Terms Of Data Consistency Research Articles

Score Prior Guided Iterative Solver for Speckles Removal in Optical Coherent Tomography Images.

Optical coherence tomography (OCT) is a widely used non-invasive imaging modality for ophthalmic diagnosis. However, the inherent speckle noise becomes the leading cause of OCT image quality, and efficient speckle removal algorithms can improve image readability and benefit automated clinical analysis. As an ill-posed inverse problem, it is of utmost importance for speckle removal to learn suitable priors. In this work, we develop a score prior guided iterative solver (SPIS) with logarithmic space to remove speckles in OCT images. Specifically, we model the posterior distribution of raw OCT images as a data consistency term and transform the speckle removal from a nonlinear into a linear inverse problem in the logarithmic domain. Subsequently, the learned prior distribution through the score function from the diffusion model is utilized as a constraint for the data consistency term into the linear inverse optimization, resulting in an iterative speckle removal procedure that alternates between the score prior predictor and the subsequent non-expansive data consistency corrector. Experimental results on the private and public OCT datasets demonstrate that the proposed SPIS has an excellent performance in speckle removal and out-of-distribution (OOD) generalization. Further downstream automatic analysis on the OCT images verifies that the proposed SPIS can benefit clinical applications. The data and code are available at https://github.com/ lisanqian1212/SPIS.

Solving Zero-Shot Sparse-View CT Reconstruction With Variational Score Solver.

Computed tomography (CT) stands as a ubiquitous medical diagnostic tool. Nonetheless, the radiation-related concerns associated with CT scans have raised public apprehensions. Mitigating radiation dosage in CT imaging poses an inherent challenge as it inevitably compromises the fidelity of CT reconstructions, impacting diagnostic accuracy. While previous deep learning techniques have exhibited promise in enhancing CT reconstruction quality, they remain hindered by the reliance on paired data, which is arduous to procure. In this study, we present a novel approach named Variational Score Solver (VSS) for solving sparse-view reconstruction without paired data. Our approach entails the acquisition of a probability distribution from densely sampled CT reconstructions, employing a latent diffusion model. High-quality reconstruction outcomes are achieved through an iterative process, wherein the diffusion model serves as the prior term, subsequently integrated with the data consistency term. Notably, rather than directly employing the prior diffusion model, we distill prior knowledge by finding the fixed point of the diffusion model. This framework empowers us to exercise precise control over the process. Moreover, we depart from modeling the reconstruction outcomes as deterministic values, opting instead for a distribution-based approach. This enables us to achieve more accurate reconstructions utilizing a trainable model. Our approach introduces a fresh perspective to the realm of zero-shot CT reconstruction, circumventing the constraints of supervised learning. Our extensive qualitative and quantitative experiments unequivocally demonstrate that VSS surpasses other contemporary unsupervised and achieves comparable results compared with the most advance supervised methods in sparse-view reconstruction tasks. Codes are available in https://github.com/fpsandnoob/vss.

Multi-Channel Optimization Generative Model for Stable Ultra-Sparse-View CT Reconstruction.

Score-based generative model (SGM) has risen to prominence in sparse-view CT reconstruction due to its impressive generation capability. The consistency of data is crucial in guiding the reconstruction process in SGM-based reconstruction methods. However, the existing data consistency policy exhibits certain limitations. Firstly, it employs partial data from the reconstructed image of the iteration process for image updates, which leads to secondary artifacts with compromising image quality. Moreover, the updates to the SGM and data consistency are considered as distinct stages, disregarding their interdependent relationship. Additionally, the reference image used to compute gradients in the reconstruction process is derived from the intermediate result rather than ground truth. Motivated by the fact that a typical SGM yields distinct outcomes with different random noise inputs, we propose a Multi-channel Optimization Generative Model (MOGM) for stable ultra-sparse-view CT reconstruction by integrating a novel data consistency term into the stochastic differential equation model. Notably, the unique aspect of this data consistency component is its exclusive reliance on original data for effectively confining generation outcomes. Furthermore, we pioneer an inference strategy that traces back from the current iteration result to ground truth, enhancing reconstruction stability through foundational theoretical support. We also establish a multi-channel optimization reconstruction framework, where conventional iterative techniques are employed to seek the reconstruction solution. Quantitative and qualitative assessments on 23 views datasets from numerical simulation, clinical cardiac and sheep's lung underscore the superiority of MOGM over alternative methods. Reconstructing from just 10 and 7 views, our method consistently demonstrates exceptional performance.

DERnet: a deep neural network for end-to-end reconstruction in magnetic particle imaging

Objective. Magnetic particle imaging (MPI) shows potential for contributing to biomedical research and clinical practice. However, MPI images are effectively affected by noise in the signal as its reconstruction is an ill-posed inverse problem. Thus, effective reconstruction method is required to reduce the impact of the noise while mapping signals to MPI images. Traditional methods rely on the hand-crafted data-consistency (DC) term and regularization term based on spatial priors to achieve noise-reducing and reconstruction. While these methods alleviate the ill-posedness and reduce noise effects, they may be difficult to fully capture spatial features. Approach. In this study, we propose a deep neural network for end-to-end reconstruction (DERnet) in MPI that emulates the DC term and regularization term using the feature mapping subnetwork and post-processing subnetwork, respectively, but in a data-driven manner. By doing so, DERnet can better capture signal and spatial features without relying on hand-crafted priors and strategies, thereby effectively reducing noise interference and achieving superior reconstruction quality. Main results. Our data-driven method outperforms the state-of-the-art algorithms with an improvement of 0.9–8.8 dB in terms of peak signal-to-noise ratio under various noise levels. The result demonstrates the advantages of our approach in suppressing noise interference. Furthermore, DERnet can be employed for measured data reconstruction with improved fidelity and reduced noise. In conclusion, our proposed method offers performance benefits in reducing noise interference and enhancing reconstruction quality by effectively capturing signal and spatial features. Significance. DERnet is a promising candidate method to improve MPI reconstruction performance and facilitate its more in-depth biomedical application.

Sparse-view reconstruction for photoacoustic tomography combining diffusion model with model-based iteration

As a non-invasive hybrid biomedical imaging technology, photoacoustic tomography combines high contrast of optical imaging and high penetration of acoustic imaging. However, the conventional standard reconstruction under sparse view could result in low-quality image in photoacoustic tomography. Here, a novel model-based sparse reconstruction method for photoacoustic tomography via diffusion model was proposed. A score-based diffusion model is designed for learning the prior information of the data distribution. The learned prior information is utilized as a constraint for the data consistency term of an optimization problem based on the least-square method in the model-based iterative reconstruction, aiming to achieve the optimal solution. Blood vessels simulation data and the animal in vivo experimental data were used to evaluate the performance of the proposed method. The results demonstrate that the proposed method achieves higher-quality sparse reconstruction compared with conventional reconstruction methods and U-Net. In particular, under the extreme sparse projection (e.g., 32 projections), the proposed method achieves an improvement of ∼ 260 % in structural similarity and ∼ 30 % in peak signal-to-noise ratio for in vivo data, compared with the conventional delay-and-sum method. This method has the potential to reduce the acquisition time and cost of photoacoustic tomography, which will further expand the application range.

Deep learning‐assisted model‐based off‐resonance correction for non‐Cartesian SWI

PurposePatient‐induced inhomogeneities in the static magnetic field cause distortions and blurring (off‐resonance artifacts) during acquisitions with long readouts such as in SWI. Conventional versatile correction methods based on extended Fourier models are too slow for clinical practice in computationally demanding cases such as 3D high‐resolution non‐Cartesian multi‐coil acquisitions.TheoryMost reconstruction methods can be accelerated when performing off‐resonance correction by reducing the number of iterations, compressed coils, and correction components. Recent state‐of‐the‐art unrolled deep learning architectures could help but are generally not adapted to corrupted measurements as they rely on the standard Fourier operator in the data consistency term. The combination of correction models and neural networks is therefore necessary to reduce reconstruction times.MethodsHybrid pipelines using UNets were trained stack‐by‐stack over 99 SWI 3D SPARKLING 20‐fold accelerated acquisitions at 0.6 mm isotropic resolution using different off‐resonance correction methods. Target images were obtained using slow model‐based corrections based on self‐estimated field maps. The proposed strategies, tested over 11 volumes, are compared to model‐only and network‐only pipelines.ResultsThe proposed hybrid pipelines achieved scores competing with two to three times slower baseline methods, and neural networks were observed to contribute both as pre‐conditioner and through inter‐iteration memory by allowing more degrees of freedom over the model design.ConclusionA combination of model‐based and network‐based off‐resonance correction was proposed to significantly accelerate conventional methods. Different promising synergies were observed between acceleration factors (iterations, coils, correction) and model/network that could be expanded in the future.

Accelerated partial separable model using dimension-reduced optimization technique for ultra-fast cardiac MRI

Objective. Imaging dynamic objects with high temporal resolution is challenging in magnetic resonance imaging (MRI). The partial separable (PS) model was proposed to improve imaging quality by reducing the degrees of freedom of the inverse problem. However, the PS model still suffers from a long acquisition time and an even longer reconstruction time. The main objective of this study is to accelerate the PS model, shorten the time required for acquisition and reconstruction, and maintain good image quality simultaneously. Approach. We proposed to fully exploit the dimension-reduction property of the PS model, which means implementing the optimization algorithm in subspace. We optimized the data consistency term and used a Tikhonov regularization term based on the Frobenius norm of temporal difference. The proposed dimension-reduced optimization technique was validated in free-running cardiac MRI. We have performed both retrospective experiments on a public dataset and prospective experiments on in vivo data. The proposed method was compared with four competing algorithms based on the PS model and two non-PS model methods. Main results. The proposed method has robust performance against a shortened acquisition time or suboptimal hyper-parameter settings, and achieves superior image quality over all other competing algorithms. The proposed method is 20-fold faster than the widely accepted PS+sparse method, enabling image reconstruction to be finished in just a few seconds. Significance. The accelerated PS model has the potential to save a great deal of time in clinical dynamic MRI examinations and is promising for real-time MRI applications.

Joint-Prior-Based Uneven Illumination Image Enhancement for Surface Defect Detection

Images in real surface defect detection scenes often suffer from uneven illumination. Retinex-based image enhancement methods can effectively eliminate the interference caused by uneven illumination and improve the visual quality of such images. However, these methods suffer from the loss of defect-discriminative information and a high computational burden. To address the above issues, we propose a joint-prior-based uneven illumination enhancement (JPUIE) method. Specifically, a semi-coupled retinex model is first constructed to accurately and effectively eliminate uneven illumination. Furthermore, a multiscale Gaussian-difference-based background prior is proposed to reweight the data consistency term, thereby avoiding the loss of defect information in the enhanced image. Last, by using the powerful nonlinear fitting ability of deep neural networks, a deep denoised prior is proposed to replace existing physics priors, effectively reducing the time consumption. Various experiments are carried out on public and private datasets, which are used to compare the defect images and enhanced results in a symmetric way. The experimental results demonstrate that our method is more conducive to downstream visual inspection tasks than other methods.

Seismic data recovery using deep targeted denoising priors in an alternating optimization framework

The problem of recovering the complete seismic data from undersampled field-observed data is a long-term challenge. Many recent efforts to address this problem develop model-based recovery methods. However, current model-based methods cannot accurately capture inherent priors of seismic data to obtain optimal recovery results. For this issue, we have developed a novel model-based seismic data recovery method, which integrates a deep learning (DL)-based targeted denoiser into the seismic data recovery model and leverages the deep targeted denoising priors learned by this denoiser to implement high accuracy data recovery. Specifically, we first use operator-splitting technology to decouple the data-consistency term and prior constraint term in a seismic data recovery model, resulting in an alternating optimization scheme composed of a least-squares inversion subtask and a proximal minimization subtask. The DL-based targeted denoiser, a dual-channel deep denoising network (DcDDNet), is then plugged into the alternating optimization scheme as a modular component, according to the mathematical equivalence between the proximal operator and the targeted denoiser. This modular component replaces the formalized proximal minimization subtask and plays the role of an implicit prior in the recovery optimization problem. Finally, the least-squares inversion and deep denoising subtasks in the alternating optimization scheme are iteratively executed to achieve seismic data recovery. Due to the integration of the powerful DcDDNet, this method not only enjoys high flexibility and impressive generalization capability but also has high computational efficiency and excellent performance. Synthetic and field data with regular and irregular undersampling are used to evaluate the recovery capability of this method. The results demonstrate that, compared with the f- x adaptive interpolation and curvelet-based recovery methods, our method has advantages in visual and quality metrics. In addition, this method also is more practical in seismic applications because it works in the time-space domain and can handle spatial aliasing and spectral leakage.

Hybrid data fidelity term approach for quantitative susceptibility mapping

PurposeSusceptibility maps are usually derived from local magnetic field estimations by minimizing a functional composed of a data consistency term and a regularization term. The data‐consistency term measures the difference between the desired solution and the measured data using typically the L2‐norm. It has been proposed to replace this L2‐norm with the L1‐norm, due to its robustness to outliers and reduction of streaking artifacts arising from highly noisy or strongly perturbed regions. However, in regions with high SNR, the L1‐norm yields a suboptimal denoising performance. In this work, we present a hybrid data fidelity approach that uses the L1‐norm and subsequently the L2‐norm to exploit the strengths of both norms.MethodsWe developed a hybrid data fidelity term approach for QSM (HD‐QSM) based on linear susceptibility inversion methods, with total variation regularization. Each functional is solved with ADMM. The HD‐QSM approach is a two‐stage method that first finds a fast solution of the L1‐norm functional and then uses this solution to initialize the L2‐norm functional. In both norms we included spatially variable weights that improve the quality of the reconstructions.ResultsThe HD‐QSM approach produced good quantitative reconstructions in terms of structural definition, noise reduction, and avoiding streaking artifacts comparable with nonlinear methods, but with higher computational efficiency. Reconstructions performed with this method achieved first place at the lowest RMS error category in stage 1 of the 2019 QSM Reconstruction Challenge.ConclusionsThe proposed method allows robust and accurate QSM reconstructions, obtaining superior performance to state‐of‐the‐art methods.

Learning Data Consistency and its Application to Dynamic MR Imaging.

Magnetic resonance (MR) image reconstruction from undersampled k-space data can be formulated as a minimization problem involving data consistency and image prior. Existing deep learning (DL)-based methods for MR reconstruction employ deep networks to exploit the prior information and integrate the prior knowledge into the reconstruction under the explicit constraint of data consistency, without considering the real distribution of the noise. In this work, we propose a new DL-based approach termed Learned DC that implicitly learns the data consistency with deep networks, corresponding to the actual probability distribution of system noise. The data consistency term and the prior knowledge are both embedded in the weights of the networks, which provides an utterly implicit manner of learning reconstruction model. We evaluated the proposed approach with highly undersampled dynamic data, including the dynamic cardiac cine data with up to 24-fold acceleration and dynamic rectum data with the acceleration factor equal to the number of phases. Experimental results demonstrate the superior performance of the Learned DC both quantitatively and qualitatively than the state-of-the-art.

Iterative material decomposition for spectral CT using self-supervised Noise2Noise prior

Compared to conventional computed tomography (CT), spectral CT can provide the capability of material decomposition, which can be used in many clinical diagnosis applications. However, the decomposed images can be very noisy due to the dose limit in CT scanning and the noise magnification of the material decomposition process. To alleviate this situation, we proposed an iterative one-step inversion material decomposition algorithm with a Noise2Noise prior. The algorithm estimated material images directly from projection data and used a Noise2Noise prior for denoising. In contrast to supervised deep learning methods, the designed Noise2Noise prior was built based on self-supervised learning and did not need external data for training. In our method, the data consistency term and the Noise2Noise network were alternatively optimized in the iterative framework, respectively, using a separable quadratic surrogate (SQS) and the Adam algorithm. The proposed iterative algorithm was validated and compared to other methods on simulated spectral CT data, preclinical photon-counting CT data and clinical dual-energy CT data. Quantitative analysis showed that our proposed method performs promisingly on noise suppression and structure detail recovery.

Deep Learning-Based Detection and Correction of Cardiac MR Motion Artefacts During Reconstruction for High-Quality Segmentation

Segmenting anatomical structures in medical images has been successfully addressed with deep learning methods for a range of applications. However, this success is heavily dependent on the quality of the image that is being segmented. A commonly neglected point in the medical image analysis community is the vast amount of clinical images that have severe image artefacts due to organ motion, movement of the patient and/or image acquisition related issues. In this paper, we discuss the implications of image motion artefacts on cardiac MR segmentation and compare a variety of approaches for jointly correcting for artefacts and segmenting the cardiac cavity. The method is based on our recently developed joint artefact detection and reconstruction method, which reconstructs high quality MR images from k-space using a joint loss function and essentially converts the artefact correction task to an under-sampled image reconstruction task by enforcing a data consistency term. In this paper, we propose to use a segmentation network coupled with this in an end-to-end framework. Our training optimises three different tasks: 1) image artefact detection, 2) artefact correction and 3) image segmentation. We train the reconstruction network to automatically correct for motion-related artefacts using synthetically corrupted cardiac MR k-space data and uncorrected reconstructed images. Using a test set of 500 2D+time cine MR acquisitions from the UK Biobank data set, we achieve demonstrably good image quality and high segmentation accuracy in the presence of synthetic motion artefacts. We showcase better performance compared to various image correction architectures.

Mean gradient descent: an optimization approach for single-shot interferogram analysis.

Complex object wave recovery from a single-shot interference pattern is an important practical problem in interferometry and digital holography. The most popular single-shot interferogram analysis method involves Fourier filtering of the cross term, but this method suffers from poor resolution. To obtain full pixel resolution, it is necessary to model the object wave recovery as an optimization problem. The optimization approach typically involves minimizing a cost function consisting of a data consistency term and one or more constraint terms. Despite its potential performance advantages, this method is not used widely due to several tedious and difficult tasks such as empirical tuning of free parameters. We introduce a new optimization approach, mean gradient descent (MGD), for single-shot interferogram analysis that is simple to implement. MGD does not have any free parameters whose empirical tuning is critical to the object wave recovery. The MGD iteration does not try to achieve minimization of a cost function but instead aims to reach a solution point where the data consistency and the constraint terms balance each other. This is achieved by iteratively progressing the solution in the direction that bisects the descent directions associated with the error and constraint terms. Numerical illustrations are shown for recovery of a step phase object from its corresponding off-axis as well as on-axis interferograms simulated with multiple noise levels. Our results show full pixel resolution as evident from the recovery of the phase step and excellent rms phase accuracy relative to the ground truth phase map. The concept of MGD as presented here can potentially find applications to a wider class of optimization problems.

A strategy for designing of customized electromechanical actuators of blood pumps.

Congestive heart failure is a pathology of global incidence that affects millions of people worldwide. When the heart weakens and failsto pump blood at physiological rates commensurate with the requirements of tissues, two main alternatives are cardiac transplant and ventricular assist devices (VADs). This article presents the design strategy for development of a customized VAD electromagnetic actuator. Electromagnetic actuator is a brushless direct current motor customized to drive thepump impeller by permanent magnets located in rotor-stator coupling. In this case, ceramic pivot bearings support theVAD impeller. Electronic circuitry controls rotation switching current in stator coils. The proposed methodology consisted of analytical numerical design, tridimensional computational modeling, numerical simulations using Maxwell software, actuator prototyping, and validation inthedynamometer. The axial flow actuator was chosen by its size and high power density compared to theradial flow type. First step consisted of estimating the required torque to drive thepump. Torque was estimated at 2100rpm and mean current of 0.5A. Numerical analysis using finite element method mapped vectors and fields to build stator coils and actuator assemblage. After tests in the dynamometer, experimental results werecompared with numerical simulation and validated the proposed model. In conclusion, the proposed methodology for designing of VAD electromechanical actuator was considered satisfactory in terms of data consistency, feasibility, and reliability.

Real-Time Magnetic Resonance Imaging: Radial Gradient-Echo Sequences With Nonlinear Inverse Reconstruction.

The aim of this study is to evaluate a real-time magnetic resonance imaging (MRI) method that not only promises high spatiotemporal resolution but also practical robustness in a wide range of scientific and clinical applications. The proposed method relies on highly undersampled gradient-echo sequences with radial encoding schemes. The serial image reconstruction process solves the true mathematical task that emerges as a nonlinear inverse problem with the complex image and all coil sensitivity maps as unknowns. Extensions to model-based reconstructions for quantitative parametric mapping further increase the number of unknowns, for example, by adding parameters for phase-contrast flow or T1 relaxation. In all cases, an iterative numerical solution that minimizes a respective cost function is achieved with use of the iteratively regularized Gauss-Newton method. Convergence is supported by regularization, for example, to the preceding frame, whereas temporal fidelity is ensured by downsizing the regularization strength in comparison to the data consistency term in each iterative step. Practical implementations of highly parallelized algorithms are realized on a computer with multiple graphical processing units. It is "invisibly" integrated into a commercial 3-T MRI system to allow for conventional usage and to provide online reconstruction, display, and storage of regular DICOM image series. Depending on the application, the proposed method offers serial imaging, that is, the recording of MRI movies, with variable spatial resolution and up to 100 frames per second (fps)-corresponding to 10 milliseconds image acquisition times. For example, movements of the temporomandibular joint during opening and closing of the mouth are visualized with use of simultaneous dual-slice movies of both joints at 2 × 10 fps (50 milliseconds per frame). Cardiac function may be studied at 30 to 50 fps (33.3 to 20 milliseconds), whereas articulation processes typically require 50 fps (20 milliseconds) or orthogonal dual-slice acquisitions at 2 × 25 fps (20 milliseconds). Methodological extensions to model-based reconstructions achieve improved quantitative mapping of flow velocities and T1 relaxation times in a variety of clinical scenarios. Real-time gradient-echo MRI with extreme radial undersampling and nonlinear inverse reconstruction allows for direct monitoring of arbitrary physiological processes and body functions. In many cases, pertinent applications offer hitherto impossible clinical studies (eg, of high-resolution swallowing dynamics) or bear the potential to replace existing MRI procedures (eg, electrocardiogram-gated cardiac examinations). As a consequence, many novel opportunities will require a change of paradigm in MRI-based radiology. At this stage, extended clinical trials are needed.

ARMAX Modeling and Impedance Analysis of Voltammetric E-Tongue for Evaluation of Infused Tea

This paper presents a modeling technique to analyze the performance of the electrodes of a custom made voltammetric e-tongue. In this methodology, autoregressive moving average models are estimated for five working electrodes of the e-tongue made of different noble metals in classifying three different classes of infused tea. The experimental input-output responses of the electrodes are used for modeling. The model transfer functions are fitted to an equivalent circuit from which the circuit impedances and electrical parameters are derived. We propose that there is a transition frequency at which values of the electrical parameters shift from positive to negative. The performance of the electrodes is analyzed in terms of data consistency, stability, and formation of negative parameters. Therefore, the proposed modeling technique can be used for selecting the electrodes and the operating frequency to improve the performance of the e-tongue.

Dynamic MRI using model-based deep learning and SToRM priors: MoDL-SToRM.

To introduce a novel framework to combine deep-learned priors along with complementary image regularization penalties to reconstruct free breathing & ungated cardiac MRI data from highly undersampled multi-channel measurements. Image recovery is formulated as an optimization problem, where the cost function is the sum of data consistency term, convolutional neural network (CNN) denoising prior, and SmooThness regularization on manifolds (SToRM) prior that exploits the manifold structure of images in the dataset. An iterative algorithm, which alternates between denoizing of the image data using CNN and SToRM, and conjugate gradients (CG) step that minimizes the data consistency cost is introduced. Unrolling the iterative algorithm yields a deep network, which is trained using exemplar data. The experimental results demonstrate that the proposed framework can offer fast recovery of free breathing and ungated cardiac MRI data from less than 8.2s of acquisition time per slice. The reconstructions are comparable in image quality to SToRM reconstructions from 42s of acquisition time, offering a fivefold reduction in scan time. The results show the benefit in combining deep learned CNN priors with complementary image regularization penalties. Specifically, this work demonstrates the benefit in combining the CNN prior that exploits local and population generalizable redundancies together with SToRM, which capitalizes on patient-specific information including cardiac and respiratory patterns. The synergistic combination is facilitated by the proposed framework.

An Empirical Orthogonal Function-Based Algorithm for Estimating Terrestrial Latent Heat Flux from Eddy Covariance, Meteorological and Satellite Observations.

Accurate estimation of latent heat flux (LE) based on remote sensing data is critical in characterizing terrestrial ecosystems and modeling land surface processes. Many LE products were released during the past few decades, but their quality might not meet the requirements in terms of data consistency and estimation accuracy. Merging multiple algorithms could be an effective way to improve the quality of existing LE products. In this paper, we present a data integration method based on modified empirical orthogonal function (EOF) analysis to integrate the Moderate Resolution Imaging Spectroradiometer (MODIS) LE product (MOD16) and the Priestley-Taylor LE algorithm of Jet Propulsion Laboratory (PT-JPL) estimate. Twenty-two eddy covariance (EC) sites with LE observation were chosen to evaluate our algorithm, showing that the proposed EOF fusion method was capable of integrating the two satellite data sets with improved consistency and reduced uncertainties. Further efforts were needed to evaluate and improve the proposed algorithm at larger spatial scales and time periods, and over different land cover types.

Wideband impedance spectroscopy from 1 mHz to 10 MHz by combination of four- and two-electrode methods

Impedance Spectroscopy (IS) measurements allow to study a wide range of polarization mechanisms associated with different frequency ranges. Experimental devices usually cover limited frequency ranges with sufficient accuracy. We propose (a) a combination of four-electrode and two-electrode devices and (b) a data combination and mutual verification procedure using the actual sample under test. Hereby, we cover a frequency range from 1mHz to 10MHz. The data combination relies on the precondition that any dispersive disturbance decayed at some mutual point within an overlapping frequency range between 1Hz and 45kHz. We validate our data combination procedure by IS measurements on simple reference systems and comparison with widely accepted model functions, e.g. the complex refractive index model (CRIM) for high frequency behavior and Kramers–Kronig relations in terms of data consistency. In this respect, our suggested processing approach is superior to two selected alternative approaches. We successfully adapt typical empirical model functions, e.g. multi-Cole–Cole, to the resulting wideband data to show that they are fully applicable for further data analysis.