Ill-posed Nature Research Articles

Image De-Raining Using a Conditional Generative Adversarial Network

Severe weather conditions, such as rain and snow, adversely affect the visual quality of images captured under such conditions, thus rendering them useless for further usage and sharing. In addition, such degraded images drastically affect the performance of vision systems. Hence, it is important to address the problem of single image de-raining. However, the inherent ill-posed nature of the problem presents several challenges. We attempt to leverage powerful generative modeling capabilities of the recently introduced conditional generative adversarial networks (CGAN) by enforcing an additional constraint that the de-rained image must be indistinguishable from its corresponding ground truth clean image. The adversarial loss from GAN provides additional regularization and helps to achieve superior results. In addition to presenting a new approach to de-rain images, we introduce a new refined loss function and architectural novelties in the generator-discriminator pair for achieving improved results. The loss function is aimed at reducing artifacts introduced by GANs and ensure better visual quality. The generator sub-network is constructed using the recently introduced densely connected networks, whereas the discriminator is designed to leverage global and local information to decide if an image is real/fake. Based on this, we propose a novel single image de-raining method called image de-raining conditional generative adversarial network (ID-CGAN) that considers quantitative, visual, and also discriminative performance into the objective function. The experiments evaluated on synthetic and real images show that the proposed method outperforms many recent state-of-the-art single image de-raining methods in terms of quantitative and visual performances. Furthermore, the experimental results evaluated on object detection datasets using the Faster-RCNN also demonstrate the effectiveness of proposed method in improving the detection performance on images degraded by rain.

FAMED-Net: A Fast and Accurate Multi-Scale End-to-End Dehazing Network.

Single image dehazing is a critical image pre-processing step for subsequent high-level computer vision tasks. However, it remains challenging due to its ill-posed nature. Existing dehazing models tend to suffer from model overcomplexity and computational inefficiency or have limited representation capacity. To tackle these challenges, here, we propose a fast and accurate multi-scale end-to-end dehazing network, called FAMED-Net, which comprises encoders at three scales and a fusion module to efficiently and directly learn the haze-free image. Each encoder consists of cascaded and densely connected point-wise convolutional layers and pooling layers. Since no larger convolutional kernels are used and features are reused layer-by-layer, FAMED-Net is lightweight and computationally efficient. Thorough empirical studies on public synthetic datasets (including RESIDE) and real-world hazy images demonstrate the superiority of FAMED-Net over other representative state-of-the-art models with respect to model complexity, computational efficiency, restoration accuracy, and cross-set generalization. The code will be made publicly available.

Mirror, Mirror, on the Wall, Who's Got the Clearest Image of Them All?-A Tailored Approach to Single Image Reflection Removal.

Removing reflection artefacts from a single image is a problem of both theoretical and practical interest, which still presents challenges because of the massively ill-posed nature of the problem. In this paper, we propose a technique based on a novel optimization problem. First, we introduce a simple user interaction scheme, which helps minimize information loss in the reflection-free regions. Second, we introduce an H2 fidelity term, which preserves fine detail while enforcing the global color similarity. We show that this combination allows us to mitigate the shortcomings in structure and color preservation, which presents some of the most prominent drawbacks in the existing methods for reflection removal. We demonstrate, through numerical and visual experiments, that our method is able to outperform the state-of-the-art model-based methods and compete with recent deep-learning approaches.

Substituting smoothing with low-rank decomposition — Applications to least-squares reverse time migration of simultaneous source and incomplete seismic data

Seismic migration can be formulated as an inverse problem, the model of which can be iteratively inverted via the least-squares migration framework instead of approximated by applying the adjoint operator to the observed data. Least-squares reverse time migration (LSRTM) has attracted more and more attention in modern seismic imaging workflows because of its exceptional performance in obtaining high-resolution true-amplitude seismic images and the fast development of the computational capability of modern computing architecture. However, due to a variety of reasons, e.g., insufficient shot coverage and data sampling, the image from least-squares inversion still contains a large amount of artifacts. This phenomenon results from the ill-posed nature of the inverse problem. In traditional LSRTM, the minimum least-squares energy of the model is used as a constraint to regularize the inverse problem. Considering the residual noise caused by the smoothing operator in traditional LSRTM, we regularize the model using a powerful low-rank decomposition operator, which can better suppress the migration artifacts in the image during iterative inversion. We evaluate in detail the low-rank decomposition operator and the way to apply it along the geologic structure of seismic reflectors. We comprehensively analyze the performance of our algorithm in attenuating crosstalk noise caused by simultaneous source acquisition and migration artifacts caused by insufficient space sampling via two synthetic examples and one field data example. Our results indicate that compared to the conventional smoothing operator, our low-rank decomposition operator can help obtain a cleaner LSRTM image and obtain a slightly better edge-preserving performance.

METHODS FOR DESCRIBING THE SHAPE OF DEFECTIVE NANOSTRUCTURED FORMATIONS IN MATERIALS UNDER IRRADIATION

Within the framework of the program of using modern computer methods in the task of developing radiation-resistant materials for IV-generation reactors, several methods for describing the form of local atomic segregations or compact radiation defects of the nanometer range have been considered. A numerical method for measuring the shape of an arbitrary atomic formation possessing a well-defined external boundary is proposed. The shape of the sequence of equilibrium clusters is measured, the interaction of the particles in which is described by the Lennard-Jones potential. It is shown that the proposed method correctly reproduces the oscillations of size effects and the sequence of magic numbers for these clusters. The possibility of replacing geometric moments by the moments of Zernike 3D functions is considered. Such a replacement allows us to get rid of the ill-posed nature of the inverse problem in the transition from the source space of clusters form to the space of their descriptors.

A hybrid approach based on inverse neural network to determine optimal level of energy consumption in electrical power generation

Power plants are a strategic infrastructure industry in each country and provide a strong driving force for the development of other industries. Hence, the performance of a power plant should be optimized by adjusting input parameters to maximize efficiency. This paper mainly proposes a novel hybrid approach that aims to present an optimal level of input parameters of a power plant integrating Data Envelopment Analysis (DEA), Artificial Neural Network and Inverse Problem in a new way. The inputs for a power plant system include internal electricity, fossil fuel and water consumption which are used to generate electrical power. First, the collected data are evaluated using a DEA model to identify and determine the days that operated efficiently. Then, the efficient vectors including resources consumption and generated power in the days evaluated in the previous stage are entered into the artificial neural network. Afterward, the weights and biases of the trained network are extracted for use in the inverse neural network. The inverse neural network model is presented as a nonlinear optimization problem with Gaussian constraints. Because of the severely ill-posed nature of the problem, to solve and obtain reasonable solutions, an innovative approach is used to determine the optimal level of inputs in less time and more accuracy. Based on this approach, for solving the nonlinear model and reducing the number of candidate solutions, the optimal interval is computed for each input and each day. A real case study of the thermal power plant in Iran is presented to show the abilities of the proposed approach.

Connectomes from streamlines tractography: Assigning streamlines to brain parcellations is not trivial but highly consequential

When using diffusion MRI streamlines tractograms to construct structural connectomes, ideally, each streamline should connect exactly 2 regions-of-interest (i.e. network nodes) as defined by a given brain parcellation scheme. However, the ill-posed nature of termination criteria in many tractography algorithms can cause streamlines apparently being associated with zero, one, or more than two grey matter (GM) nodes; streamlines that terminate in white matter or cerebrospinal fluid may even end up being assigned to nodes if the definitions of these nodes are not strictly constrained to genuine GM areas, resulting in a misleading connectome in non-trivial ways. Based on both in-house MRI data and state-of-the-art data provided by the Human Connectome Project, this study investigates the actual influence of streamline-to-node assignment methods, and their interactions with fibre-tracking terminations and brain parcellations, on the construction of pairwise regional connectivity and subsequent connectomic measures. Our results show that the frequency of generating successful pairwise connectivity is heavily affected by the convoluted interactions between the applied strategies for connectome construction, and that minor changes in the mechanism can cause significant variations in the within- and between-module connectivity strengths as well as in the commonly-used graph theory metrics. Our data suggest that these fundamental processes should not be overlooked in structural connectomics research, and that improved data quality is not in itself sufficient to solve the underlying problems associated with assigning streamlines to brain nodes. We demonstrate that the application of advanced fibre-tracking techniques that are designed to correct for inaccuracies of track terminations with respect to anatomical information at the fibre-tracking stage is advantageous to the subsequent connectome construction process, in which pairs of parcellation nodes can be more robustly identified from streamline terminations via a suitable assignment mechanism.

Single-Image De-Raining With Feature-Supervised Generative Adversarial Network

De-raining, which aims at rain-steak removal from images, is a practical task in computer vision. However, it is difficult due to its ill-posed nature. In this letter, we propose a deep neural network architecture, feature-supervised generative adversarial network (FS-GAN) for single-image rain removal. Its main idea is to train a generative adversarial network (GAN) for which the supervision from ground truth is imposed on different layers of the generator network. We design a feature-supervised generator, a discriminator, an optimization target, as well as the detailed structure of FS-GAN. Experiments show that the proposed FS-GAN achieves better performance than state-of-the-art de-raining methods on both synthetic and real-world images in terms of quantitative and visual quality.

Generalised NMR-moisture correlation function of building materials based on a capillary bundle model

Quantitative determination of moisture with nuclear magnetic resonance is usually a simple task, since the initial amplitude is proportional to the moisture content. However, situations can arise where the combination of short relaxation times, low signal-to-noise ratio and the ill-posed nature of the inverse Laplace transformation lead to a significant bias of the initial amplitude impeding it being an accurate proxy for the moisture content. This is often met when applying single-sided NMR to building materials with small pores, like concrete. We present a method to derive a generalised correlation function linking not only the initial amplitude, but relaxation attenuated signal amplitudes with moisture content. Therefore, the effect of de-saturation on the T2 distribution of the respective material near saturation, which is the input to the model, is simulated using a capillary bundle model. Predicted and measured moisture coincide, and the uncertainty is significantly smaller compared to the conventional approach.

Semiglobal viscoacoustic full-waveform inversion

Full-waveform inversion deals with estimating physical properties of the earth’s subsurface by matching simulated to recorded seismic data. Intrinsic attenuation in the medium leads to the dispersion of propagating waves and the absorption of energy — media with this type of rheology are not perfectly elastic. Accounting for that effect is necessary to simulate wave propagation in realistic geologic media, leading to the need to estimate intrinsic attenuation from the seismic data. That increases the complexity of the constitutive laws leading to additional issues related to the ill-posed nature of the inverse problem. In particular, the joint estimation of several physical properties increases the null space of the parameter space, leading to a larger domain of ambiguity and increasing the number of different models that can equally well explain the data. We have evaluated a method for the joint inversion of velocity and intrinsic attenuation using semiglobal inversion; this combines quantum particle-swarm optimization for the estimation of the intrinsic attenuation with nested gradient-descent iterations for the estimation of the P-wave velocity. This approach takes advantage of the fact that some physical properties, and in particular the intrinsic attenuation, can be represented using a reduced basis, substantially decreasing the dimension of the search space. We determine the feasibility of the method and its robustness to ambiguity with 2D synthetic examples. The 3D inversion of a field data set for a geologic medium with transversely isotropic anisotropy in velocity indicates the feasibility of the method for inverting large-scale real seismic data and improving the data fitting. The principal benefits of the semiglobal multiparameter inversion are the recovery of the intrinsic attenuation from the data and the recovery of the true undispersed infinite-frequency P-wave velocity, while mitigating ambiguity between the estimated parameters.

An enhanced sparse regularization method for impact force identification

• An enhanced sparse regularization method is developed for improving impact force identification. • A weighted l 1 -norm convex optimization model for impact force identification is developed. • Iteratively reweighted l 1 -norm minimization algorithm is proposed for solving impact force identification. • Compared with existing regularizations, the enhanced sparse regularization has much sparser and more accurate result. The standard sparse regularization method based on l 1 -norm minimization for impact force identification has already proved to be an interesting alternative to the classical regularization method based on l 2 -norm minimization. However, choosing the l 1 -norm as a convex relaxation of the l 0 -norm, the corresponding sparse regularization model generally offers a sparse but underestimated solution. In this paper, considering the sparsity of impact force, an enhanced sparse regularization method based on reweighted l 1 -norm minimization is developed for reducing the peak force error and improving the identification accuracy of impact force. First, a weighted l 1 -norm convex optimization model is presented to overcome the ill-posed nature of the inverse problem of impact force identification. Second, to solve such a regularized model efficiently, an iteratively reweighted l 1 -norm minimization algorithm is introduced, where the weights are adaptively updated from the previous solution. The application of the iteratively reweighted scheme is to overcome the mismatch between l 1 -norm minimization and l 0 -norm minimization, while keeping the enhanced sparse regularization problem solvable and convex. Finally, numerical simulation and experimental verification including the single and double impact force identification on a plate structure are presented to illustrate the superior performance of the enhanced sparse regularization method compared to classical regularization approaches. Effects of reweighting iteration number, tuning parameters, initial conditions and response locations are successfully investigated in detail. Results demonstrate that compared with the standard l 1 -norm regularization method and the classical l 2 -norm regularization method, the enhanced sparse regularization method based on reweighted l 1 -norm minimization whose solution is much sparser, can greatly improve the identification accuracy of impact force. Moreover, the proposed method is much more robust to the choice of tuning parameters and noisy measurements.

3D human pose estimation from a single image via exemplar augmentation

3D human pose estimation from a single image is a challenging problem due to occlusion, viewpoint variance, and the ill-posed nature of back projection. We follow a standard two-step pipeline which first detects 2D joint locations and uses them to infer 3D pose. For the first step, we use a recent deep learning-based detector. For the second step, we propose a novel exemplar-based algorithm to implicitly augment the exemplar set for 3D human pose estimation. The motivation of this algorithm is to well represent various poses in the real world with finite real exemplars. We achieve it by a strategy of synthesizing virtual candidate poses which ensures that the augmented exemplar set has much more variety. Moreover, we also present an effective approach to select the best exemplar from candidate set to well match the detected 2D pose. Experimental results show that our method achieves competitive performance on Human3.6M dataset.

A thermo-sensitive fluorescent agent based method for excitation light leakage rejection for fluorescence molecular tomography

Fluorescence molecular tomography (FMT) is widely used in preclinical oncology research. FMT is the only imaging technique able to provide 3D distribution of fluorescent probes within thick highly scattering media. However, its integration into clinical medicine has been hampered by its low spatial resolution caused by the undetermined and ill-posed nature of its reconstruction algorithm. Another major factor degrading the quality of FMT images is the large backscattered excitation light component leaking through the rejection filters and coinciding with the weak fluorescent signal arising from a low tissue fluorescence concentration. In this paper, we present a new method based on the use of a novel thermo-sensitive fluorescence probe. In fact, the excitation light leakage is accurately estimated from a set of measurements performed at different temperatures and then is corrected for in the tomographic data. The obtained results show a considerable improvement in both spatial resolution and quantitative accuracy of FMT images due to the proper correction of fluorescent signals.

Optimal observations-based retrieval of topography in 2D shallow water equations using PC-EnKF

Parameter estimation is an important problem because in many instance uncertain parameters cannot be measured accurately, especially in real-time applications. Information about them is commonly inferred via parameter estimation techniques from available measurements of different aspects of the system response. In this work, we consider the reduction of the uncertain topography parameters of 2D shallow water equations to be inconsistency with the physical observations. This is often quite challenging due to its ill-posed nature of the inverse problem, particularly for the present nonlinear case in high-dimensional random space. We have explored an efficient computational strategy for the solution of the problem in the framework of the polynomial chaos (PC)-based ensemble Kalman filter (PC-EnKF for short). The main idea pursued in this methodology is to introduce a determination of the potential optimal observation location followed by the update of the input topography parameters to be retrieved through the PC-EnKF, wherein the identification of the optimal observation locations is accomplished sequentially via the predictive uncertainty controlled by standard deviation, and then places the corresponding measurement for data assimilation purpose. This is not only to provide more informative measurements but also to improve the topography parameters estimation. The numerical experiments indicate that the optimal observations-based PC-EnKF algorithm is effective in dealing with the current retrieval of topography parameters. It is worth mentioning that an iterative PC-basis rotation technique is particularly useful when attempting to enhance the sparsity and the resulting accuracy. The solution strategy is well suited in the current high-dimensional nonlinear inverse modeling and has shown its appealing potential in the real-world application of complex systems.

Joint Transmission Map Estimation and Dehazing using Deep Networks

Single image haze removal is an extremely challenging problem due to its inherent ill-posed nature. Several prior-based and learning-based methods have been proposed in the literature to solve this problem and they have achieved superior results. However, most of the existing methods assume constant atmospheric light model and tend to follow a two-step procedure involving prior-based methods for estimating transmission map followed by calculation of dehazed image using the closed form solution. In this paper, we relax the constant atmospheric light assumption and propose a novel unified single image dehazing network that jointly estimates the transmission map and performs dehazing. In other words, our new approach provides an end-to-end learning framework, where the inherent transmission map and dehazed result are learned directly from the loss function. Extensive experiments on synthetic and real datasets with challenging hazy images demonstrate that the proposed method achieves significant improvements over the state-of-the-art methods.

Single Image Reflection Removal Based on GAN With Gradient Constraint

When we take a picture through glass windows, the photographs are often degraded by undesired reflections. To separate reflection layer and background layer is an important problem for enhancing image quality. However, single-image reflection removal is a challenging process because of the ill-posed nature of the problem. In this paper, we propose a single-image reflection removal method based on generative adversarial network. Our network is an end-to-end trained network with four types of losses. It includes pixel loss, feature loss, adversarial loss and gradient constraint loss. We propose a novel gradient constraint loss in order to separate the background layer and the reflection layer clearly. Gradient constraint loss is applied in a gradient domain and it minimize the correlation between the background and reflection layer. Owing to the novel loss and our new synthetic dataset, our reflection removal method outperforms state-of-the-art methods in PSNR and SSIM, especially in real world images.

Reduction of Effects of Noise on the Inverse Problem of Electrocardiography with Bayesian Estimation.

To overcome the ill-posed nature of the inverse problem of electrocardiography (ECG) and stabilize the solutions, regularization is used. Despite several studies on noise, effect of prefiltering of ECG signals on the regularized inverse solutions has not been explored. We used Bayesian estimation for solving the inverse ECG problem with and without applying various prefiltering methods, and evaluated our results using experimental data that came from a Langendorff-perfused pig heart suspended in a human-shaped torso-tank. Epicardial electrograms were recorded during RV pacing using a 108-electrode array, simultaneously with ECGs from 128 electrodes embedded in the tank surface. Leave-one-beat-out protocol was used to obtain the prior probability density function (pdf) of electro-grams and noise statistics. Noise pdf was assumed to be zero mean-Gaussian, with covariance assumptions: a) independent and identically distributed (noi-iid), b) correlated (noi-corr). Reconstructed electrograms and activation times were compared to those directly recorded by the sock for 3 beats selected from the recording. Noi-corr is superior to noi-iid when the training set is a good match to data, but for applications requiring activation time derivation, careful selection of preprocessing methods, in particular to adequately remove high-frequency noise, and an appropriate noise model is needed.

Single image dehazing using heterogeneous atmospheric light estimation

Single image dehazing is a challenging problem because of its severely ill-posed nature. Single image dehazing mainly includes two important tasks, estimating the atmospheric light and calculating the medium transmission map. A single image dehazing algorithm using heterogeneous atmospheric light estimation is presented to enhance the quality of hazy images. First, a max-pooling-based strategy is developed to estimate the heterogeneous atmospheric light, which can accurately describe how the amount of scattering from one or multiple point light sources is spatial-variant. And then, an efficient adaptive filtering approach is introduced to refine the medium transmission map and suppress the annoying halo artifacts produced during the process of dehazing. Finally, based on the heterogeneous atmospheric scattering model, a photorealistic haze-free image can be recovered with the estimated atmospheric light and the refined medium transmission map. The experimental results on a variety of real-world images and synthetic hazy ones demonstrate that the addressed method outperforms state-of-the-art approaches through qualitative and quantitative metrics.

Diagnosis of Array Antennas Using Eigenmode Currents and Near-Field Data

A novel method for the diagnosis of array antennas is proposed in this paper. The current distribution of the array antennas is reconstructed by the proposed method, which is based on the eigenmode currents over the entire array antennas and its near-field data. The eigenmode currents over the entire array antennas are numerically obtained via the method of moments. Only the dominant eigenmode currents are used for the reconstruction of the current distribution of the array antennas to alleviate the ill-posed nature of an inverse problem. The current distribution of the array antennas is reconstructed using the proposed method, and the optimum parameters for the proposed method, i.e., the number of dominant eigenmode currents and the length of a cylindrical scanning surface, are clarified. Finally, the proposed method is applied to the diagnosis of array antennas with abnormal excitations.

Hyperspectral Unmixing Based on Dual-Depth Sparse Probabilistic Latent Semantic Analysis

This paper presents a novel approach for spectral unmixing of remotely sensed hyperspectral data. It exploits probabilistic latent topics in order to take advantage of the semantics pervading the latent topic space when identifying spectral signatures and estimating fractional abundances from hyperspectral images. Despite the contrasted potential of topic models to uncover image semantics, they have been merely used in hyperspectral unmixing as a straightforward data decomposition process. This limits their actual capabilities to provide semantic representations of the spectral data. The proposed model, called dual-depth sparse probabilistic latent semantic analysis (DEpLSA), makes use of two different levels of topics to exploit the semantic patterns extracted from the initial spectral space in order to relieve the ill-posed nature of the unmixing problem. In other words, DEpLSA defines a first level of deep topics to capture the semantic representations of the spectra, and a second level of restricted topics to estimate endmembers and abundances over this semantic space. An experimental comparison in conducted using the two standard topic models and the seven state-of-the-art unmixing methods available in the literature. Our experiments, conducted using four different hyperspectral images, reveal that the proposed approach is able to provide competitive advantages over available unmixing approaches.