Low-frequency Errors Research Articles

Evaluating Bioinformatics Processing of Somatic Variant Detection in cfDNA Using Targeted Sequencing with UMIs.

Circulating tumor DNA (ctDNA) is a promising cancer biomarker, but accurately detecting tumor mutations in cell-free DNA (cfDNA) is challenging due to their low frequency and sequencing errors. Our study benchmarked Mutect2, VarScan2, shearwater, and DREAMS-vc using deep targeted sequencing of cfDNA with Unique Molecular Identifiers (UMIs) from 111 colorectal cancer patients. Performance was assessed at both the mutation level (distinguish tumor variants from errors) and the sample level (detect if an individual has cancer). Additionally, we investigated the effects of various UMI grouping and consensus strategies. The shearwater-AND variant calling method demonstrated the highest precision in detecting tumor-derived mutations from plasma, and reached the highest ROC-AUC of 0.984 for sample classification in tumor-informed cfDNA analyses. DREAMS-vc exhibited the highest ROC-AUC of 0.808 for sample classification in tumor-agnostic studies. We also found that sequencing depth differences in PBMCs could lead to false positives, particularly with VarScan2 and Mutect2, which was addressed by downsampling to equivalent mean depths. Additionally, network-based UMI grouping methods outperformed those using identical UMIs when all reads were retained. Our findings emphasize that the optimal variant caller depends on the study context-whether focused on mutation or sample classification, and whether conducted under tumor-informed or tumor-agnostic conditions.

Correction of systematic low-frequency time delay errors in THz systems by absorption line shape optimization

Time-domain terahertz systems can face challenges due to systematic delay errors introduced by the employed delay mechanism, potentially leading to poor data quality. This article introduces a procedure to address these challenges by correcting low-frequency systematic errors that distort the acquired spectra and incorrectly diminish narrow absorption features. Our procedure solves an optimization problem aiming to find the corrected time-signal pairs that maximize the depth of narrow absorption features, and we highlight how the flexibility of the procedure, in principle, allows for correcting error profiles of arbitrary shape. We demonstrate the effectiveness of this approach through experiments using both simulated and experimentally recorded THz data, and the results show significant improvements in spectral accuracy. We believe this can pave the way for more reliable and precise terahertz spectroscopy measurements, enhancing its applications in various scientific and industrial fields.

Extrinsic parameters optimization for fringe projection system based on standard components

Fringe projection profilometry (FPP) is a wildly used three-dimension reconstruction method, where the reconstruction accuracy is closely related to the calibration precision. However, various sources of error in the calibration process can result in inaccurate calibration results. In particular, the calibration results of extrinsic parameters are more likely to deviate from the true values, which in turn leads to low-frequency errors in the reconstruction results. In order to obtain the extrinsic parameters closer to the true values, a simple but effective method is proposed in this paper. The proposed method utilizes the standard plane and the dumbbell bat, which are commonly used in measurements, to optimize the extrinsic parameters. First, the standard plane and dumbbell bat are reconstructed using the initial calibration results to transfer the errors in the extrinsic parameters to the plane fitting residuals, as well as to the fitting residuals for the radius and the center distance of dumbbell bat. The residuals and errors are then minimized using nonlinear optimization, resulting in the more accurate extrinsic parameters. Experimental results demonstrate that the proposed method can effectively compensate the calibration error of the extrinsic parameters. The root mean square (RMS) error of planar reconstruction is reduced from 0.0291 mm to 0.0106 mm, which is reduced by about 63.6 %. The RMS error of spherical reconstruction is reduced from 0.0358 mm to 0.0166 mm, which is about 53.6 %. The measurement accuracy of the FPP system is further improved.

A Multi-Scale Numerical Simulation Method Considering Anisotropic Relative Permeability

Most of the oil reservoirs in China are fluvial deposits with firm reservoir heterogeneity, where differences in fluid flow capacity in individual directions should not be ignored; however, the available commercial reservoir simulation software cannot consider the anisotropy of the relative permeability. To handle this challenge, this paper takes full advantage of the parallelism of the multi-scale finite volume (MsFV) method and establishes a multi-scale numerical simulation approach that incorporates the effects of reservoir anisotropy. The methodology is initiated by constructing an oil–water black-oil model considering the anisotropic relative permeability. Subsequently, the base model undergoes decoupling through a sequential solution, formulating the pressure and transport equations. Following this, a multi-scale grid system is configured, within which the pressure and transport equations are progressively developed in the fine-scale grid domain. Ultimately, the improved multi-scale finite volume (IMsFV) method is applied to mitigate low-frequency error in the coarse-scale grid, thereby enhancing computational efficiency. This paper introduces two primary innovations. The first is the development of a multi-scale solution method for the pressure equation incorporating anisotropic relative permeability. Validated using the Egg model, a comparative analysis with traditional numerical simulations demonstrates a significant improvement in computational speed without sacrificing accuracy. The second innovation involves applying the multi-scale framework to investigate the impact of anisotropy relative permeability on waterflooding performance, uncovering distinct mechanisms by which absolute and relative permeability anisotropy influence waterflooding outcomes. Therefore, the IMsFV method can be used as an effective tool for high-resolution simulation and precise residual oil prediction in anisotropic reservoirs.

Wavelength Cut-Off Error of Spectral Density from MTF3 of SWIM Instrument Onboard CFOSAT: An Investigation from Buoy Data

The Surface Waves Investigation and Monitoring instrument (SWIM) provides the directional wave spectrum within the wavelength range of 23–500 m, corresponding to a frequency range of 0.056–0.26 Hz in deep water. This frequency range is narrower than the 0.02–0.485 Hz frequency range of buoys used to validate the SWIM nadir Significant Wave Height (SWH). The modulation transfer function used in the current version of the SWIM data product normalizes the energy of the wave spectrum using the nadir SWH. A discrepancy in the cut-off frequency/wavelength ranges between the nadir and off-nadir beams can lead to an overestimation of off-nadir cut-off SWHs and, consequently, the spectral densities of SWIM wave spectra. This study investigates such errors in SWHs due to the wavelength cut-off effect using buoy data. Results show that this wavelength cut-off error of SWH is small in general thanks to the high-frequency extension of the resolved frequency range. The corresponding high-frequency cut-off errors are systematic errors amenable to statistical correction, and the low-frequency cut-off error can be significant under swell-dominated conditions. By leveraging the properties of these errors, we successfully corrected the high-frequency cut-off SWH error using an artificial neural network and mitigated the low-frequency cut-off SWH error with the help of a numerical wave hindcast. These corrections significantly reduced the error in the estimated cut-off SWH, improving the bias, root-mean-square error, and correlation coefficient from 0.086 m, 0.111 m, and 0.9976 to 0 m, 0.039 m, and 0.9994, respectively.

Study on the influence of a magnetorheological finishing path on the mid-frequency errors of optical element surfaces

Magnetorheological finishing (MRF) is a deterministic optical processing technique based on CCOS that achieves high removal efficiency and processing accuracy while reducing subsurface damage. This technique still suffers from multiple iterations of processing due to variations in removal efficiency and the inability to fully correct mid-frequency errors below the cut-off frequency of the removal function. For the above problems, this paper attempted to establish the error model of removal function efficiency change for predicting the change of MRF efficiency. Based on the analysis of the distribution of surface shape residuals under different machining paths, a process combining spiral scanning and raster scanning is proposed, which can realize the correction of surface shape and restrain the deterioration of mid-frequency errors. The experimental results show that when the low-frequency errors of fused silica element surface converge rapidly, by optimizing the machining removal coefficient and using the spiral scanning and raster scanning combined method, the PSD analysis results show that the mid-frequency errors of the combined process is lower than the initial value, which expands the process route for the MRF of high-precision optical elements.

Near-field beamforming method based on motion model analysis for UAVs communication

This study presents a near-field beamforming method for the moving swarm composed of unmanned aerial vehicles (UAVs) to address the challenges of position errors that hinder effective beamforming. Firstly, a model with positional errors in moving UAVs was developed. The sources and characteristics of UAVs’ position errors were analyzed and classified into low-frequency motion errors and high-frequency vibration errors, and their effects on UAVs array beamforming were analyzed using coordinate transformation and decomposition. Secondly, a parameter estimation algorithm was proposed based on the Fast Fourier Transformation (FFT) and the Least Square (LS) method to estimate the unknown parameters of the UAV's low-frequency motion errors. Lastly, a near-field beamforming algorithm for UAVs was proposed based on the Interpolation Kalman filter (IKF). The effectiveness of the proposed model and algorithms was verified through simulations, which provided a theoretical basis for the near-field beamforming under the existence of the UAVs position errors.

Predicting bathymetry based on vertical gravity gradient anomaly and analyses for various influential factors

The prediction of bathymetry has advanced significantly with the development of satellite altimetry. However, the majority of its data originate from marine gravity anomaly. In this study, based on the expression of vertical gravity gradient (VGG) of a rectangular prism, the governing equations for determining sea depths to invert bathymetry. The governing equation is solved by linearization through an iterative process, and numerical simulations verify its algorithm and its stability. We also study the processing methods of different interference errors. The regularization method improves the stability of the inversion process for errors. A piecewise bilinear interpolation function roughly replaces the low-frequency error, and numerical simulations show that the accuracy can be improved by 41.2 % after this treatment. For variable ocean crust density, simulation simulations verify that the root-mean-square (RMS) error of prediction is approximately 5 m for the sea depth of 6 km if density is chosen as the average one. Finally, two test regions in the South China Sea are predicted and compared with ship soundings data, RMS errors of predictions are 71.1 m and 91.4 m, respectively.

Analysis of false reasons based on the artificial intelligence RRCART model to identify frozen sections of lymph nodes in breast cancer.

Breast cancer is the most common malignant tumor in the world. Intraoperative frozen section of sentinel lymph nodes is an important basis for determining whether axillary lymph node dissection is required for breast cancer surgery. We propose an RRCART model based on a deep-learning network to identify metastases in 2362 frozen sections and count the wrongly identified sections and the associated reasons. The purpose is to summarize the factors that affect the accuracy of the artificial intelligence model and propose corresponding solutions. We took the pathological diagnosis of senior pathologists as the gold standard and identified errors. The pathologists and artificial intelligence engineers jointly read the images and heatmaps to determine the locations of the identified errors on sections, and the pathologists found the reasons (false reasons) for the errors. Through NVivo 12 Plus, qualitative analysis of word frequency analysis and nodal analysis was performed on the error reasons, and the top-down error reason framework of "artificial intelligence RRCART model to identify frozen sections of breast cancer lymph nodes" was constructed based on the importance of false reasons. There were 101 incorrectly identified sections in 2362 slides, including 42 false negatives and 59 false positives. Through NVivo 12 Plus software, the error causes were node-coded, and finally, 2 parent nodes (high-frequency error, low-frequency error) and 5 child nodes (section quality, normal lymph node structure, secondary reaction of lymph nodes, micrometastasis, and special growth pattern of tumor) were obtained; among them, the error of highest frequency was that caused by normal lymph node structure, with a total of 45 cases (44.55%), followed by micrometastasis, which occurred in 30 cases (29.70%). The causes of identification errors in examination of sentinel lymph node frozen sections by artificial intelligence are, in descending order of influence, normal lymph node structure, micrometastases, section quality, special tumor growth patterns and secondary lymph node reactions. In this study, by constructing an artificial intelligence model to identify the error causes of frozen sections of lymph nodes in breast cancer and by analyzing the model in detail, we found that poor quality of slices was the preproblem of many identification errors, which can lead to other errors, such as unclear recognition of lymph node structure by computer. Therefore, we believe that the process of artificial intelligence pathological diagnosis should be optimized, and the quality control of the pathological sections included in the artificial intelligence reading should be carried out first to exclude the influence of poor section quality on the computer model. For cases of micrometastasis, we suggest that by differentiating slices into high- and low-confidence groups, low-confidence micrometastatic slices can be separated for manual identification. The normal lymph node structure can be improved by adding samples and training the model in a targeted manner.

Comparative Study on Predicting Topography from Gravity Anomaly and Gravity Gradient Anomaly

Owing to the dependence of algorithms on the measurement of ship soundings and geophysical parameters, the accuracy and coverage of topography still need to be improved. Previous studies have mostly predicted topography using gravity or gravity gradient, However, there is a relative lack of integrated research combining or comparing gravity and gravity gradient. In this study, we develop observation equations to predict topography based on vertical gravity anomalies (VG; also called gravity anomalies) and vertical gravity gradient (VGG) anomalies generated by a rectangular prism. The sources of interference are divided into medium- to high-frequency errors and low-frequency errors, and these new methods reduce these errors through regularization and error equations. We also use numerical simulations to test the efficiency of the algorithm and error-reduction method. Statistics show that VGG anomalies are more sensitive to topographic fluctuations; however, the linear correlation between VG anomalies and topography is stronger. Additionally, we use the EIGEN-6C4 model of VG and VGG anomalies to predict topography in shallow and deep-sea areas, with maximum depths of 2 km and 5 km, respectively. In the shallow and deep-sea areas, the root mean square (RMS) errors of VGG anomalies prediction are 93.8 m and 233.8 m, and the corresponding accuracies improved by 7.3% and 2.3% compared with those of VG anomaly prediction, respectively. Furthermore, we use cubic spline interpolation to fuse ship soundings and improve the accuracy of the final topography results. We develop a novel analytical algorithm by constructing an observation equation system applicable to VG and VGG anomalies. This will provide new insights and directions to refine topography prediction based on VG and VGG anomalies.

Design and frequency control study of small-sized magnetorheological finishing device applied in optical manufacturing

With the continuous development of various advanced optical systems, there is an increasing demand for optical components with small apertures (generally ranging from a few millimeters to tens of millimeters in diameter), steep slopes, or even specific relief structures on their surfaces (such as continuous phase elements). These optical components all require high surface quality and shape accuracy. However, existing magnetorheological finishing (MRF) devices have larger dimensions, and the obtained removal function size is relatively larger than the size of small-diameter optical components, making it difficult to achieve high surface shape accuracy after processing. To achieve high-precision machining of small-aperture optical components and obtain higher frequency control capabilities, this study first designed and optimized a small-size MRF device with a 13 mm polishing wheel. Based on theoretical and finite element simulation analyses, the magnetic pole structure of the small-size MRF device was designed. The orthogonal experimental method was used to optimize the key parameters of the magnetic pole according to the magnetic field design requirements, and the device was constructed. Its performance and stability were experimentally analyzed, and the results showed that the peak magnetic field intensity in the polishing area of the device was about 230mT, which met the polishing requirements, and both its long-term and short-term processing stabilities met the design requirements. In addition, different sizes of removal functions were analyzed for frequency control ability, and theoretical and spectral analyses of the removal function indicated that the small-size removal function had better low-frequency error correction ability, while for mid-frequency band and mid-frequency ripple error, the opposite was true. The experimental results showed that when the optical component was shaped by 20 %, the low-frequency convergence capability of the 100 mm polishing device was only 18.72 %, much lower than that of the 13 mm polishing device, which was 52.51 %.Moreover, the mid-frequency ripple spectrum amplitude for the 13 mm polishing device was more than 15 times higher than that for the 100 mm polishing device when removing 50 nm material, and the mid-frequency root mean square (RMS) increased significantly, deteriorating the surface mid-frequency error of the optical component. Therefore, when performing magnetorheological polishing on an optical component surface, a process of using large-size MRF devices for roughing combined with small-size MRF devices for finishing can ensure machining efficiency while controlling low-frequency and mid-frequency errors well. This study provides theoretical support for the magnetic pole design of MRF devices and broadens the frequency spectrum correction ability and application range of MRF processes, which has great application value.

The Impact of Different Filters on the Gravity Field Recovery Based on the GOCE Gradient Data

The electrostatic gravity gradiometer carried by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite is affected by accelerometer noise and other factors; hence, the observation data present complex error characteristics in the low-frequency domain. The accuracy of the recovered gravity field will be directly affected by the design of the filters based on the error characteristics of the gradient data. In this study, the applicability of various filters to different errors in observation is evaluated, such as the 1/f error and the orbital frequency errors. The experimental results show that the cascade filter (DARMA), which is formed of a differential filter and an autoregressive moving average filter (ARMA) filter, has the best accuracy for the characteristic of the 1/f low-frequency error. The strategy of introducing empirical parameters can reduce the orbital frequency errors, whereas the application of a notch filter will worsen the final solution. Frequent orbit changes and other changes in the observed environment have little impact on the new version gradient data (the data product is coded 0202), while the influence cannot be ignored on the results of the old version data (the data product is coded 0103). The influence can be effectively minimized by shortening the length of the arc. By analyzing the above experimental findings, it can be concluded that the inversion accuracy can be effectively improved by choosing the appropriate filter combination and filter estimation frequency when solving the gravity field model based on the gradient data of the GOCE satellite. This is of reference significance for the updating of the existing models.

Characterized environmental influences on autocollimator measurement uncertainty using an extended Allan variance

Autocollimators play an important role in the high-precision testing of the slope errors of X-ray and large flat mirrors. However, the time-varying errors caused by environmental changes exhibit different characteristics over time, such as low-frequency drift errors and high-frequency random errors. Time-varying errors can seriously affect the accuracy of the autocollimator (AC) and the read repeatability. They have become important factors limiting the continued improvement of nano-optic-measuring machines and scanning pentaprism system accuracy. Considering the difficulty in quantitatively analyzing the influence of time-varying errors on the measurement uncertainties of the AC, this paper proposes the extended Allan variance to characterize environmental influences on the AC measurement uncertainty based on a point-wise scanning measurement mode. Taking advantage of the extended Allan variance's characteristics, which allow the identification of various errors and provide stability information about the AC measurement, the characteristic curves of the AC measurement uncertainty in a specific environment were obtained. Based on the characteristic curve parameters, the ultimate accuracy of AC in the current environment was obtained by optimizing the measurement strategy. Experimental results show that the measurement uncertainty of the AC can reach 2.3 nrad RMS in the measurement time-domain window.

Research on the influence of the non-stationary effect of the magnetorheological finishing removal function on mid-frequency errors of optical component surfaces.

With the continuous development of modern optical systems, the demand for full spatial frequency errors of optical components in the system is increasing. Although computer-controlled sub-aperture polishing technology can quickly correct low-frequency errors, this technology significantly worsens the mid-frequency errors on the surface of the component, which greatly inhibits the improvement of optical system performance. Therefore, we conducted in-depth research on the non-stationary effect of the removal function caused by the fluctuation in magnetorheological polishing and their influence on the mid-frequency errors of the component surface. We established a non-stationary profile model of the removal function and applied this model to simulate the distribution of mid-frequency errors on the surface of the processed component, considering the non-stationary effect. The simulation results showed that the non-stationary effect of the removal function weaken the mid-frequency ripple errors but increase other mid-frequency errors. Therefore, we first proposed the optimal single-material removal thickness corresponding to the non-stationary effect and experimentally verified the effectiveness of the optimal material removal thickness in suppressing mid-frequency errors. The experimental results showed that when the magnetorheological finishing single-material removal thickness is set to the optimal value, both the mid-frequency ripple errors and the mid-frequency RMS on the surface significantly decrease. Therefore, this work provides a basis for improving the existing magnetorheological finishing process and effectively suppressing the mid-frequency errors on the surface of processed components. It also provides theoretical and technical support for the magnetorheological processing and manufacturing of high-precision optical components. At the same time, the non-stationary effect and the corresponding analytical models has the potential to be extended to other polishing tools.

An Improved Coupled Data Assimilation System with a CGCM Using Multi-Time-Scale High-Efficiency EnOI-Like Filtering

Abstract Coupled data assimilation (CDA), which combines coupled models and observations from multiple Earth system domains, plays a critical role in climate studies by producing a four-dimensional estimation of Earth system states. Traditional ensemble Kalman filter (EnKF) CDA algorithms, while convenient to implement in multiple DA components in a coupled system, are, however, expensive and lack sufficient representativeness for low-frequency background flows. Here, a multi-time-scale high-efficiency approximate filter with ensemble optimal interpolation (MSHea-EnOI) scheme has been implemented with a global fully coupled model. It consists of stationary, low-frequency, and high-frequency filters constructed from the time series of a single-model solution with improved representativeness for low-frequency background error statistics and enhanced computational efficiency. The MSHea-EnOI is evaluated in a biased twin experiment framework with synthetic “observations” produced by another coupled model, and a three-decade coupled reanalysis experiment with real observations. Results show that with increased representativeness on multiscale background flows, while computationally costing only a small fraction of ensemble-based CDA, the MSHea-EnOI shows the potential to improve CDA quality with synthetic observations. The coupled reanalysis experiment with real observations also shows reasonable fittings to observations and comparable results to other reanalysis products using different DA schemes. While reconstructing a close-to-rapid Atlantic meridional overturning circulation, the coupled reanalysis reproduces most of the atmosphere and ocean reanalysis signals such as the Hadley circulation and upper ocean heat content. The MSHea-EnOI could have good application potential in ensemble-based DA systems in terms of its multiscale property and computational efficiency.

BDS Dual-Frequency Carrier Phase Multipath Hemispherical Map Model and Its Application in Real-Time Deformation Monitoring.

The BDS multipath delay error is highly related to the surrounding monitoring environment, which cannot be eliminated or mitigated by applying the double difference observation model. In the actual monitoring environment, due to the complexity of the BDS constellation, it is difficult for existing algorithms to consider GEO, IGSO, MEO and other different orbital types of satellites for real-time and efficient multipath error reduction. Therefore, we propose a novel BDS dual-frequency multipath error reduction method for real deformation monitoring for BDS considering various satellite orbit types. This method extracts the single error residual of each satellite based on the assumption of "zero mean" and divides the appropriate grid density of GEO and IGSO/MEO, respectively, to construct a dual-frequency multipath hemispherical map model suitable for BDS satellites with different orbital types. This method can realize the multipath error elimination of the observed values of different orbits and different frequencies. The results of simulation experiments and real deformation monitoring data demonstrate that this method can effectively eliminate low-frequency multipath delay errors in the observation domain and coordinate domain. After multipath correction, the precision of the horizontal coordinates and height coordinates are 1.7 mm and 4.6 mm. The precision of the horizontal coordinate and height coordinate is increased by 50% and 60%, respectively. The fixed rate of ambiguity increased by 5-7%.

Comprehensive analysis on the magnetic field error of a K–Rb–21Ne comagnetometer with low-frequency bias magnetic field sensitivity

The spin-exchange relaxation-free comagnetometer (SERFC) is of important research value compared to existing high-precision gyroscopes because of its extremely high theoretical limit sensitivity and long-term stability, in which one significant limiting factor is the magnetic field error. First, the relationship between the magnetic field gradient and the nuclear spin relaxation mechanism is introduced into the frequency response and steady-state response models of SERFC. Then, a novel method for suppression of the low-frequency magnetic field error based on the modified bias magnetic field sensitivity model is proposed. Finally, the effectiveness of the proposed suppression methods is demonstrated by optimizing the cell temperature, pump light power, and compensation magnetic field gradient to increase the suppression factor by 72.19%, 20.24%, and 69.86%, and the corresponding bias instability increased by 55.41%, 20.84%, and 27.63%, respectively. This study contributes to improving the long-term zero bias stability of the SERFC.

High-order implicit time integration scheme with controllable numerical dissipation based on mixed-order Padé expansions

A single-step high-order implicit time integration scheme with controllable numerical dissipation at high frequencies is presented for the transient analysis of structural dynamic problems. The amount of numerical dissipation is controlled by a user-specified value of the spectral radius ρ∞ in the high frequency limit. Using this user-specified parameter as a weight factor, a Padé expansion of the matrix exponential solution of the equation of motion is constructed by mixing the diagonal and sub-diagonal expansions. An efficient time-stepping scheme is designed where systems of equations, similar in complexity to the standard Newmark method, are solved recursively. It is shown that the proposed high-order scheme achieves high-frequency dissipation, while minimizing low-frequency dissipation and period errors. The effectiveness of the provided dissipation control and the efficiency of the scheme are demonstrated by numerical examples. A simple guideline for the choice of the controlling parameter and time step size is provided. The source codes written in MATLAB and FORTRAN are available for download at: https://github.com/ChongminSong/HighOrderTimeIntegration.

Mid-high-frequency error suppression of small optical aspheric molds.

To suppress the mid-high-frequency error of small optical tungsten carbide aspheric molds, it is proposed to quickly select the critical process parameters by simulating the residual error after convolution of the tool influence function (TIF). After polishing for 10.47min by the TIF, two simulation optimizations, RMS and Ra, converge to 9.3 and 5.347nm, respectively. Their convergence rates are improved by 40% and 7.9%, respectively, compared to ordinary TIF. Then, a faster and more high-quality multi-tool combination smoothing suppression method is proposed, and the corresponding polishing tools are designed. Finally, the global Ra of the aspheric surface converges from 5.9 to 4.5nm after smoothing for 5.5min with a disc-shaped polishing tool with a fine microstructure and maintains an excellent low-frequency error (PV 0.0781µm).

An interpretable MRI reconstruction network with two-grid-cycle correction and geometric prior distillation

Although existing deep learning compressed-sensing-based Magnetic Resonance Imaging (CS-MRI) methods have achieved considerably impressive performance, explainability and generalizability continue to be challenging for such methods since the transition from mathematical analysis to network design not always natural enough, often most of them are not flexible enough to handle multi-sampling-ratio reconstruction assignments. In this work, to tackle explainability and generalizability, we propose a unifying deep unfolding multi-sampling-ratio interpretable CS-MRI framework. The combined approach offers more generalizability than previous works whereas deep learning gains explainability through a geometric prior module. Inspired by the multigrid algorithm, we first embed the CS-MRI-based optimization algorithm into correction-distillation scheme that consists of three ingredients: pre-relaxation module, correction module and geometric prior distillation module. Furthermore, we employ a condition module to learn adaptively step-length and noise level, which enables the proposed framework to jointly train multi-ratio tasks through a single model. The proposed model not only compensates for the lost contextual information of reconstructed image which is refined from low frequency error in geometric characteristic k-space, but also integrates the theoretical guarantee of model-based methods and the superior reconstruction performances of deep learning-based methods. Therefore, it can give us a novel perspective to design biomedical imaging networks. Numerical experiments show that our framework outperforms state-of-the-art methods in terms of qualitative and quantitative evaluations. Our method achieves 3.18 dB improvement at low CS ratio 10% and average 1.42 dB improvement over other comparison methods on brain dataset using Cartesian sampling mask.