Imaging Problems Research Articles

HMCLab: a framework for solving diverse geophysical inverse problems using the Hamiltonian Monte Carlo method

SUMMARY The use of the probabilistic approach to solve inverse problems is becoming more popular in the geophysical community, thanks to its ability to address nonlinear forward problems and to provide uncertainty quantification. However, such strategy is often tailored to specific applications and therefore there is a need for common platforms to solve different geophysical inverse problems and showing potential and pitfalls of the methodology. In this work, we demonstrate a common framework within which it is possible to solve such inverse problems ranging from, for example, earthquake source location to potential field data inversion and seismic tomography. This allows us to fully address nonlinear problems and to derive useful information about the subsurface, including uncertainty estimation. This approach can, in fact, provide probabilities related to certain properties or structures of the subsurface, such as histograms of the value of some physical property, the expected volume of buried geological bodies or the probability of having boundaries defining different layers. Thanks to its ability to address high-dimensional problems, the Hamiltonian Monte Carlo (HMC) algorithm has emerged as the state-of-the-art tool for solving geophysical inverse problems within the probabilistic framework. HMC requires the computation of gradients, which can be obtained by adjoint methods. This unique combination of HMC and adjoint methods is what makes the solution of tomographic problems ultimately feasible. These results can be obtained with ‘HMCLab’, a numerical laboratory for solving a range of different geophysical inverse problems using sampling methods, focusing in particular on the HMC algorithm. HMCLab consists of a set of samplers (HMC and others) and a set of geophysical forward problems. For each problem its misfit function and gradient computation are provided and, in addition, a set of prior models can be combined to inject additional information into the inverse problem. This allows users to experiment with probabilistic inverse problems and also address real-world studies. We show how to solve a selected set of problems within this framework using variants of the HMC algorithm and analyse the results. HMCLab is provided as an open source package written both in Python and Julia, welcoming contributions from the community.

Medical Image Despeckling Using the Invertible Sparse Fuzzy Wavelet Transform with Nature-Inspired Minibatch Water Wave Swarm Optimization.

Speckle noise is a pervasive problem in medical imaging, and conventional methods for despeckling often lead to loss of edge information due to smoothing. To address this issue, we propose a novel approach that combines a nature-inspired minibatch water wave swarm optimization (NIMWVSO) framework with an invertible sparse fuzzy wavelet transform (ISFWT) in the frequency domain. The ISFWT learns a non-linear redundant transform with a perfect reconstruction property that effectively removes noise while preserving structural and edge information in medical images. The resulting threshold is then used by the NIMWVSO to further reduce multiplicative speckle noise. Our approach was evaluated using the MSTAR dataset, and objective functions were based on two contrasting reference metrics, namely the peak signal-to-noise ratio (PSNR) and the mean structural similarity index metric (MSSIM). Our results show that the suggested approach outperforms modern filters and has significant generalization ability to unknown noise levels, while also being highly interpretable. By providing a new framework for despeckling medical images, our work has the potential to improve the accuracy and reliability of medical imaging diagnosis and treatment planning.

Retrieving space-dependent polarization transformations via near-optimal quantum process tomography.

An optical waveplate rotating light polarization can be modeled as a single-qubit unitary operator. This analogy can be exploited to experimentally retrieve a polarization transformation within the paradigm of quantum process tomography. Standard approaches to tomographic problems rely on the maximum-likelihood estimation, providing the most likely transformation to yield the same outcomes as a set of experimental projective measurements. The performances of this method strongly depend on the number of input measurements and the numerical minimization routine that is adopted. Here we investigate the application of genetic and machine learning approaches to this problem, finding that both allow for accurate reconstructions and fast operations when processing a set of projective measurements very close to the minimal one. We apply these techniques to the case of space-dependent polarization transformations, providing an experimental characterization of the optical action of spin-orbit metasurfaces having patterned birefringence. Our efforts thus expand the toolbox of methodologies for optical process tomography. In particular, we find that the neural network-based scheme provides a significant speed-up, that may be critical in applications requiring a characterization in real-time. We expect these results to lay the groundwork for the optimization of tomographic approaches in more general quantum processes, including non-unitary gates and operations in higher-dimensional Hilbert spaces.

BOLD-net: Brightness enhancement for old images using deep curve estimation and attention modules

In this paper, a novel deep-learning network for the brightness enhancement of old images is proposed. Although the task for brightness enhancement of old images is similar to the low-light enhancement problem of modern images, the causes of darkness and image characteristics are significantly different. Unlike modern images, bright degradation in old images is due to low-quality camera sensors, unsophisticated techniques that capture the images, and the harsh environment where the photos/films were stored. Though existing low-light enhancement networks show good reconstruction capabilities for modern images, they result in overexposed, color-distorted outputs if applied to old images. To resolve these, we propose a novel deep-learning network with a combination of two convolutional neural networks, which estimates curve maps to adjust the dynamic range, and an attention-guided illumination map to adjust the illumination of the given input image. In addition, channel attention blocks in the illumination map estimation network are further performed to reduce image noise and prevent over- or underexposure. The networks perform in parallel to enhance the brightness of the image and preserve inherent colors and texture details. The proposed method was evaluated on the peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and learned perceptual image patch similarity (LPIPS) and compared with the state-of-the-art methods on a dataset containing old video frames from different decades. Experimental results show that the proposed method outperforms state-of-the-art methods in terms of visual quality for brightness enhancement on old photo and video datasets.

Interpretable model learning in variational imaging: a bilevel optimization approach

Abstract In this paper, we investigate the use of bilevel optimization for model learning in variational imaging problems. Bilevel learning is an alternative approach to deep learning methods, which leads to fully interpretable models. However, it requires a detailed analytical insight into the underlying mathematical model. We focus on the bilevel learning problem for total variation models with spatially- and patch-dependent parameters. Our study encompasses the directional differentiability of the solution mapping, the derivation of optimality conditions, and the characterization of the Bouligand subdifferential of the solution operator. We also propose a two-phase trust-region algorithm for solving the problem and present numerical tests using the CelebA dataset.

Mitigating the Limited View Problem in Photoacoustic Tomography for a Planar Detection Geometry by Regularized Iterative Reconstruction.

The use of a planar detection geometry in photoacoustic tomography results in the so- called limited-view problem due to the finite extent of the acoustic detection aperture. When images are reconstructed using one-step reconstruction algorithms, image quality is compromised by the presence of streaking artefacts, reduced contrast, image distortion and reduced signal-to-noise ratio. To mitigate this, model-based iterative reconstruction approaches based on least squares minimisation with and without total variation regularization were evaluated using in-silico, experimental phantom, ex vivo and in vivo data. Compared to one-step reconstruction methods, it has been shown that iterative methods provide better image quality in terms of enhanced signal-to-artefact ratio, signal-to-noise ratio, amplitude accuracy and spatial fidelity. For the total variation approaches, the impact of the regularization parameter on image feature scale and amplitude distribution was evaluated. In addition, the extent to which the use of Bregman iterations can compensate for the systematic amplitude bias introduced by total variation was studied. This investigation is expected to inform the practical application of model-based iterative image reconstruction approaches for improving photoacoustic image quality when using finite aperture planar detection geometries.

The problem of country image in politological approach

Examination of the concept of “country image”, which recently entered the field of political research, offers the authors the opportunity to find it important to examine how to interpret this concept, to highlight the importance of its capitalization in the conditions of a society, in which the image of the country can and must obtain a “social-profitable” dimension, adding value to the efforts of advancing of the society. The article is aimed at elucidating the direct attribution of the country image problem to the essential political categories as a state, small state, national interest, country reputa tion, national security, public opinion, information society, international communication, international relations, political communication, government communication, etc. A special attention is paid to the political elements of the symbolic action: building the national identity, soft power, country branding. The exemplification of the investigative parameters of the country image in the field of political science is carried out based on the opinions of the notorious researchers, which allows the argumentation of the multidimensionality of the phenomenon in question and reveals the multitude of possible approaches, including from a political perspective.

AN STABILITY ESTIMATE IN 3D SOURCE PROBLEM FOR THE STATIONARY RADIATIVE TRANSFER EQUATION

It is given a stability estimate of a solution of a source problem for the stationary radiative transfer equation. It is suppose that the source is an isotropic distribution. Earlier stability estimates for this problem were studied in several papers, the most part of those was related to a partial case of the emission tomography problem, when the scattering operator vanishes. For the complete transfer equation the stability estimate were given under additional conditions for the absorption coefficient and the scattering kernel, those are sufficiently difficult for checking. Moreover, it is still open the question about dependence a constant in the stability estimate on the coefficients of the transfer equation. In the present work, the stationary transfer equation is considered in an compact strongly convex domain of the tree-dimension space. In a forward problem it is assumed that incoming radiation is absent. In an inverse problem for recovering an unknown source some data for solutions of the forward problem are given. A new simple approach is suggested to obtain a stability estimate for the problem under the consideration. Using this way, an explicit constant in this estimate is given.

Prior Image Guided Snapshot Compressive Spectral Imaging.

Spectral images with rich spatial and spectral information have wide usage, however, traditional spectral imaging techniques undeniably take a long time to capture scenes. We consider the computational imaging problem of the snapshot spectral spectrometer, i.e., the Coded Aperture Snapshot Spectral Imaging (CASSI) system. For the sake of a fast and generalized reconstruction algorithm, we propose a prior image guidance-based snapshot compressive imaging method. Typically, the prior image denotes the RGB measurement captured by the additional uncoded panchromatic camera of the dual-camera CASSI system. We argue that the RGB image as a prior image can provide valuable semantic information. More importantly, we design the Prior Image Semantic Similarity (PIDS) regularization term to enhance the reconstructed spectral image fidelity. In particular, the PIDS is formulated as the difference between the total variation of the prior image and the recovered spectral image. Then, we solve the PIDS regularized reconstruction problem by the Alternating Direction Method of Multipliers (ADMM) optimization algorithm. Comprehensive experiments on various datasets demonstrate the superior performance of our method.

Multi-scale feature fusion network with local attention for lung segmentation

Computer-assisted medical care can benefit from the lung region segmentation method. Numerous methods provide end-to-end solutions, these methods employ convolution neural networks to segment lung regions from images. The low contrast, unpredictable appearance, and other problems in medical images have an effect on the accuracy of existing methods. In order to overcome the aforementioned issues, the MSDC (multi-scale dilated convolution) module is added to the short-cut connection, so as to fuse multi-scale features with various receptive fields to obtain more global information of lung area. Moreover, a local attention module which includes channel attention and spatial attention is suggested to give more weight to the lung area to lower the influence of background. Several lung segmentation datasets are employed to evaluate the segmentation performance of images qualitatively and quantitatively. From the experimental results, we can see that the segmentation accuracy of our model outperforms many recent image segmentation methods.

Effects of collar eccentricity on azimuthal response characteristics for acoustic reflection measurement while drilling

Acoustic reflection imaging has been successfully applied in postdrilling wireline logging, and the technique is potentially more valuable in acoustic logging while drilling (ALWD), particularly in geosteering while drilling. Because of the common occurrence of tool eccentering in drilling, the impact of drill collar eccentricity on the acoustic wavefield inside and outside the borehole must be considered. Therefore, we analyze the effect of an eccentric drill collar on acoustic reflection imaging while drilling using analytical solutions in a dual-cylindrical coordinate system. The virtual source analogy and the translational addition theorem for cylindrical Bessel functions are used to calculate the response of the fluid-filled borehole with an eccentric collar to the incident wavefield from a formation reflector. The analysis results are validated with those from 3D finite-difference simulations. We also have studied the azimuthal variation of the received wavefield and compared the results with their centralized counterparts, for which the effects of collar eccentricity, frequency of the source, and formation elastic property are analyzed. The results indicate that the asymmetric feature of the wavefield due to the eccentric collar allows for determining the azimuth of the reflector, providing a solution to the azimuth ambiguity problem of borehole acoustic reflection imaging. Our results, besides developing an effective method for eccentric collar ALWD modeling, can be used to provide a theoretical foundation for ALWD tool development and data interpretation.

An efficient automatic clustering algorithm for probability density functions and its applications in surface material classification

AbstractClustering is a technique used to partition a dataset into groups of similar elements. In addition to traditional clustering methods, clustering for probability density functions (CDF) has been studied to capture data uncertainty. In CDF, automatic clustering is a clever technique that can determine the number of clusters automatically. However, current automatic clustering algorithms update the new probability density function (pdf) based on the weighted mean of all previous pdfs , resulting in slow convergence. This paper proposes an efficient automatic clustering algorithm for pdfs. In the proposed approach, the update of is based on the weighted mean of , where is the number of pdfs and . This technique allows for the incorporation of recently updated pdfs, leading to faster convergence. This paper also pioneers the applications of certain CDF algorithms in the field of surface image recognition. The numerical examples demonstrate that the proposed method can result in a rapid convergence at some early iterations. It also outperforms other state‐of‐the‐art automatic clustering methods in terms of the Adjusted Rand Index and the Normalized Mutual Information. Additionally, the proposed algorithm proves to be competitive when clustering material images contaminated by noise. These results highlight the applicability of the proposed method in the problem of surface image recognition.

Level Set and Optimal Control for the Inverse Inclusion Reconstruction in Electrical Impedance Tomography Modeling

In this paper, we address the identification of an unknown inclusion in an elliptic equation, which arises in the context of electrical impedance tomography and multiphase problems. We present a novel approach by formulating the overdetermined system as an optimal design problem based on the unknown inclusion and two state solutions, which is derived from by introducing a least square functional. We establish the existence results and first optimality conditions, and employ the finite element method to discretize the involved variational equations. Furthermore, we update the unknown inclusion using the level-set method. To demonstrate the effectiveness and validity of our proposed algorithm, we investigate simple and complex geometries numerically. Our results showcase the efficiency and accuracy of the method, making it a promising tool for solving similar inverse problems in various engineering applications.

Source separation and noise reduction in single-pixel imaging

Degradation of imaging quality due to noise sources is one of the most essential problems for single-pixel imaging (SPI). This paper presents a method that separates, identifies, and reduces noise from the 1-D signal of the SPI before reconstructing the image. The proposed method raises the quality of the picture significantly, for example, PSNR from 9.14 dB to 30.29 dB and SSIM from 5.55% to 91.99% when SNR is -15 dB in simulation. This method has a strong robustness to a variety of noise types compared to the traditional filtering methods. The experimental results verified the proposed method's feasibility and improved the image's quality from a chaotic state to an acceptable stage. The method proposed in this paper can separate, identify and remove the noise component from the sources in SPI, which may open a branch by removing noise from sources rather than post-processing.

The Future of Earth Imaging

Abstract Imaging of Earth’s interior has led to a large number of successful discoveries of plausible structures and associated geophysical processes. However, due to the limitations of geophysical data, Earth imaging has many trade-offs between the underlying features, and most approaches apply smoothing to reduce the effect of such trade-offs. Unfortunately, this smoothing often results in blurry images that are not clear enough either to infer the geologic processes of interest or to make quantitative inferences about the various geologic properties. Here, we first summarize some of the basic issues that make Earth imaging so difficult and explain how Earth imagers must choose between more open-ended discovery-oriented goals and more specific, scientific-inference-oriented goals. We discuss how the choice of the optimal imaging framework depends crucially on the desired goal, and particularly on whether plausible discovery or inference is the desired outcome. We argue that as Earth imaging has become more mature, sufficiently many plausible structures have been imaged that it is becoming more crucial for Earth imaging to serve the inference goal and would benefit from an inference-oriented imaging framework, despite the additional challenges in posing imaging problems in this manner. Examples of inference-oriented imaging frameworks are provided and contrasted with discovery-oriented frameworks. We discuss how the success of the various frameworks depends critically on the data quality and suggest that a careful balance must be struck between the ambition of the imager and the reality of the data. If Earth imaging is to move beyond presenting qualitatively plausible structures, it should move toward making quantitative estimates of the underlying geologic processes inferred through a self-consistent framework.

Real-time gait biometrics for surveillance applications: A review

Deep learning (DL) pipelines have evolved for over a decade now and are efficient at solving many challenging problems of image and signal processing applications. Designing deep learning pipelines for a particular application requires a good understanding of deep learning and various intermediate layers available. To develop a DL pipeline, one uses available dataset(s) suitable for an application, and the pipeline is refined by iterating over intermediate layers. A large amount of time and extensive thinking goes into these selections and validating the performance of each configuration. Thus, it is hard to choose the correct and robust DL pipeline that performs well on all relevant datasets. This review aims to aid researchers in understanding different gait sensing technologies and provide foundational knowledge of the deep learning concepts for faster solutions for a given problem. Gait recognition is more recent since it hasn’t yet been used in a real-world situation. This article provides a comprehensive overview of gait biometrics suited to real-time surveillance applications. All the important parameters of deep learning pipelines are explained, along with their selection and implication for a given problem. Authors have reviewed important research articles recently on deep learning models and how these perform across different application datasets. The benefits and drawbacks of the approaches are elucidated to help arrive at the optimized pipeline derived from a fusion of available pipelines to achieve faster but accurate results for a given problem.

Bilevel inverse problems in neuromorphic imaging

Event or neuromorphic cameras are novel biologically inspired sensors that record data based on the change in light intensity at each pixel asynchronously. They have a temporal resolution of microseconds. This is useful for scenes with fast moving objects that can cause motion blur in traditional cameras, which record the average light intensity over an exposure time for each pixel synchronously. This paper presents a bilevel inverse problem framework for neuromorphic imaging. Existence of solution to the inverse problem is established. Second order sufficient conditions are derived under special situations for this nonconvex problem. A second order Newton type solver is derived to solve the problem. The efficacy of the approach is shown on several examples.

Two-dimensional biaxial magnetic field imaging with millisecond resolution

Multi-axial dynamic magnetic field imaging with femto-Tesla sensitivity paves a promising route for acquiring comprehensive information of the extremely-weak magnetic source. Here we propose a two-dimensional (2D) scanning imaging configuration that can realize rapid biaxial magnetic field measurement. Based on the Bragg diffraction, the configuration utilizes two orthogonally-arranged acousto-optic modulators to scan the probe laser temporally and spatially, realizing a 2D (7 × 7 pixels) magnetic field detection. To solve the multi-axial dynamic magnetic field imaging problem, a non-modulated time-sharing technique is theoretically and experimentally verified. Profiting from the non-modulated biaxial working mode that avoids long demodulation time, the magnetometer realizes millisecond temporal resolution (17.15 ms) for each sensitive axis. Operation in the spin-exchange relaxation-free regime, the single-pixel measurement sensitivity reaches around 2.6 fT/Hz1/2 (y-axis) and 7.5 fT/Hz1/2 (z-axis). Furthermore, weak pump and probe lasers power (500 μW and 350 μW) make it a low-power imaging device.

Reconstruction of Convex Sets from One or Two X-rays

We consider a class of problems of Discrete Tomography which has been deeply investigated in the past: the reconstruction of convex lattice sets from their horizontal and/or vertical X-rays, i.e. from the number of points in a sequence of consecutive horizontal and vertical lines. The reconstruction of the HV-convex polyominoes works usually in two steps, first the filling step consisting in filling operations, second the convex aggregation of the switching components. We prove three results about the convex aggregation step: (1) The convex aggregation step used for the reconstruction of HV-convex polyominoes does not always provide a solution. The example yielding to this result is called the bad guy and disproves a conjecture of the domain. (2) The reconstruction of a digital convex lattice set from only one X-ray can be performed in polynomial time. We prove it by encoding the convex aggregation problem in a Directed Acyclic Graph. (3) With the same strategy, we prove that the reconstruction of fat digital convex sets from their horizontal and vertical X-rays can be solved in polynomial time. Fatness is a property of the digital convex sets regarding the relative position of the left, right, top and bottom points of the set. The complexity of the reconstruction of the digital convex sets which are not fat remains an open question.

Self-supervised learning of hologram reconstruction using physics consistency

Existing applications of deep learning in computational imaging and microscopy mostly depend on supervised learning, requiring large-scale, diverse and labelled training data. The acquisition and preparation of such training image datasets is often laborious and costly, leading to limited generalization to new sample types. Here we report a self-supervised learning model, termed GedankenNet, that eliminates the need for labelled or experimental training data, and demonstrate its effectiveness and superior generalization on hologram reconstruction tasks. Without prior knowledge about the sample types, the self-supervised learning model was trained using a physics-consistency loss and artificial random images synthetically generated without any experiments or resemblance to real-world samples. After its self-supervised training, GedankenNet successfully generalized to experimental holograms of unseen biological samples, reconstructing the phase and amplitude images of different types of object using experimentally acquired holograms. Without access to experimental data, knowledge of real samples or their spatial features, GedankenNet achieved complex-valued image reconstructions consistent with the wave equation in free space. The GedankenNet framework also shows resilience to random, unknown perturbations in the physical forward model, including changes in the hologram distances, pixel size and illumination wavelength. This self-supervised learning of image reconstruction creates new opportunities for solving inverse problems in holography, microscopy and computational imaging.