Damped Least-squares Algorithm Research Articles

Effective Electrical Impedance Tomography Based on Enhanced Encoder–Decoder Using Atrous Spatial Pyramid Pooling Module

Electrical impedance tomography (EIT) is a noninvasive and radiation-free imaging method. As a "soft-field" imaging technique, in EIT, the target signal in the center of the measured field is frequently swamped by the target signal at the edge, which restricts its further application. To alleviate this problem, this study presents an enhanced encoder-decoder (EED) method with an atrous spatial pyramid pooling (ASPP) module. The proposed method enhances the ability to detect central weak targets by constructing an ASPP module that integrates multiscale information in the encoder. The multilevel semantic features are fused in the decoder to improve the boundary reconstruction accuracy of the center target. The average absolute error of the imaging results by the EED method reduced by 82.0%, 83.6%, and 36.5% in simulation experiments and 83.0%, 83.2%, and 36.1% in physical experiments compared with the errors of the damped least-squares algorithm, Kalman filtering method, and U-Net-based imaging method, respectively. The average structural similarity improved by 37.3%, 42.9%, and 3.6%, and 39.2%, 45.2%, and 3.8% in the simulation and physical experiments, respectively. The proposed method provides a practical and reliable means of extending the application of EIT by solving the problem of weak central target reconstruction under the effect of strong edge targets in EIT.

Fast Iterative Shrinkage-Thresholding Algorithm with Continuation for Brain Injury Monitoring Imaging Based on Electrical Impedance Tomography.

Electrical impedance tomography (EIT) is low-cost and noninvasive and has the potential for real-time imaging and bedside monitoring of brain injury. However, brain injury monitoring by EIT imaging suffers from image noise (IN) and resolution problems, causing blurred reconstructions. To address these problems, a least absolute shrinkage and selection operator model is built, and a fast iterative shrinkage-thresholding algorithm with continuation (FISTA-C) is proposed. Results of numerical simulations and head phantom experiments indicate that FISTA-C reduces IN by 63.2%, 47.2%, and 29.9% and 54.4%, 44.7%, and 22.7%, respectively, when compared with the damped least-squares algorithm, the split Bergman, and the FISTA algorithms. When the signal-to-noise ratio of the measurements is 80-50 dB, FISTA-C can reduce IN by 83.3%, 72.3%, and 68.7% on average when compared with the three algorithms, respectively. Both simulation and phantom experiments suggest that FISTA-C produces the best image resolution and can identify the two closest targets. Moreover, FISTA-C is more practical for clinical application because it does not require excessive parameter adjustments. This technology can provide better reconstruction performance and significantly outperforms the traditional algorithms in terms of IN and resolution and is expected to offer a general algorithm for brain injury monitoring imaging via EIT.

Enhanced Heart Rate Prediction Model Using Damped Least-Squares Algorithm.

Monitoring a patient's vital signs is considered one of the most challenging problems in telehealth systems, especially when patients reside in remote locations. Companies now use IoT devices such as wearable devices to participate in telehealth systems. However, the steady adoption of wearables can result in a significant increase in the volume of data being collected and transmitted. As these devices run on limited battery power, they can run out of power quickly due to the high processing requirements of the device for data collection and transmission. Given the importance of medical data, it is imperative that all transmitted data adhere to strict integrity and availability requirements. Reducing the volume of healthcare data and the frequency of transmission can improve a device's battery life via an inference algorithm. Furthermore, this approach creates issues for improving transmission metrics related to accuracy and efficiency, which are traded-off against each other, with increasing accuracy reducing efficiency. This paper demonstrates that machine learning (ML) can be used to overcome the trade-off problem. The damped least-squares algorithm (DLSA) is used to enhance both metrics by taking fewer samples for transmission whilst maintaining accuracy. The algorithm is tested with a standard heart rate dataset to compare the metrics. The results showed that the DLSA provides the best performance, with an efficiency of 3.33 times for reduced sample data size and an accuracy of 95.6%, with similar accuracies observed in seven different sampling cases adopted for testing that demonstrate improved efficiency. This proposed method significantly improve both metrics using ML without sacrificing one metric over the other compared to existing methods with high efficiency.

An Improved Weighted Gradient Projection Method for Inverse Kinematics of Redundant Surgical Manipulators.

Different from traditional redundant manipulators, the redundant manipulators used in the surgical environment require the end effector (EE) to have high pose (position and orientation) accuracy to ensure the smooth progress of the operation. When analyzing the inverse kinematics (IK) of traditional redundant manipulators, gradient-projection method (GPM) and weighted least-norm (WLN) method are commonly used methods to avoid joint position limits. However, for the traditional GPM and WLN method, when joints are close to their limits, they stop moving, which greatly reduces the accuracy of the IK solution. When robotic manipulators enter a singular region, although traditional damped least-squares (DLS) algorithms are used to handle singularities effectively, motion errors of the EE will be introduced. Furthermore, selecting singular region through trial and error may cause some joint velocities exceed their corresponding limits. More importantly, traditional DLS algorithms cannot guide robotic manipulators away from singular regions. Inspired by the merits of GPM, WLN, and DLS methods, an improved weighted gradient projection method (IWGPM) is proposed to solve the IK problem of redundant manipulators used in the surgical environment with avoiding joint position limits and singularities. The weighted matrix of the WLN method and the damping factor of the DLS algorithm have been improved, and a joint limit repulsive potential field function and singular repulsive potential field function belong to the null space are introduced to completely keep joints away from the damping interval and redundant manipulators away from the unsafe region. To verify the validity of the proposed IWGPM, simulations on a 7 degree of freedom (DOF) redundant manipulator used in laparoscopic surgery indicate that the proposed method can not only achieve higher accuracy IK solution but also avoid joint position limits and singularities effectively by comparing them with the results of the traditional GPM and WLN method, respectively. Furthermore, based on the proposed IWGPM, simulation tests in two cases show that joint position limits have a great impact on the orientation accuracy, and singular potential energy function has a great impact on the position accuracy.

Design and development of an optical reflective notch filter using the ion assisted deposition technique with stepwise modulated thickness for avionics applications.

This paper presents research work about the design and fabrication of a 44-layer optical reflective notch filter. The performance of the fabricated notch filter was studied at normal (0°) and oblique (45°) incidence angle. In addition, the paper also discusses a three-layer broadband antireflective coating on both sides of the multilayer stack to suppress the ripples in the passband region. The thickness-modulated reflective stack of the filter was designed by using the materials Al2O3 (1.63) and SiO2 (1.46). Optimization of the multilayer stack was carried out by using the damped least-squares algorithm. The theoretical and experimental results from the ion-assisted e-beam deposited samples for single notch reflective filters are presented. Good agreement in the design and experimental results was observed when the deposition process was controlled by time of evaporation. Further, the filter was characterized for the optical properties by using a UV-VIS-NIR spectrophotometer, surface morphology and protective properties using field emission scanning electron microscopy, a coherence correlation interferometer, and water contact angle.

Transient electromagnetic 1D inversion based on the PSO–DLS combination algorithm

ABSTRACTTo improve the inversion results of roadway or tunnel transient electromagnetic detection data, particle swarm optimisation (PSO) and damped least squares (DLS) algorithms are combined. This overcomes the shortcomings of the PSO algorithm, namely that it has lower optimisation efficiency in the later stage, and the DLS algorithm, which requires manual assignment of initial values. With reference to actual stratum data, the mathematical model is established, and the inversion trial calculation is carried out using PSO, DLS and the proposed combined PSO–DLS algorithm. The results show that the combined PSO–DLS algorithm has higher optimisation efficiency without manual assignment of the starting model. The combined PSO–DLS algorithm is used to invert the measured transient electromagnetic data of the mine roadway, which realises separation of the mine roof and floor resistivity anomalies. Compared with PSO and DLS, the interpretation results for PSO–DLS are most consistent with the logging data, geological data and roadway exposure conditions.

An iterative damped least-squares algorithm for simultaneously monitoring the development of hemorrhagic and secondary ischemic lesions in brain injuries.

Electrical impedance tomography (EIT) is a non-invasive and real-time imaging method that has the potential to be used for monitoring intracerebral hemorrhage (ICH). Recent studies have proposed that ischemia secondary to ICH occurs simultaneously in the brain. Real-time monitoring of the development of hemorrhage and risk of secondary ischemia is crucial for clinical intervention. However, few studies have explored the performance of EIT monitoring in cases where hemorrhage and secondary ischemia exist. When these lesions get close to each other, or their conductivity and volume changes differ greatly, it becomes challenging for dynamic EIT algorithms to simultaneously reconstruct subtle injuries. To address this, an iterative damped least-squares (IDLS) algorithm is proposed in this study. The quality of the IDLS algorithm was assessed using blur radius and temporal response during computer simulation and a phantom 3D head-shaped model where bidirectional disturbance targets were simulated. The results showed that the IDLS algorithm enhanced contrast and concurrently reconstructed bidirectional disturbance targets in images. Moreover, it showed superior performance in decreasing the blur radius and was time cost-effective. With further improvement, the IDLS algorithm has the potential to be used for monitoring the development of hemorrhage and risk of ischemia secondary to ICH. Graphical abstract (a) and (b) are simulation images of bidirectional disturbance targets with different change ratios of volume (Vr) and conductivity (σr) based on the damped least-squares (DLS) algorithm and iterative damped least-squared (IDLS) algorithm, respectively. (c) shows the performance metrics of blur radius and temporal response with different volume ratio (corresponding to Vr). (d) shows the performance metrics of blur radius and temporal response with different conductivity change percentage (corresponding to σr).

Estimation of fracture weaknesses and integrated attenuation factors from azimuthal variations in seismic amplitudes

Seismic wave propagation in fractured reservoirs exhibits anisotropy and attenuation, which are in turn related to fracture properties (e.g., fracture density) and fluid parameters (e.g., moduli and viscosity). Based on the linear slip theory, stiffness parameters can be determined for fractured and dissipative rocks, from which integrated attenuation factors involving host-rock intrinsic attenuation and fracture-induced attenuation emerge. Using a simplified mathematical form for these stiffness parameters, a linearized mathematical relationship directly relating the reflection coefficient to fracture weaknesses and integrated attenuation factors is available. A two-step inversion approach, involving (1) an iterative damped least-squares algorithm to predict P- and S-wave moduli using seismic angle gathers along the fracture orientation azimuth and (2) an iterative inversion method to estimate fracture weaknesses and integrated attenuation factors from azimuthal amplitude differences, is examined. The objective function for the second step is constructed based on a Bayesian framework. Synthetic testing confirms that fracture weaknesses and integrated attenuation factors are stably determined from seismic amplitudes exhibiting a moderate signal-to-noise ratio. The approach is applied to a field data set from a fractured carbonate reservoir. We observe that geologically reasonable results of fracture weaknesses and integrated attenuation factors are obtained. We conclude that this estimation procedure provides a reliable tool in fracture prediction and inverted attenuation factors appear as additional proofs to identify fluid type in fractured reservoirs.

Unidirectional coupler optimization of surface plasmon polaritons based on the damped least-squares method

Controlling the launching efficiency and the directionality of surface plasmon polaritons is a major goal for the development of plasmonic devices. This study presents the use of the damped least-squares method to optimize the geometry parameters of a surface plasmon polariton unidirectional coupler. A damped least-squares algorithm has been constructed and the performance of a surface plasmon polariton unidirectional coupler has been obtained with COMSOL LiveLink for MATLAB. We have optimized a quasi-periodic surface plasmon polariton unidirectional grating coupler, which consists of five groups of sub-wavelength groove-doublets with an extinction ratio of nearly 71 dB. Combination of the COMSOL and the damped least-squares method in a MATLAB environment is a practicable method for the design of a surface plasmon polariton unidirectional coupler. Moreover, the general design principles behind this study can readily be extended to other numeric algorithms and other plasmonic devices.

Shear-wave velocity structure of the shallow sediments in the Bohai Sea from an ocean-bottom-seismometer survey

To investigate the seismic velocity structure of the shallow sediments in the Bohai Sea of China, we conducted a shear-wave velocity inversion of the surface-wave dispersion data from a survey of 12 ocean-bottom seismometers (OBSs) and 377 shots of a [Formula: see text] air gun. With OBS station spacing of approximately 5 km and air-gun shot spacing of approximately 190 m, high-quality Scholte-wave data were recorded by the OBSs within 0.4–5 km offset. We retrieved the Scholte-wave phase-velocity dispersion for the fundamental mode and first overtone in the frequency band of 0.9–3.0 Hz with the phase-shift method and inverted for the shear-wave velocity structure of the shallow sediments with a damped iterative least-squares algorithm. Pseudo-2D shear-wave velocity profiles with a depth of approximately 400 m revealed coherent features of relatively weak lateral velocity variation. We also estimated the uncertainty in shear-wave velocity structure based on the pseudo-2D profiles from six trial inversions with different initial models, which suggested a velocity uncertainty less than [Formula: see text] for most parts of the 2D profiles. The layered structure with little lateral variation may be attributable to the continuous sedimentary environment in the Cenozoic sedimentary basin of the Bohai Bay basin. The shear-wave velocity of 200–300 [Formula: see text] in the top 100 m of the Bohai seafloor may provide important information for offshore site response studies in earthquake engineering. Furthermore, the very low shear-wave velocity structure (150–600 [Formula: see text]) down to 400 m depth could produce a significant traveltime delay of approximately 1 s in the shear-wave arrivals, which needs to be considered to avoid serious bias in shear-wave traveltime tomographic models.

Modelling and compact inversion of magnetic data: A Matlab code

The modelling and inversion of the total magnetic field (TMF), its vertical gradient (VGTMF) and the vertical component of TMF (VMF) according to the basic principle to minimize the cross-sectional area of the source bodies are described. The software code, with an interactive graphical interface, operates in Matlab environment (version 7.0). The code of the inversion procedure is based on a weighted–damped least-squares algorithm, according to a criterion of balancing the weight of the data inaccuracies and the compactness of the solution. We have applied the approach to both synthetic and field data. This software can be used for didactical purposes or for a fast estimate of magnetic source bodies in archaeological and environmental prospecting.

Chaotic behavior in an algorithm to escape from poor local minima in lens design

In lens design, damped least-squares methods are typically used to find the nearest local minimum to a starting configuration in the merit function landscape. In this paper, we explore the use of such a method for a purpose that goes beyond local optimization. The merit function barrier, which separates an unsatisfactory solution from a neighboring one that is better, can be overcome by using low damping and by allowing the merit function to temporarily increase. However, such an algorithm displays chaos, chaotic transients and other types of complex behavior. A successful escape of the iteration trajectory from a poor local minimum to a better one is associated with a crisis phenomenon that transforms a chaotic attractor into a chaotic saddle. The present analysis also enables a better understanding of peculiarities encountered with damped least-squares algorithms in conventional local optimization tasks.

Instabilities and fractal basins of attraction in optical system optimization

Many optical design programs use various forms of the damped least-squares method for local optimization. In this paper, we show that damped least-squares algorithms, with maximized computational speed, can create sensitivity with respect to changes in initial conditions. In such cases, starting points, which are very close to each other, lead to different local minima after optimization. Computations of the fractal capacity dimension show that sets of these starting points, which lead to the same minimum (the basins of attraction for that minimum), have a fractal structure. Introducing more damping makes the optimization process stable.

Simulation methods for multipole imaging systems and aberration correctors

Two different methods have been derived and implemented for simulation of multipole imaging systems and aberration correctors. The first method uses an aberration theory for combinations of multipole lenses and deflectors, including primary and secondary aberrations up to the fifth order. A damped least-squares algorithm is used to minimise the dynamically correctable aberrations. This yields the appropriate signals for the dynamic correction elements, e.g. stigmators and dynamic focus lenses. The second method uses a direct ray-tracing approach. The numerically computed multipole lens and deflection fields are fitted with analytic functions through which trajectories are directly traced with a high degree of self-consistency. By computing the paths of many particles simultaneously, the combined effects of aberrations and discrete Coulomb interactions are accurately simulated. Furthermore, the effects of electrical and mechanical asymmetries on the multipole elements can readily be simulated with this approach.

An Experimental Study of Resolved Acceleration Control of Robots at Singularities: Damped Least-Squares Approach

Most of the robot task space control methods based on inverse Jacobian matrix suffer from instability in singular regions of workspace. Methods based on damped least-squares algorithm (DLS) for matrix inversion have been developed but not experimentally confirmed. The application of DLS method at the kinematic control level has been reported in (Chiaverini et al., 1994). In this article, a modified DLS method combined with the resolved-acceleration control scheme, is experimentally verified on two degrees of freedom of a PUMA-560 robot. In order to decrease the position error introduced by the damping, only small singular values are damped, in contrast to the conventional damping method were all the singular values are damped. The symbolic expressions of the singular value decomposition of the Jacobian matrix were used, to decrease the computational burden.

Numerical calibration of the angle of incidence in ellipsometers

The experimental error in the angle of incidence strongly affects the film optical constants and thickness sought from the ellipsometric data, particularly when the film is thinner than 200 Å. This angle should therefore be accurately measured and this has been a frequently faced difficulty, especially in fixed-angle-of-incidence and in situ ellipsometers. We describe in this paper two numerical calibration procedures evaluating the angle of incidence from the ellipsometric data and measured on well-identified film - substrate reflecting structures either with a known or with an unknown film refractive index. The procedures rapidly determine the angle of incidence independently of the film thickness. An error analysis shows that the angle of incidence can thus be determined with an uncertainty of a few hundredths of a degree from ellipsometers inducing the same order of angular errors. The thickness ranges of films yielding such lower uncertainties are deduced from the error analysis. The effect of substrate real index error on this uncertainty is studied in particular. The supplementary results produced therein may be used in data interpretation while checking the angle of incidence if it is accurately measured by some other method. The procedures may also be easily adopted to variably damped least-squares (VDLS) algorithms employed in real-time monitoring of films during growth. The calibration procedures are illustrated for all these aspects with experimental data from real reflecting systems.

Moment tensor inversion of local earthquake data-I. Investigation of the method and its numerical stability with model calculations

SUMMARY Two methods for moment tensor inversion of waveform data (Sipkin 1982) are examined for applicability to high-frequency near-source data. This study focuses on two subjects, namely the numerical aspects of the inversion method and the various kinds of assumptions being made from the theory. It is shown that the moment tensor inversion methods are theoretically unstable if only far-field SH seismograms are used due to dependencies and vanishing of different Green's functions. Additional instabilities are found even for the P–SV problem, which are caused by numerical effects. In order to remove these problems the inversion methods are modified by a damped least-squares algorithm, estimating the useful range of damping parameters from singular value analysis. Numerical tests are performed on synthetic near-source data with simulated traveltime errors assuming a wrong source location or misidentification of phases. Bias from extended sources with directivity is investigated. It is concluded that the modified inversion method is robust with respect to such data sets.

Optimisation and fabrication of grating beamsplitters

Optimisation of certain holographic 1 to N and 1 to N*N beamsplitters (Dammann gratings) with the aid of simulated annealing and damped least-squares algorithms is considered. Structures with N=5 to 53 uniform beams have been calculated. A photolithographic technique for fabrication of these elements is also presented, and its accuracy analysed with the aid of numerical simulations and actual test results.

Digital restoration of blurred images in speckle noise by a two-step procedure

A two-step procedure for restoring blurred images in speckle noise is described. The restoration method includes a local-statistics algorithm for smoothing speckle noise and an iterative damped least-squares algorithm for removal of the blur. We present some experimental results that demonstrate the effectiveness of the proposed procedure.

パーソナルコンピュータによる高効率ピーク分離法 ＩＩ 波形分割とデータ削減

To speed up the curve-fitting calculation for peak-separation, efficient data division and data reduction techniques were developed on the DLS (damped least-squares) algrithm. According to those techniques, the observed curve is automatically divided to several limits of isolated overlapping peaks. After that the curve-fitting based on the DLS algorithm is carried out for each limits separately with reducing the data by equal-interval samplings. The reduction interval is changed after three iterations to reduce the calculation time, and these intervals were determined from the chi square test of fitting-errors. A visible emission and an IR absorption spectra were separated to several Gaussian and Lorentzian peaks by a personal computer in BASIC language. The calculation time was reduced less than one-third of a conventional DLS method.