Nonblind Image Deblurring via Deep Learning in Complex Field

Nonblind image deblurring is about recovering the latent clear image from a blurry one generated by a known blur kernel, which is an often-seen yet challenging inverse problem in imaging. Its key is how to robustly suppress noise magnification during the inversion process. Recent approaches made a breakthrough by exploiting convolutional neural network (CNN)-based denoising priors in the image domain or the gradient domain, which allows using a CNN for noise suppression. The performance of these approaches is highly dependent on the effectiveness of the denoising CNN in removing magnified noise whose distribution is unknown and varies at different iterations of the deblurring process for different images. In this article, we introduce a CNN-based image prior defined in the Gabor domain. The prior not only utilizes the optimal space-frequency resolution and strong orientation selectivity of the Gabor transform but also enables using complex-valued (CV) representations in intermediate processing for better denoising. A CV CNN is developed to exploit the benefits of the CV representations, with better generalization to handle unknown noises over the real-valued ones. Combining our Gabor-domain CV CNN-based prior with an unrolling scheme, we propose a deep-learning-based approach to nonblind image deblurring. Extensive experiments have demonstrated the superior performance of the proposed approach over the state-of-the-art ones.

Towards a Very Fast Feedforward Multilayer Neural Networks Training Algorithm

**This paper presents a novel fast algorithm for feedforward neural networks training. It is based on the Recursive Least Squares (RLS) method commonly used for designing adaptive filters. Besides, it utilizes two techniques of linear algebra, namely the orthogonal transformation method, called the Givens Rotations (GR), and the QR decomposition, creating the GQR (symbolically we write GR + QR = GQR) procedure for solving the normal equations in the weight update process. In this paper, a novel approach to the GQR algorithm is presented. The main idea revolves around reducing the computational cost of a single rotation by eliminating the square root calculation and reducing the number of multiplications. The proposed modification is based on the scaled version of the Givens rotations, denoted as SGQR. This modification is expected to bring a significant training time reduction comparing to the classic GQR algorithm. The paper begins with the introduction and the classic Givens rotation description. Then, the scaled rotation and its usage in the QR decomposition is discussed. The main section of the article presents the neural network training algorithm which utilizes scaled Givens rotations and QR decomposition in the weight update process. Next, the experiment results of the proposed algorithm are presented and discussed. The experiment utilizes several benchmarks combined with neural networks of various topologies. It is shown that the proposed algorithm outperforms several other commonly used methods, including well known Adam optimizer.

Using a Blur Metric to Estimate Linear Motion Blur Parameters

Motion blur is a common artifact in image processing, specifically in e-health services, which is caused by the motion of a camera or scene. In linear motion cases, the blur kernel, i.e., the function that simulates the linear motion blur process, depends on the length and direction of blur, called linear motion blur parameters. The estimation of blur parameters is a vital and sensitive stage in the process of reconstructing a sharp version of a motion blurred image, i.e., image deblurring. The estimation of blur parameters can also be used in e-health services. Since medical images may be blurry, this method can be used to estimate the blur parameters and then take an action to enhance the image. In this paper, some methods are proposed for estimating the linear motion blur parameters based on the extraction of features from the given single blurred image. The motion blur direction is estimated using the Radon transform of the spectrum of the blurred image. To estimate the motion blur length, the relation between a blur metric, called NIDCT (Noise-Immune Discrete Cosine Transform-based), and the motion blur length is applied. Experiments performed in this study showed that the NIDCT blur metric and the blur length have a monotonic relation. Indeed, an increase in blur length leads to increase in the blurriness value estimated via the NIDCT blur metric. This relation is applied to estimate the motion blur. The efficiency of the proposed method is demonstrated by performing some quantitative and qualitative experiments.

Improved estimation of motion blur parameters for restoration from a single image

This paper presents an improved method to estimate the blur parameters of motion deblurring algorithm for single image restoration based on the point spread function (PSF) in frequency spectrum. We then introduce a modification to the Radon transform in the blur angle estimation scheme with our proposed difference value vs angle curve. Subsequently, the auto-correlation matrix is employed to estimate the blur angle by measuring the distance between the conjugated-correlated troughs. Finally, we evaluate the accuracy, robustness and time efficiency of our proposed method with the existing algorithms on the public benchmarks and the natural real motion blurred images. The experimental results demonstrate that the proposed PSF estimation scheme not only could obtain a higher accuracy for the blur angle and blur length, but also demonstrate stronger robustness and higher time efficiency under different circumstances.

A Blur Classification Approach Using Deep Convolution Neural Network

Computer vision-based gesture identification is designed to recognize human actions with the help of images. During the process of gesture image acquisition, images suffer various degradations. The method of recovering these degraded images is called restoration. In the case of blind restoration of such a degraded image where blur information is unavailable, it is essential to determine the exact blur type. This article presents a convolution neural network model for blur classification which categories a blur found in a hand gesture image into one of the four blur categories: motion, defocus, Gaussian, and box blur. The simulation results demonstrate the improved preciseness of the CNN model when compared to the MLP model.

Star Image Prediction and Restoration under Dynamic Conditions

The star sensor is widely used in attitude control systems of spacecraft for attitude measurement. However, under high dynamic conditions, frame loss and smearing of the star image may appear and result in decreased accuracy or even failure of the star centroid extraction and attitude determination. To improve the performance of the star sensor under dynamic conditions, a gyroscope-assisted star image prediction method and an improved Richardson-Lucy (RL) algorithm based on the ensemble back-propagation neural network (EBPNN) are proposed. First, for the frame loss problem of the star sensor, considering the distortion of the star sensor lens, a prediction model of the star spot position is obtained by the angular rates of the gyroscope. Second, to restore the smearing star image, the point spread function (PSF) is calculated by the angular velocity of the gyroscope. Then, we use the EBPNN to predict the number of iterations required by the RL algorithm to complete the star image deblurring. Finally, simulation experiments are performed to verify the effectiveness and real-time of the proposed algorithm.

A MLMVN with Arbitrary Complex-Valued Inputs and a Hybrid Testability Approach for the Extraction of Lumped Models Using FRA

A procedure for the identification of lumped models of distributed parameter electromagnetic systems is presented in this paper. A Frequency Response Analysis (FRA) of the device to be modeled is performed, executing repeated measurements or intensive simulations. The method can be used to extract the values of the components. The fundamental brick of this architecture is a multi-valued neuron (MVN), used in a multilayer neural network (MLMVN); the neuron is modified in order to use arbitrary complex-valued inputs, which represent the frequency response of the device. It is shown that this modification requires just a slight change in the MLMVN learning algorithm. The method is tested over three completely different examples to clearly explain its generality.

Boundedness and complete stability of complex-valued neural networks with time delay

In this paper, the boundedness and complete stability of complex-valued neural networks (CVNNs) with time delay are studied. Some conditions to guarantee the boundedness of the CVNNs are derived using local inhibition. Moreover, under the boundedness conditions, a compact set that globally attracts all the trajectories of the network is also given. Additionally, several conditions in terms of real-valued linear matrix inequalities (LMIs) for complete stability of the CVNNs are established via the energy minimization method and the approach that converts the complex-valued LMIs to real-valued ones. Examples with simulation results are given to show the effectiveness of the theoretical analysis.

Projection-based fast learning fully complex-valued relaxation neural network

This paper presents a fully complex-valued relaxation network (FCRN) with its projection-based learning algorithm. The FCRN is a single hidden layer network with a Gaussian-like sech activation function in the hidden layer and an exponential activation function in the output layer. For a given number of hidden neurons, the input weights are assigned randomly and the output weights are estimated by minimizing a nonlinear logarithmic function (called as an energy function) which explicitly contains both the magnitude and phase errors. A projection-based learning algorithm determines the optimal output weights corresponding to the minima of the energy function by converting the nonlinear programming problem into that of solving a set of simultaneous linear algebraic equations. The resultant FCRN approximates the desired output more accurately with a lower computational effort. The classification ability of FCRN is evaluated using a set of real-valued benchmark classification problems from the University of California, Irvine machine learning repository. Here, a circular transformation is used to transform the real-valued input features to the complex domain. Next, the FCRN is used to solve three practical problems: a quadrature amplitude modulation channel equalization, an adaptive beamforming, and a mammogram classification. Performance results from this paper clearly indicate the superior classification/approximation performance of the FCRN.

MULTICHANNEL DECODING FOR PHASE-CODED SSVEP BRAIN–COMPUTER INTERFACE

We propose a complex-valued multilayer feedforward neural network classifier for decoding of phase-coded information from steady-state visual evoked potentials. To optimize the performance of the classifier we supply it with two filter-based feature selection strategies. The proposed approaches could be used for a phase-coded brain–computer interface, enabling to encode several targets using only one stimulation frequency. The proposed classifier is a multichannel one, which distinguishes our approach from the existing single-channel ones. We show that the proposed approach outperforms others in terms of accuracy and length of the data segments used for decoding. We show that the decoding based on one optimally selected channel yields an inferior performance compared to the one based on several features, which supports our argument for a multichannel approach.

Generalization characteristics of complex-valued feedforward neural networks in relation to signal coherence

Applications of complex-valued neural networks (CVNNs) have expanded widely in recent years-in particular in radar and coherent imaging systems. In general, the most important merit of neural networks lies in their generalization ability. This paper compares the generalization characteristics of complex-valued and real-valued feedforward neural networks in terms of the coherence of the signals to be dealt with. We assume a task of function approximation such as interpolation of temporal signals. Simulation and real-world experiments demonstrate that CVNNs with amplitude-phase-type activation function show smaller generalization error than real-valued networks, such as bivariate and dual-univariate real-valued neural networks. Based on the results, we discuss how the generalization characteristics are influenced by the coherence of the signals depending on the degree of freedom in the learning and on the circularity in neural dynamics.

Artificial neural networks using complex numbers and phase encoded weights

The model of a simple perceptron using phase-encoded inputs and complex-valued weights is proposed. The aggregation function, activation function, and learning rule for the proposed neuron are derived and applied to Boolean logic functions and simple computer vision tasks. The complex-valued neuron (CVN) is shown to be superior to traditional perceptrons. An improvement of 135% over the theoretical maximum of 104 linearly separable problems (of three variables) solvable by conventional perceptrons is achieved without additional logic, neuron stages, or higher order terms such as those required in polynomial logic gates. The application of CVN in distortion invariant character recognition and image segmentation is demonstrated. Implementation details are discussed, and the CVN is shown to be very attractive for optical implementation since optical computations are naturally complex. The cost of the CVN is less in all cases than the traditional neuron when implemented optically. Therefore, all the benefits of the CVN can be obtained without additional cost. However, on those implementations dependent on standard serial computers, CVN will be more cost effective only in those applications where its increased power can offset the requirement for additional neurons.

LINEAR MOTION BLUR IDENTIFICATION IN NOISY IMAGES USING BISPECTRUM AND FEED-FORWARD BACK PROPAGATION NEURAL NETWORKS

Motion blur is one of the most common causes of image corruptions caused by blurring. Several methods have been presented up to now, which precisely identify linear motion blur parameters, but most of them possessed low precision in the presence of the noise. The present paper is aimed to introduce an algorithm for estimating linear motion blur parameters in noisy images. This study presents a method to estimate motion direction by using Radon transform, which is followed by the application of two other different methods to estimate motion length; the first of which is based on one-dimensional power spectrum to estimate parameters of noise free images and the second uses bispectrum modeling in noisy images. A Feed-Forward Back Propagation neural network has been designed on the basis of Weierstrass approximation theorem to model bispectrum and the Delta rule as the network learning rule. The methods were tested on several standard images like Camera man, Lena, Lake, etc. that were degraded by linear motion blur and additive noise. The experimental results have been satisfactory. The proposed method, compared to other related methods, suggests an improvement in the supported lowest SNR and precision of estimation.

Blind and semi-blind deblurring of natural images

A method for blind image deblurring is presented. The method only makes weak assumptions about the blurring filter and is able to undo a wide variety of blurring degradations. To overcome the ill-posedness of the blind image deblurring problem, the method includes a learning technique which initially focuses on the main edges of the image and gradually takes details into account. A new image prior, which includes a new edge detector, is used. The method is able to handle unconstrained blurs, but also allows the use of constraints or of prior information on the blurring filter, as well as the use of filters defined in a parametric manner. Furthermore, it works in both single-frame and multiframe scenarios. The use of constrained blur models appropriate to the problem at hand, and/or of multiframe scenarios, generally improves the deblurring results. Tests performed on monochrome and color images, with various synthetic and real-life degradations, without and with noise, in single-frame and multiframe scenarios, showed good results, both in subjective terms and in terms of the increase of signal to noise ratio (ISNR) measure. In comparisons with other state of the art methods, our method yields better results, and shows to be applicable to a much wider range of blurs.