Nonlinear Reconstruction Method Research Articles

Short-wavelength-infrared upconversion edge enhancement imaging based on a Laguerre-Gaussian composite vortex filter

Edge-enhanced imaging by spiral phase contrast has proven instrumental in revealing phase or amplitude gradients of an object, with notable applications spanning feature extraction, target recognition, and biomedical fields. However, systems deploying spiral phase plates encounter limitations in phase mask modulation, hindering the characterization of the modulation function during image reconstruction. To address this need, we propose and demonstrate an innovative nonlinear reconstruction method using a Laguerre-Gaussian composite vortex filter, which modulates the spectrum of the target. The involved nonlinear process spectrally transforms the incident short-wavelength-infrared (SWIR) signal from 1550 to 864 nm, subsequently captured by a silicon charge-coupled device. Compared with conventional schemes, our novel filtering method effectively suppresses the diffraction noise, significantly enhancing image contrast and resolution. By loading specific phase holograms on the spatial light modulator, bright-field imaging, isotropic, amplitude-controlled anisotropic, and directional second-order edge-enhanced imaging are realized. Anticipated applications for the proposed SWIR edge-enhanced imaging system encompass domains such as artificial intelligence recognition, deep tissue medical diagnostics, and non-destructive defect inspection. These applications underscore the valuable potential of our cutting-edge methodology in furthering both scientific exploration and practical implementations.

Euclid: The search for primordial features

Primordial features, in particular oscillatory signals, imprinted in the primordial power spectrum of density perturbations represent a clear window of opportunity for detecting new physics at high-energy scales. Future spectroscopic and photometric measurements from the Euclid space mission will provide unique constraints on the primordial power spectrum, thanks to the redshift coverage and high-accuracy measurement of nonlinear scales, thus allowing us to investigate deviations from the standard power-law primordial power spectrum. We consider two models with primordial undamped oscillations superimposed on the matter power spectrum described by 1 + 𝒜X sin (ωXΞX + 2 πϕX), one linearly spaced in k space with Ξlin ≡ k/k* where k* = 0.05 Mpc−1 and the other logarithmically spaced in k space with Ξlog ≡ ln(k/k*). We note that 𝒜X is the amplitude of the primordial feature, ωX is the dimensionless frequency, and ϕX is the normalised phase, where X = {lin, log}. We provide forecasts from spectroscopic and photometric primary Euclid probes on the standard cosmological parameters Ωm, 0, Ωb, 0, h, ns, and σ8, and the primordial feature parameters 𝒜X, ωX, and ϕX. We focus on the uncertainties of the primordial feature amplitude 𝒜X and on the capability of Euclid to detect primordial features at a given frequency. We also study a nonlinear density reconstruction method in order to retrieve the oscillatory signals in the primordial power spectrum, which are damped on small scales in the late-time Universe due to cosmic structure formation. Finally, we also include the expected measurements from Euclid’s galaxy-clustering bispectrum and from observations of the cosmic microwave background (CMB). We forecast uncertainties in estimated values of the cosmological parameters with a Fisher matrix method applied to spectroscopic galaxy clustering (GCsp), weak lensing (WL), photometric galaxy clustering (GCph), the cross correlation (XC) between GCph and WL, the spectroscopic galaxy clustering bispectrum, the CMB temperature and E-mode polarisation, the temperature-polarisation cross correlation, and CMB weak lensing. We consider two sets of specifications for the Euclid probes (pessimistic and optimistic) and three different CMB experiment configurations, that is, Planck, Simons Observatory (SO), and CMB Stage-4 (CMB-S4). We find the following percentage relative errors in the feature amplitude with Euclid primary probes: for the linear (logarithmic) feature model, with a fiducial value of 𝒜X = 0.01, ωX = 10, and ϕX = 0: 21% (22%) in the pessimistic settings and 18% (18%) in the optimistic settings at a 68.3% confidence level (CL) using GCsp+WL+GCph+XC. While the uncertainties on the feature amplitude are strongly dependent on the frequency value when single Euclid probes are considered, we find robust constraints on 𝒜X from the combination of spectroscopic and photometric measurements over the frequency range of (1, 102.1). Due to the inclusion of numerical reconstruction, the GCsp bispectrum, SO-like CMB reduces the uncertainty on the primordial feature amplitude by 32%–48%, 50%–65%, and 15%–50%, respectively. Combining all the sources of information explored expected from Euclid in combination with the future SO-like CMB experiment, we forecast 𝒜lin ≃ 0.010 ± 0.001 at a 68.3% CL and 𝒜log ≃ 0.010 ± 0.001 for GCsp(PS rec + BS)+WL+GCph+XC+SO-like for both the optimistic and pessimistic settings over the frequency range (1, 102.1).

Constraining Neutrino Cosmologies with Nonlinear Reconstruction

Nonlinear gravitational evolution induces strong nonlinearities in the observed cosmological density fields, leading to positive off-diagonal correlations in the power spectrum covariance. This has caused the information saturation in the power spectrum, e.g., the neutrino mass constraints from the nonlinear power spectra are lower than their linear counterparts by a factor of ∼2 at z = 0. In this paper, we explore how nonlinear reconstruction methods improve the cosmological information from nonlinear cosmic fields. By applying nonlinear reconstruction to cold dark matter fields from the Quijote simulations, we find that nonlinear reconstruction can improve the constraints on cosmological parameters significantly, nearly reaching the linear theory limit. For neutrino mass, the result is only 12% lower than the linear power spectrum, i.e., the theoretical best result. This makes nonlinear reconstruction an efficient and useful method to extract neutrino information from current and upcoming galaxy surveys.

Nonlinear edge enhancement imaging based on Laguerre-Gaussian superimposed vortex filters.

Nonlinear reconstruction, which is based on the principle of cross correlation, is a commonly employed reconstruction technique in incoherent correlated digital holography systems. However, the modulation of phase masks in these systems is suppressed during the reconstruction process, resulting in an inability to express the characteristics of the phase masks. Consequently, achieving edge enhancement within these systems is constrained. We propose a nonlinear reconstruction method utilizing Laguerre-Gaussian superimposed vortex filters, which modulates the spectrum of the target during the reconstruction process. Experimental results demonstrate that this method performs well in reconstructing image edges for various phase-masked incoherent imaging systems and effectively suppresses noise. Additionally, this method enables directional edge enhancement.

Artificial intelligence achieves easy-to-adapt nonlinear global temperature reconstructions using minimal local data

Understanding monthly-to-annual climate variability is essential for adapting to future climate extremes. Key ways to do this are through analysing climate field reconstructions and reanalyses. However, producing such reconstructions can be limited by high production costs, unrealistic linearity assumptions, or uneven distribution of local climate records. Here, we present a machine learning-based non-linear climate variability reconstruction method using a Recurrent Neural Network that is able to learn from existing model outputs and reanalysis data. As a proof-of-concept, we reconstructed more than 400 years of global, monthly temperature anomalies based on sparse, realistically distributed pseudo-station data and show the impact of different training data sets. Our reconstructions show realistic temperature patterns and magnitude reproduction costing about 1 hour on a middle-class laptop. We highlight the method’s capability in terms of mean statistics compared to more established methods and find that it is also suited to reconstruct specific climate events. This approach can easily be adapted for a wide range of regions, periods and variables.

A multithreaded real-time solution for 2D EIT reconstruction with the D-bar algorithm

Electrical impedance tomography (EIT) is a non-ionizing real-time imaging tool for bedside pulmonary imaging. Dynamic cross-sectional images of ventilation and perfusion can be produced in real time with fast algorithms from measured voltage data arising from current applied on electrodes placed around the circumference of the patient’s chest. The D-bar method is a direct (non-iterative) reconstruction algorithm for EIT that uses equations of inverse scattering to independently reconstruct the conductivity at each point in the region of interest. However, this nonlinear reconstruction method has a computational complexity that makes real-time imaging a challenge. At the same time, it has the attributes that it does not require successive solutions of the forward problem, as is the case with iterative methods, and it is trivially parallelizable in the spatial variable. Here, we present a novel multithreaded implementation of the D-bar method with a front-end MATLAB/Octave program interfaced with C code that uses the pthreads library. The implementation is analyzed on several different platforms with concurrent threads ranging from 2 to 32 for spatial grids of several sizes. We demonstrate that on a CPU with many cores, very high frame rates (50 frames/s) with high resolution (6000 grid points) are achievable, and on a single AMD CPU real-time reconstructions (faster than 30 frames/s) are achieved with this implementation using 10 or more threads on a grid of 1969 points.

Fast absolute 3D CGO-based electrical impedance tomography on experimental tank data

Objective. To present the first 3D CGO-based absolute EIT reconstructions from experimental tank data. Approach. CGO-based methods for absolute EIT imaging are compared to traditional TV regularized non-linear least squares reconstruction methods. Additional robustness testing is performed by considering incorrect modeling of domain shape. Main Results. The CGO-based methods are fast, and show strong robustness to incorrect domain modeling comparable to classic difference EIT imaging and fewer boundary artefacts than the TV regularized non-linear least squares reference reconstructions. Significance. This work is the first to demonstrate fully 3D CGO-based absolute EIT reconstruction on experimental data and also compares to TV-regularized absolute reconstruction. The speed (1–5 s) and quality of the reconstructions is encouraging for future work in absolute EIT.

A Height Nonlinear Velocity Field Algorithm for CORS Station Based on GARCH Model.

In this study, the basic concept of height nonlinear velocity field modeling in the CORS station is described. The noise results in a large deviation between the observation and predicted height. An ARCH testing method for heteroscedasticity of CORS height residual square series was proposed and the non-stationary characteristic of CORS height residual square time series was proved. A CORS height nonlinear velocity field reconstruction method based on the GARCH model was proposed. First, a nonlinear LS periodic fitting model was established for CORS height series data. Then, a GARCH model was established for the fitted non-stationary residual series. Finally, the signal term, linear trend term, and GARCH model noise term of nonlinear LS modeling were combined to reconstruct the nonlinear velocity field of the CORS height. The RMSE of nonlinear LS cycle modeling for 25 CORS stations worldwide ranged from 5 to 10 mm. The differences between the velocity, approximate annual and semi-annual amplitudes, and SOPAC results were 0.73 mm/a, 0.94 mm, and 0.51 mm, respectively. Compared with the centimeter amplitude of the CORS station height, the accuracy of the nonlinear model established in this study met the requirements. The results of height nonlinear velocity field reconstruction at 25 CORS stations worldwide showed that the mean square error of prediction of the one-year height movement reached 9 mm, and the average prediction accuracy of the semi-annual was 7 mm. Compared with the calculation accuracy of the current global CORS elevation component of 3–5 mm, the prediction error in this study was about 3 mm. The expected goal was achieved regarding the accuracy of the CORS station height nonlinear velocity field model.

A Convolutional Sparsity Regularization for Solving Inverse Scattering Problems

In this letter, a convolutional sparsity regularization (CSR) is introduced into the framework of nonlinear iterative methods for solving inverse scattering problems (ISPs). The permittivity image of scatterers is sparsely represented in a convolutional form with prelearned dictionary filters. The CSR is then incorporated with the subspace-based optimization method (SOM), termed as (SOM-CSR), to reconstruct the target image as a sparse coding by dictionary filters. The whole optimization function of SOM-CSR is solved using an alternative iteration method. Both synthetic and experimental data are employed to validate the effectiveness of the proposed SOM-CSR method. The results demonstrate that the CSR, as a structural constraint, is beneficial to nonlinear iterative reconstruction methods for solving ISP in contrast to pixel-based inversion.

Framework for reconstructing wave loads on a floating cylinder using monitored data of structural motion and wave elevation

This study develops a framework for reconstructing the wave loads on a floating cylinder by utilising the monitored data of wave elevation and structural motions, which involve surge, sway, roll, and pitch motions. The proposed method can be applied to perform wave load monitoring and data collection for offshore structures in a stochastic wave field. The derivation of the wave load reconstruction based on the potential flow theory is presented in detail. The linear reconstruction method (as the basis of the proposed method) is first established to simplify the reconstruction process. A nonlinear reconstruction method considering the second-order wave effects is introduced to improve the reconstruction accuracy for nonlinear wave loads. The concept of wave load reconstruction on a complex structure is also addressed. A case analysis is performed on a floating circular cylinder under three conditions. When the structural motions are pure translational motions or pure rotational motions, the wave loads on the cylinder can be reconstructed accurately with the transfer functions ατ,n and βτ,n. When the structural motions consist of both translational and rotational motions, the transfer functions are dependent on the structural motion pattern. Singularity points with a specific motion pattern are present, whereby the reconstruction would fail. In the cases where diffraction and radiation waves occur simultaneously, the two types of waves need to be decoupled from the monitored wave elevation, and the wave loads caused by the diffraction and radiation waves are reconstructed separately.

Abnormal driving behavior detection based on kernelization-sparse representation in video surveillance

The detection of abnormal driving behaviors based on video surveillance systems is an important part of Intelligent Transportation System (ITS), which can help reduce disturbances on traffic flow and improve traffic safety. First, the study proposes a novel nonlinear sparse reconstruction method for abnormal driving behavior detection in video surveillance. A hybrid kernel function formed by convexly combining a local kernel of radial basis function (RBF) and a global kernel of homogeneous polynomial is been applied in sparse reconstruction method. Then, a novel Hybrid Kernel Orthogonal Matching Pursuit (HKOMP) algorithm is designed to solve the proposed sparse reconstruction model. Finally, the performance of the abnormal detection method is tested on two datasets i.e. stop sign dataset and car parking dataset. In addition, comparative experiments with five classical methods are carried out. The experimental results indicate that the proposed method outperforms other five comparison methods in terms of accuracy.

Novel nonlinear reconstruction method with grey-level quantisation units for electron tomography

We report a new computed tomography reconstruction method, named quantisation units reconstruction technique (QURT), applicable to electron and other fields of tomography. Conventional electron tomography methods such as filtered back projection, weighted back projection, simultaneous iterative reconstructed technique, etc. suffer from the ‘missing wedge’ problem due to the limited tilt-angle range. QURT demonstrates improvements to solve this problem by recovering a structural image blurred due to the missing wedge and substantially reconstructs the structure even if the number of projection images is small. QURT reconstructs a cross-section image by arranging grey-level quantisation units (QU pieces) in three-dimensional image space via unique discrete processing. Its viability is confirmed by model simulations and experimental results. An important difference from recently developed methods such as discrete algebraic reconstruction technique (DART), total variation regularisation—DART, and compressed sensing is that prior knowledge of the conditions regarding the specimen or the expected cross-section image is not necessary.

Model-based reconstruction for simultaneous multi-slice mapping using single-shot inversion-recovery radial FLASH.

To develop a single-shot multi-slice mapping method by combing simultaneous multi-slice (SMS) excitations, single-shot inversion-recovery (IR) radial fast low-angle shot (FLASH), and a nonlinear model-based reconstruction method. SMS excitations are combined with a single-shot IR radial FLASH sequence for data acquisition. A previously developed single-slice calibrationless model-based reconstruction is extended to SMS, formulating the estimation of parameter maps and coil sensitivities from all slices as a single nonlinear inverse problem. Joint-sparsity constraints are further applied to the parameter maps to improve precision. Validations of the proposed method are performed for a phantom and for the human brain and liver in 6 healthy adult subjects. Phantom results confirm good accuracy and precision of the simultaneously acquired multi-slice maps in comparison to single-slice references. In vivo human brain studies demonstrate the better performance of SMS acquisitions compared to the conventional spoke-interleaved multi-slice acquisition using model-based reconstruction. Aside from good accuracy and precision, the results of 6 healthy subjects in both brain and abdominal studies confirm good repeatability between scan and re-scans. The proposed method can simultaneously acquire maps for 5 slices of a human brain ( ) or 3 slices of the abdomen ( ) within 4 seconds. The IR SMS radial FLASH acquisition together with a nonlinear model-based reconstruction enable rapid high-resolution multi-slice mapping with good accuracy, precision, and repeatability.

Real-time nonlinear cylinder wave force reconstruction in stochastic wave field considering second-order wave effects

This study provides a novel method for reconstructing real-time nonlinear wave forces on a large-scale circular cylinder by considering second-order wave effects. Potential theory is utilized for deriving the expression of wave forces with the measured data of wave elevation. Approximate expressions of quadratic transfer functions are built with undetermined coefficients, which are resolved by using the historical data of measured wave elevation. Two different algorithms, including fast Fourier transform (FFT) and recursive least squares (RLS), are adopted for real-time reconstruction. Hydrodynamic tests are conducted in the wave flume on a circular cylinder to examine the effectiveness of the nonlinear reconstruction method. Comparative results demonstrate that the accuracy of real-time reconstructed wave forces is significantly enhanced by the present method. The over-prediction errors at force crests and the under-prediction errors at force troughs have been reduced. Furthermore, comparative results show that the nonlinear method implemented by the FFT algorithm provides more accurate results, whereas the RLS algorithm is more time cost efficient.

Numerical assessments of a parametric implicit large eddy simulation model

This study proposes a parametric implicit large eddy simulation (LES) strategy for the simulation of incompressible turbulence given by the Taylor–Green vortex. Our proposed scheme is derived from the dispersion-relation-preserving (DRP) philosophy to provide a specified numerical dissipation through a free modeling parameter. The specification of this dissipation control parameter represents a unique formulation for computing inviscid fluxes within the finite volume method. It is shown that the specification of a zero dissipation recovers the classical central DRP scheme. For comparison, we also evaluate multiple closure strategies from both implicit and explicit LES techniques through the use of various statistical quantities such as kinetic energy spectrum and energy dissipation rate. Some of the closure strategies examined, in addition to our scheme, include the use of established linear and nonlinear state reconstruction methods for implicit LES as well as the use of relaxation filtering utilized for explicit closure. In particular, it is seen that the proposed method embeds an identical low-pass spatial filtering through a state-reconstruction compared to our choice of the relaxation filter. In addition, consistency with the finite volume framework ensures more controllable dissipation. Our assessments indicate that the proposed numerical formulation obtains excellent reconstructions for statistical measures utilizing coarser grids and represents a viable approach for computationally efficient user-defined upwind based dissipation in implicit LES.

Experimental testing on phantom image for improved MRI compressed sensing

This paper presents a possible way for improving the techniques of compressed sensing and parallel imaging techniques for brain MRI. Experimental tests have been performed over a phantom test image. An exclusive elliptical sampling mask has been generated, which in combination with double-density wavelet transforms offers improvement over the standard approach. Additional tests undertaken as part of this research propose the usage of nonlinear reconstruction method, generated elliptical sampling mask and double-density wavelet transform for application of compressed sensing to brain MRI. An assessment of the results for diagnostic usage has been done by a specialist of radiology.

ЭМПИРИЧЕСКОЕ ИССЛЕДОВАНИЕ КРИТИЧЕСКОГО ПЕРЕХОДА В КЛИМАТЕ ПЛЕЙСТОЦЕНА НА ОСНОВЕ НЕЛИНЕЙНОДИНАМИЧЕСКОЙ РЕКОНСТРУКЦИИ

Until now, cause of the Mid-Pleistocene Transition (MPT), when the dominant periodicity of climate cycles changed from 41,000 to 100,000 years in the absence of significant change in orbital forcing, are still an open question in Paleoclimatology. Here we show how a Bayesian data analysis and nonlinear dynamical reconstruction methods can help to reveal the main mechanisms underlying the Pleistocene variability. Our Bayesian data-driven model from benthic d18O records (LR04 stack) accounts the main factors which may potentially impact climate of the Pleistocene: internal climate dynamics, gradual trends, variations of insolation, and millennial variability. In contrast to some theories, we uncover that under long-term trends in climate, the strong glacial cycles have appeared due to internal nonlinear oscillations induced by millennial noise. We find that while the orbital Milankovitch forcing does not matter for the MPT onset, the obliquity oscillation phase-locks the climate cycles through the meridional gradient of insolation. The research was supported by the RAS Presidium Program «Nonlinear dynamics: fundamental problems and applications».

Field data-based evaluation of methods for recovering surface wave elevation from pressure measurements

We compare different methods to reconstruct the surface elevation of irregular waves propagating outside the surf zone from pressure measurements at the bottom. The traditional transfer function method (TFM), based on the linear wave theory, predicts reasonably well the significant wave height but cannot describe the highest frequencies of the wave spectrum. This is why the TFM cannot reproduce the skewed shape of nonlinear waves and strongly underestimates their crest elevation. The surface elevation reconstructed from the TFM is very sensitive to the value of the cutoff frequency. At the individual wave scale, high-frequency tail correction strategies associated with this method do not significantly improve the prediction of the highest waves. Unlike the TFM, the recently developed weakly-dispersive nonlinear reconstruction method correctly reproduces the wave energy over a large number of harmonics leading to an accurate estimation of the peaked and skewed shape of the highest waves. This method is able to recover the most nonlinear waves within wave groups which some can be characterized as extreme waves. It is anticipated that using relevant reconstruction method will improve the description of individual wave transformation close to breaking.

Improving DOT reconstruction with a Born iterative method and US-guided sparse regularization.

Ultrasound (US)-guided diffuse optical tomography (DOT) is a promising low-cost imaging technique for diagnosis and assessment of breast cancer. US-guided DOT is best implemented in reflection geometry, which can be co-registered with US pulse-echo imaging and also minimizes the tissue depth for adequate light penetration. However, due to intense light scattering, the DOT reconstruction problem is ill-posed. In this communication, we describe a new non-linear Born iterative reconstruction method with US-guided depth-dependent sparse regularization for improving DOT reconstruction by incorporating a priori lesion depth and shape information from the co-registered US image. Our method iteratively solves the inverse problem by updating the photon-density wave using the finite difference method, computing the weight matrix based on Born approximation, and reconstructing the absorption map using the fast iterative shrinkage-thresholding optimization algorithm (FISTA). We validate our method using both phantom and patient data and compare the results with those using the first order linear Born method. Phantom experiments demonstrate that the non-linear Born method provides more accurate target absorption reconstruction and better resolution than the linear Born method. Clinical studies on 20 patients show that non-linear Born reconstructs more realistic tumor shapes than linear Born, and improves the malignant-to-benign lesion contrast ratio from to , which is a improvement. For lesions approximately more than cm in diameter, the average malignant-to-benign lesion contrast ratio is increased from to , which is a improvement.

Reconstructing the baryon acoustic oscillations using biased tracers

The reconstruction of the initial conditions of the Universe is an important topic in cosmology, particularly in the context of sharpening the measurement of the baryon acoustic oscillation (BAO) peak. Nonlinear reconstruction algorithms developed in recent years, when applied to late-time matter fields, can recover to a substantial degree the initial density distribution, however, when applied to sparse tracers of the matter field, the performance is poorer. In this paper we apply the Shi et al. non-linear reconstruction method to biased tracers in order to establish what factors affect the reconstruction performance. We find that grid resolution, tracer number density and mass assignment scheme all have a significant impact on the performance of our reconstruction method, with triangular-shaped-cloud (TSC) mass assignment and a grid resolution of ${\sim}1{-}2h^{-1}$ Mpc being the optimal choice. We also show that our method can be easily adapted to include generic tracer biases up to quadratic order in the reconstruction formalism. Applying the reconstruction to halo and galaxy samples with a range of tracer number densities, we find that the linear bias is by far the most important bias term, while including nonlocal and nonlinear biases only leads to marginal improvements on the reconstruction performance. Overall, including bias in the reconstruction substantially improves the recovery of BAO wiggles, down to $k\sim0.25~h\text{Mpc}^{-1}$ for tracer number densities between $2\times10^{-4}$ and $2\times10^{-3}~(h^{-1}\text{Mpc})^{-3}$.