Two image restoration algorithms using variational PDE based neural network

The neural network method is widely used in image restoration, since its advantages such as the abilities of parallel computing, nonlinear mapping and self-adaptiveness. In this paper, an improved sequential algorithm is proposed, which uses the modified Hopfield neural network based on continuous state change, and maximal energy descent in the update rule. Experiment results show that the improved sequential algorithm could converge to a stable point with high speed, and give more precise restoration results.

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.

The authors present a new min-cut technique for standard cell placement using a modified Hopfield neural network. The neural network has the advantage of a massively parallel architecture, which can drastically reduce computation time in a hardware implementation. It also allows all partitions at a given level of the hierarchical procedure to be performed in parallel, thus overcoming a common drawback of sequential min-cut procedures. The approach has produced very good results on a number of practical standard cell circuits. >

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.

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 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.

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.

Lung cancer is cancer that starts in the lungs. Cancer is a disease where cancerous cells grow out of control, taking over normal cells and organs in the body. The early detection of lung cancer is the most effective way to decrease the mortality rate. In this paper we compare two methods, a modified Hopfield Neural Network (HNN) and a Fuzzy C-Mean (FCM) Clustering Algorithm, used in segmenting sputum color images. The segmentation results will be used as a base for a Computer Aided Diagnosis (CAD) system for early detection of lung cancer. Both methods are designed to classify the image of N pixels among M classes or regions. Due to intensity variations in the background of the raw images, a pre-segmentation process is developed to standardize the segmentation process. In this study, we used 1000 sputum color images to test both methods, and HNN has shown a better classification result than FCM; however the latter was faster in converging.

The hierarchical deep-learning neural network (HiDeNN) (Zhang et al, Computational Mechanics, 67:207-230) provides a systematic approach to constructing numerical approximations that can be incorporated into a wide variety of Partial differential equations (PDE) and/or Ordinary differential equations (ODE) solvers. This paper presents a framework of the nonlinear finite element based on HiDeNN approximation (nonlinear HiDeNN-FEM). This is enabled by three basic building blocks employing structured deep neural networks: 1) A partial derivative operator block that performs the differentiation of the shape functions with respect to the element coordinates, 2) An r-adaptivity block that improves the local and global convergence properties and 3) A materials derivative block that evaluates the material derivatives of the shape function. While these building blocks can be applied to any element, specific implementations are presented in 1D and 2D to illustrate the application of the deep learning neural network. Two-step optimization schemes are further developed to allow for the capabilities of r-adaptivity and easy integration with any existing FE solver. Numerical examples of 2D and 3D demonstrate that the proposed nonlinear HiDeNN-FEM with r-adaptivity provides much higher accuracy than regular FEM. It also significantly reduces element distortion and suppresses the hourglass mode.

Multi-modal image segmentation using a modified Hopfield neural network

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.

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

A new channel assignment algorithm using a modified Hopfield neural network is proposed. The channel assignment problem is formulated as an energy minimization problem that is implemented by a modified discrete Hopfield network. Also a new technique to escape local minima is introduced. The interconnection weights between the neurons are designed in such a way that each neuron receives inhibitory support from neurons that violate the constraint conditions and receives excitatory support from external input. Various initialization techniques which use the specific characteristics of frequency assignment problems in cellular radio networks such as co-site constraint, adjacent channel constraint, and co-channel constraint and updating methods are investigated. Other than the already proposed neural network algorithms, this new algorithm fixes no frequencies of the cells before the frequency assignment procedure. This new algorithm, together with the proposed initialization and updating techniques and with no fixed frequencies in certain cells, has better performance results than the results reported previously utilizing fixed cells.

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.