPS) algorithm with relaxation has been shown to converge to the optimal point while providing fast convergence. In this paper, we develop a relaxed OS-SPS algorithm for image restoration. Because data acquisition is different in image restoration than in tomography, we adapt a different strategy for choosing subsets in image restoration which uses pixel location rather than projection angles. Simulation results show that the order-of-magnitude acceleration of the relaxed OS-SPS algorithm can be achieved in restoration. Thus the speed and the guarantee of the convergence of the OS algorithm is advantageous for image restoration as well.

There is distortion phenomenon in image emerge, transmit and record. Image restoration is a process which recover bad image into original image. When we use genetic algorithm for image restoration, there will be premature problem. The paper discusses a new algorithm for image restoration based on combination of parallel genetic algorithm with Hopfield neural network, take the advantage of parallel GA parameter selection and then use Hopfield NN to train sample efficiently. Experiments demonstrate that this optimization method in this paper will overcome premature problem and run more rapidly, as a result obtain a better recovery image.

International audience

Region extraction and labeling is a fundamental process in building computer systems that automatically analyze and interpret images and image sequences of a scene. It involves extracting meaningful regions and their attributes from an image that are of interest in a given domain, e.g., a human face in face recognition and surveillance applications, a vehicle in intelligent highway monitoring, or an industrial tool in automated manufacturing and inspection applications. In this paper, we present a generalized and fast region labeling algorithm that can be applied to numerous image processing tasks: region extraction in binary images, region segmentation from gray scale or color images, region boundary extraction, chain code extraction, run-length coding of images, and image restoration from chain codes. The general applicability of our algorithm stems from its strengths in identifying the fundamental and common computational steps and providing robust and efficient procedures to accomplish these steps without requiring multiple scans of images. Our algorithm is shown to be more effective in terms of space and computational efficiency, in comparison with many existing approaches to region labeling and extraction. Results from our experiments with over 5,000 frames obtained from MPEG-1 video bitstreams demonstrate the good performance of our algorithm in terms of video text segmentation accuracy and computational efficiency.

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).

In this paper, based on the modified Hopfield neural network, we present two variational PDEs (Partial Differential Equations) as the regularization terms to the image restoration model. One is based on a harmonic model and the other is based on a total variation model. Then, we propose two novel variational image restoration algorithms based on the Modified Hopfield Neural Network (MHNN). Both algorithms are aiming to restore the degraded images and preserve the edges with improved visual quality. The experimental results demonstrate that our proposed algorithms perform better than other known neural network based restoration algorithms.

This paper presents a fast algorithm for a recurrent neural network that can restore a degraded image with fewer iterations and shorter processing time by using bound-constrained quadratic optimization (BCQO) and a weighted mask. The BCQO technique has already been used in signal restoration, however implementation of this method in image restoration requires considerable memory and it is computationally expensive. The proposed algorithm replaces the weight matrix of the network with a much smaller mask, thus reducing the processing time and requiring much less memory space. This algorithm produces better results than those obtained by Wiener filter, and achieves image restoration with less iterations compared to a modified Hopfield neural network.

We present a tutorial review of recent developments in restoring images that are degraded by both blur and noise. We consider three fundamental aspects of digital image restoration: modeling, identification algorithms, and restoration algorithms. An overview of modeling the degradations, and certain properties of images are given first. We then survey the methods that identify these models. Image restoration algorithms are surveyed in two categories: general algorithms and specialized algorithms. We briefly discuss present and future research topics in the field. Our emphasis here is on fundamental concepts and ideas rather than mathematical details.

Underwater laser imaging is of great significance in underwater search and marine science, <i>etc</i>. However, traditional underwater laser imaging is often of poor quality with noises and blurs, moreover, the resolution of the image is also low. In order to obtain clear underwater images with high resolution and quality, here, we have designed a range gated imaging underwater imaging system and realized an image restoration approach. In this paper, based on the introduction to the imaging system and image restoration algorithm, the experiment is established by setting the imaging system under water in the lake to capture the underwater targets. With the proposed underwater image restoration approach, images of high quality could be retrieved which proves that the method is able to identify the target ~10 meters away underwater.

Human Pose Estimation (HPE) models have varied applications and represent a cutting-edge branch of study, whose systems such as MediaPipe (MP), OpenPose (OP), and AlphaPose (ALP) show marked success. One of these areas, however, that is inadequately researched is the impact of image degradation on the accuracy of HPE models. Image degradation refers to images whose visual quality has been purposefully degraded by means of techniques, such as brightness adjustments (which can lead to an increase or a decrease in the intensity levels), geometric rotations, or resolution downscaling. The study of how these types of degradation impact the performance functionality of HPE models is an under-researched domaina that is a virtually unexplored area. In addition, current methods of the efficacy of existing image restoration techniques have not been rigorously evaluated and improving degraded images to a high quality has not been well examined in relation to improving HPE models. In this study, we explicitly clearly demonstrate a decline in the precision of the HPE model when image quality is degraded. Our qualitative and quantitative measurements identify a wide difference in performance in identifying landmarks as images undergo changes in brightness, rotation, or reductions in resolution. Additionally, we have tested a variety of existing image enhancement methods in an attempt to enhance their capability in restoring low-quality images, hence supporting improved functionality of HPE. Interestingly, for rotated images, using Pillow of OpenCV improves landmark recognition precision drastically, nearly restoring it to levels we see in high-quality images. In instances of brightness variation and in low-quality images, however, existing methods of enhancement fail to yield the improvements anticipated, highlighting a large direction of study that warrants further investigation and calls for additional research. In this regard, we proposed a wide-ranging system for classifying different types of image degradation systematically and for selecting appropriate algorithms for image restoration, in an effort to restore image quality. A key finding is that in a related study of current methods, the Tuned RotNet model achieves 92.04% accuracy, significantly outperforming the baseline model and surpassing the official RotNet model in predicting rotation degree of images, where the accuracy of official RotNet and Tuned RotNet classifiers were 61.59% and 92.04%, respectively. Furthermore, in an effort to facilitate future research and make it easier for other studies, we provide a new dataset of reference images and corresponding degenerated images, addressing a notable gap in controlled comparative studies, since currently there is a lack of controlled comparatives.

Aiming at correcting the severe chromatic aberration of the long focal lens, the traditional optical design often requires employing complex structure, introducing special dispersive glasses or even utilizing the hybrid refractive-diffractive imaging method. However, complex structure will bring several drawbacks such as large volume and heavy weight. Special glasses and refractive-diffractive hybrid imaging will greatly increase the cost, which hardly meets the needs of miniaturization and low cost of optical imaging module. Although image restoration algorithm is commonly used to optimize the image quality to a certain extent, the optical design and image restoration process are independent of each other. Therefore, it is difficult to ensure the high resolution of the image while realizing the light weight, small volume and low cost of the optical system simultaneously. Utilizing the computational imaging theory, a simple long-focus optical system design method based on the optical/image co-design is proposed and deomonstrated in this paper. On the basis of the idea of global optimization, the reported approach considers the two independent links of optical design and image restoration as a combination. The imaging quality requirements in the optical system design are relaxed at the front end, and the image restoration algorithm is used to remove the residual aberrations in the back end. This method can not only obtain the same or even higher imaging performance, but also reduce the complexity of the optical system.