Least-squares Fitting Algorithm Research Articles

Near-Infrared Broadband Cavity-Enhanced Spectroscopic Multigas Sensor Using a 1650 nm Light Emitting Diode.

A near-infrared broadband cavity-enhanced sensor system was demonstrated for the first time using an energy-efficient light emitting diode (LED) with a central emission wavelength at 1650 nm and a light power of ∼16 mW. A portable absorption gas cell was designed for realizing a compact and stable optical system for easy alignment. An ultrashort 8-cm-long cavity was fabricated consisting of two mirrors with a ∼99.35% reflectivity. Methane (CH4) measurement was performed employing two detection schemes, i.e., NIRQuest InGaAs spectrometer and scanning monochromator combined with phase-sensitive detection. Retrieval of CH4 concentration was performed using a least-squares fitting algorithm. Sensitivities (i.e., minimum detectable absorption coefficient) were achieved of 1.25 × 10-6 cm-1 for an averaging time of 45 s using the NIRQuest InGaAs spectrometer and 1.85 × 10-6 cm-1 for an averaging time of 8 min using the scanning spectrometer in combination with lock-in detection. Field monitoring of CH4 gas leakage was performed using the NIRQuest spectrometer. Multigas sensing of CH4 and acetylene (C2H2) was carried out simultaneously using the high-resolution scanning spectrometer. A linear response of the retrieved concentration level versus nominal value was observed with a large dynamic range, demonstrating the reliability of the compact LED-based near-infrared broadband cavity-enhanced absorption spectroscopy (NIR-IBBCEAS) for multigas sensing applications.

Automated measurements of lumbar lordosis in T2-MR images using decision tree classifier and morphological image processing

Lumbar spine’s lordosis is a very important parameter functionally and clinically; it is a key feature in maintaining the sagittal balance, in addition to its crucial role in evaluating the spinal deformities. The main objective of the current study is to present a fully-automated measurement of the lumbar spine’s lordotic curve angle in T2-MR images. This goal has been achieved by the automatic measurement of lordosis radius at the lumbar spine level by computer-aided methods utilizing data mining classification and image segmentation followed by morphological image processing. The spine has been segmented from the entire image using a machine-learning technique that is based on texture features for recognizing the lumbar-spine pattern. The extracted features were fed to C4.5 decision tree classifier for designing the lumbar-spine recognition system. The resultant classifier’s “if-then” rules have been employed for segmenting the spine region from the entire image. Multiple morphological image processes have been applied to the raw segmentation result to enhance the true positive rate and suppressing the false positive rate. The mean radius of lumbar spine’s curvature has been evaluated by fitting the contours average to the closest circle using least-square fitting algorithm which was followed by calculating the lumbar lordosis curvature angle. The proposed approach has been tested and validated on normal and pathological T2-MR spine images and found to perform effectively. The calculation of lumbar lordosis angles showed a strong correlation with the Cobb angle measurements (R = 93.2%).

Anisotropic Material Properties of Wild-Type and Tectb−/− Tectorial Membranes

The tectorial membrane (TM) is an extracellular matrix that is directly coupled with the mechanoelectrical receptors responsible for sensory transduction and amplification. As such, the TM is often hypothesized to play a key role in the remarkable sensory abilities of the mammalian cochlea. Genetic studies targeting TM proteins have shown that changes in TM structure dramatically affect cochlear function in mice. Precise information about the mechanical properties of the TMs of wild-type and mutant mice at audio frequencies is required to elucidate the role of the TM and to understand how these genetic mutations affect cochlear mechanics. In this study, images of isolated TM segments are used to determine both the radial and longitudinal motions of the TM in response to a harmonic radial excitation. The resulting longitudinally propagating radial displacement and highly spatially dependent longitudinal displacement are modeled using finite-element models that take into account the anisotropy and finite dimensions of TMs. An automated, least-square fitting algorithm is used to find the anisotropic material properties of wild-type and Tectb−/− mice at audio frequencies. Within the auditory frequency range, it is found that the TM is a highly viscoelastic and anisotropic structure with significantly higher stiffness in the direction of the collagen fibers. Although no decrease in the stiffness in the fiber direction is observed, the stiffness of the TM in shear and in the transverse direction is found to be significantly reduced in Tectb−/− mice. As a result, TMs of the mutant mice tend to be significantly more anisotropic within the frequency range examined in this study. The effects of the Tectb−/− mutation on the TM’s anisotropic material properties may be responsible for the changes in cochlear tuning and sensitivity that have been previously reported for these mice.

Data Reduction Pipeline of the TOU Optical Very High Resolution Spectrograph and Its sub-m s−1 Performance

TOU is an extremely high resolution optical spectrograph (R=$100,000$, 380-900~nm), which is designed to detect low mass exoplanets using the radial velocity technique.We describe an IDL-based radial velocity (RV) data reduction pipeline for the TOU spectrograph and its performance with stable stars. This pipeline uses a least-squares fitting algorithm to match observed stellar spectra to a high signal-to-noise template created for each star. By carefully controlling all of the error contributions to RV measurements in both the hardware and data pipeline, we have achieved $\sim$0.9\ms long-term RV precision with one of the most RV stable stars, Tau Ceti, similar to what has been achieved with HARPS. This paper presents steps and details in our data pipeline on how to reach the \sms RV precision and also all major error sources which contribute to the final RV measurement uncertainties. The lessons learned in this pipeline development can be applied to other environmentally controlled, very high resolution optical spectrographs to improve RV precision.

PV System Control to Provide Active Power Reserves Under Partial Shading Conditions

The challenges of modern power systems will inevitably impose increased ancillary service requirements to photovoltaic (PV) plants in the future, including operating reserves. Recent studies have investigated methods to maintain active power reserves without energy storage in the standard case of uniform illumination. In this paper, this functionality is extended to partial shading conditions, often encountered in PV systems. A new control scheme is proposed that permits operation at a reduced power level, estimating at the same time the shading conditions and maximum available power. This is achieved by applying a least-squares curve fitting algorithm on voltage and current measurements, without relying on any irradiance or temperature sensors. To the best of our knowledge, this is the first power reserves control scheme for PV systems under partial shading presented in the literature. The robustness and effectiveness of the proposed method are validated under rapidly changing shading conditions through simulations and experimental tests on a 2-kW PV system prototype.

A multi-arc approach for chaotic orbit determination problems

Chaotic dynamical systems are characterized by the existence of a predictability horizon, connected to the notion of Lyapunov time, beyond which predictions of the state of the system are meaningless. In order to study the main features of orbit determination in the presence of chaos, Spoto and Milani (Celest Mech Dyn Astron 124:295–309, 2016) applied the classical least-squares fit and differential correction algorithm to determine a chaotic orbit and a dynamical parameter of a simple discrete system—Chirikov standard map (cf. Chirikov in Phys Rep 52:263, 1979)—with observations distributed beyond the predictability horizon. They found a time limit beyond which numerical calculations are affected by numerical instability: the computability horizon. In this article, we aim at pushing forward such inherent obstacle to numerical calculations in chaotic orbit determination by applying the classical and the constrained multi-arc method (cf. Alessi et al. in Mon Not R Astron Soc 423:2270–2278, 2012) to the same dynamical system. These strategies entail the determination of an orbit when observations are grouped in separate observed arcs. For each arc, a set of initial conditions is determined and, in the case of the constrained multi-arc method, all subsequent arcs are constrained to belong to the same trajectory. We show that the use of these techniques in place of the standard least-squares method has significant advantages: Not only can we perform accurate numerical calculations well beyond the computability horizon, in particular, the constrained multi-arc strategy improves considerably the determination of the dynamical parameter.

Boosting the use of thermoacoustimetry in micellization thermodynamics studies by easing an objective determination of the cmc

The thermodynamics of micellization of decyl-β-d-glucopyranoside (β-C10G1) in aqueous solution is studied from multiple-temperature (283.15–323.15 K) speed of sound and density measurements. The Williams method being unsuited to estimate the cmc, we propose the Carpena method (widely used in the cmc determination from conductivity data) as an objective and easy-to-use alternative. Its performance is checked by comparison with a well-established but quite complex procedure: the combination of the Runge-Kutta numerical integrations method and the Levenberg–Marquardt least-squares fitting algorithm. As a result of this investigation, three temperature regions are associated to a β-C10G1 micellization governed by entropy (I), by enthalpy (III), or by both of them (II). Besides, the adsorption of β-C10G1 and β-C12G1 at the solution/air interface is revisited from surface tension measurements at several temperatures and reviews of literature data.

Characterizing anisotropic, viscoelastic material properties of the tectorial membranes of wild-type and mutant mice using longitudinally propagating waves

The tectorial membrane (TM) is an important structural component of the mammalian inner ear. Examination of cochlear physiology in genetically modified mice has demonstrated that mutation of genes affecting TM proteins causes changes in key characteristics of cochlear function. Characterizing the differences in material properties between wild-type and mutant mice could provide insight into the source of reported differences in cochlear physiology. In this study, optical images of isolated TM segments of wild-type and genetically modified mice in response to harmonic radial excitation at acoustic frequencies are used to determine the amplitude and phase of the motion. Wave propagation on the TM segments is modeled using finite element models that take into account the anisotropy, viscoelasticity, and finite dimensions of the TM and the presence of a viscous boundary layer. An automated least-square fitting algorithm is used to find anisotropic, viscoelastic material parameters of wild-type and mutant mice TMs at acoustic frequencies. The resulting material properties are compared to previous estimates of the TM properties.The tectorial membrane (TM) is an important structural component of the mammalian inner ear. Examination of cochlear physiology in genetically modified mice has demonstrated that mutation of genes affecting TM proteins causes changes in key characteristics of cochlear function. Characterizing the differences in material properties between wild-type and mutant mice could provide insight into the source of reported differences in cochlear physiology. In this study, optical images of isolated TM segments of wild-type and genetically modified mice in response to harmonic radial excitation at acoustic frequencies are used to determine the amplitude and phase of the motion. Wave propagation on the TM segments is modeled using finite element models that take into account the anisotropy, viscoelasticity, and finite dimensions of the TM and the presence of a viscous boundary layer. An automated least-square fitting algorithm is used to find anisotropic, viscoelastic material parameters of wild-type and mutant mice...

Testing the effect of computer-generated hologram fabrication error in a cylindrical interferometry system

This paper presents a method of testing the effect of computer-generated hologram (CGH) fabrication error in a cylindrical interferometry system. An experimental system is developed for calibrating the effect of this error. In the calibrating system, a mirror with high surface accuracy is placed at the focal axis of the cylindrical wave. After transmitting through the CGH, the reflected cylindrical wave can be transformed into a plane wave again, and then the plane wave interferes with the reference plane wave. Finally, the double-pass transmitted wavefront of the CGH, representing the effect of the CGH fabrication error in the experimental system, is obtained by analyzing the interferogram. The mathematical model of misalignment aberration removal in the calibration system is described, and the feasibility is demonstrated via the simulation system established in Zemax. With the mathematical polynomial, most of the possible misalignment errors can be estimated with the least-squares fitting algorithm, and then the double-pass transmitted wavefront of the CGH can be obtained by subtracting the misalignment errors from the result extracted from the real experimental system. Compared to the standard double-pass transmitted wavefront given by Diffraction International Ltd., which manufactured the CGH used in the experimental system, the result is desirable. We conclude that the proposed method is effective in calibrating the effect of the CGH error in the cylindrical interferometry system for the measurement of cylindricity error.

Quantitative chemical exchange saturation transfer (CEST) MRI of glioma using Image Downsampling Expedited Adaptive Least-squares (IDEAL) fitting

Chemical Exchange Saturation Transfer (CEST) MRI is sensitive to dilute metabolites with exchangeable protons, allowing tissue characterization in diseases such as acute stroke and tumor. CEST quantification using multi-pool Lorentzian fitting is challenging due to its strong dependence on image signal-to-noise ratio (SNR), initial values and boundaries. Herein we proposed an Image Downsampling Expedited Adaptive Least-squares (IDEAL) fitting algorithm that quantifies CEST images based on initial values from multi-pool Lorentzian fitting of iteratively less downsampled images until the original resolution. The IDEAL fitting in phantom data with superimposed noise provided smaller coefficient of variation and higher contrast-to-noise ratio at a faster fitting speed compared to conventional fitting. We further applied the IDEAL fitting to quantify CEST MRI in rat gliomas and confirmed its advantage for in vivo CEST quantification. In addition to significant changes in amide proton transfer and semisolid macromolecular magnetization transfer effects, the IDEAL fitting revealed pronounced negative contrasts of tumors in the fitted CEST maps at 2 ppm and −1.6 ppm, likely arising from changes in creatine level and nuclear overhauser effects, which were not found using conventional method. It is anticipated that the proposed method can be generalized to quantify MRI data where SNR is suboptimal.

Precise Determination of Brillouin Scattering Spectrum Using a Virtually Imaged Phase Array (VIPA) Spectrometer and Charge-Coupled Device (CCD) Camera.

Brillouin spectroscopy is an emerging tool for microscopic optical imaging as it allows noninvasive assessment of viscoelastic properties of materials. The use of atomic-molecular absorption cells as ultra-narrow notch filters allows acquisition of Brillouin spectra from turbid samples despite their strong elastic scattering. However, such systems alter the shapes of the Brillouin lines, making the precise determination of the Brillouin shift difficult. In this report, we propose a simple method for analyzing the Brillouin spectrum using a customized least-square fitting algorithm. The absorption spectrum induced by the atomic-molecular cell was taken into consideration. The capability of the method is confirmed by processing experimental spectroscopic data from the pure water at different temperatures. The accuracy of the measurements of ±1 MHz spectral line shift is experimentally demonstrated.

Stress measurement of thin film on flexible substrate by using projection moiré method and heterodyne interferometry

We propose a stress measurement system based on a projection moire method and heterodyne interferometry for thin films on a flexible substrate. In the measurement setup, a CMOS camera in which every pixel can receive a series of heterodyne moire signals by using a continuously relative displacement with a constant velocity is used. Furthermore, the phase of the optimized sinusoidal curve and the surface profile of the flexible substrate are determined using a least-squares sine fitting algorithm. The thin-film stress is obtained by representing the cross-sectional curve of the surface profile by using a polynomial fitting method, estimating the resultant curvature radii of the uncoated and coated substrates, and using these two radii in the corrected Stoney formula. The proposed measurement system has the advantages of high accuracy, high resolution, and high capacity for substrates with high flexibility and a large measurement depth.

Automatic extraction of highway light poles and towers from mobile LiDAR data

Mobile LiDAR has been recently demonstrated as a viable technique for pole-like object detection and classification. Despite that a desirable accuracy (around 80%) has been reported in the existing studies, majority of them were presented in the street level with relatively flat ground and very few of them addressed how to extract the entire pole structure from the ground or curb surface. Therefore, this paper attempts to fill the research gap by presenting a workflow for automatic extraction of light poles and towers from mobile LiDAR data point cloud, with a particular focus on municipal highway. The data processing workflow includes (1) an automatic ground filtering mechanism to separate aboveground and ground features, (2) an unsupervised clustering algorithm to cluster the aboveground data point cloud, (3) a set of decision rules to identify and classify potential light poles and towers, and (4) a least-squares circle fitting algorithm to fit the circular pole structure so as to remove the ground points. The workflow was tested with a set of mobile LiDAR data collected for a section of highway 401 located in Toronto, Ontario, Canada. The results showed that the proposed method can achieve an over 91% of detection rate for five types of light poles and towers along the study area.

Modeling of Swine Diaphragmatic Tissue Under Uniaxial Loading1

Modeling of Swine Diaphragmatic Tissue Under Uniaxial Loading1

Tone-assisted time delay interferometry on GRACE Follow-On

We have demonstrated the viability of using the Laser Ranging Interferometer on the Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) space mission to test key aspects of the interspacecraft interferometry proposed for detecting gravitational waves. The Laser Ranging Interferometer on GRACE-FO will be the first demonstration of interspacecraft interferometry. GRACE-FO shares many similarities with proposed space-based gravitational wave detectors based on the Laser Interferometer Space Antenna (LISA) concept. Given these similarities, GRACE-FO provides a unique opportunity to test novel interspacecraft interferometry techniques that a LISA-like mission will use. The LISA Experience from GRACE-FO Optical Payload (LEGOP) is a project developing tests of arm locking and time delay interferometry (TDI), two frequency stabilization techniques, that could be performed on GRACE-FO. In the proposed LEGOP TDI demonstration one GRACE-FO spacecraft will have a free-running laser while the laser on the other spacecraft will be locked to a cavity. It is proposed that two one-way interspacecraft phase measurements will be combined with an appropriate delay in order to produce a round-trip, dual one-way ranging (DOWR) measurement independent of the frequency noise of the free-running laser. This paper describes simulated and experimental tests of a tone-assisted TDI ranging (TDIR) technique that uses a least-squares fitting algorithm and fractional-delay interpolation to find and implement the delays needed to form the DOWR TDI combination. The simulation verifies tone-assisted TDIR works under GRACE-FO conditions. Using simulated GRACE-FO signals the tone-assisted TDIR algorithm estimates the time-varying interspacecraft range with a rms error of $\ifmmode\pm\else\textpm\fi{}0.2\text{ }\text{ }\mathrm{m}$, suppressing the free-running laser frequency noise by 8 orders of magnitude. The experimental results demonstrate the practicability of the technique, measuring the delay at the 6 ns level in the presence of a significant displacement signal.

An efficient calculation method for pharmacokinetic parameters in brain permeability study using dynamic contrast-enhanced MRI.

To develop an efficient method for calculating pharmacokinetic (PK) parameters in brain DCE-MRI permeability studies. A linear least-squares fitting algorithm based on a derivative expression of the two-compartment PK model was proposed to analytically solve for the PK parameters. Noise in the expression was minimized through low-pass filtering. Simulation studies were conducted in which the proposed method was compared with two existing methods in terms of accuracy and efficiency. Five in vivo brain studies were demonstrated for potential clinical application. In the simulation studies using chosen parameter values, the calculated percent difference of K(trans) by the proposed method was <5.0% with a temporal resolution (Δt) < 5 s, and the accuracies of all parameter results were better or comparable to existing methods. When analyzed within certain parameter intensity ranges, the proposed method was more accurate than the existing methods and improved the efficiency by a factor of up to 458 for a Δt = 1 s and up to 38 for a Δt = 5 s. In the in vivo study, the calculated parameters using the proposed method were comparable to those using the existing methods with improved efficiencies. An efficient method was developed for the accurate and efficient calculation of parameters in brain DCE-MRI permeability studies.

Automatic static contact angle algorithm for blurry drop images and its application in hydrophobicity measurement for insulating materials

To improve the accuracy of the static contact angle evaluation for the blurry drop images, a large number of water drop images are numerically generated or acquired by the contact angle instrument/digital camera. Based on these images, the applicability of the circle Hough transformation and circle fitting algorithms is systematically investigated and compared. The results reveal that the least-squares circle fitting algorithm is particularly suitable for the clear drop images, such as the images acquired by the contact angle instrument. The circle Hough transformation is particularly suitable for the blurry drop images, such as the images acquired by the digital camera. The influence of the contact angle on the contact angle error by the circle Hough transformation is investigated. The critical contact angle values corresponding to various water drop volumes are given, which can be used to improve the accuracy of the static contact angle measurement for the blurry drop images. A modified Hough transformation based on the critical contact angle is proposed. The modified Hough transformation is verified by the static contact angle measurements of different insulating materials. The study proposes a comparatively effective algorithm for automatic and accurate static contact angle measurement of the blurry drop images.

Improved magnetogram calibration of Solar Magnetic Field Telescope and its comparison with the Helioseismic and Magnetic Imager

In this paper, we try to improve the magnetogram calibration method of the Solar Magnetic Field Telescope (SMFT). The improved calibration process fits the observed full Stokes information, using six points on the profile of Fe i 5324.18 Å line, and the analytical Stokes profiles under the Milne–Eddington atmosphere model, adopting the Levenberg–Marquardt least-squares fitting algorithm. In comparison with the linear calibration methods, which employs one point, there is a large difference in the strength of longitudinal field Bl and transverse field Bt, caused by the non-linear relationship, but the discrepancy is little in the case of inclination and azimuth. We conclude that it is better to deal with the non-linear effects in the calibration of Bl and Bt using six points. Moreover, in comparison with Solar Dynamics Observatory/Helioseismic and Magnetic Imager (HMI), SMFT has larger stray light and acquires less magnetic field strength. For vector magnetic fields in two sunspot regions, the magnetic field strength, inclination and azimuth angles between SMFT and HMI are roughly in agreement, with the linear fitted slopes of 0.73/0.7, 0.95/1.04 and 0.99/1.1. In the case of pores and quiet regions (Bl < 600 G), the fitted slopes of the longitudinal magnetic field strength are 0.78 and 0.87, respectively.

The high precision positioning algorithm of circular landmark center in visual measurement

For vision measurement in the center circle landmark location problem, an improved center of the ellipse based on Zernike moments sub-pixel positioning algorithm was proposed. First, using Sobel operator edge of the image pixel level positioning and then use the constructed Zernike moments to solve the model, combined with Zernike orthogonal polynomials and completeness and plural moment magnitude rotational invariance calculated edge sub-pixel position; followed by analysis of the principle deviation generated by the moments template and ideals model, a correction formula was proposed to compensate and improved edge criterion used to image sub-pixel edge positioning; finally, using the least-squares ellipse fitting algorithm fitting circle center, reverse edge point, filtered residuals larger point, and then precise positioning of the ellipse center. The experimental results show that this method has good stability and high positioning accuracy can be efficiently used in many applications.

A Low-Cost Stereo Vision System for Real-Time Pose Estimation and its Application for Robot Tracking

In this paper, a 3-D pose estimation system by using stereo vision with low-cost devices is presented. It is developed as a base system for application development. Two webcams and a planar target with circular markers are used to reduce development cost and computational complexity. To avoid correspondence search problem, user has to select regions of interest (ROI’s) of each marker on the two images in the same sequence before starting the 3-D reconstruction process. Linear triangulation method is applied for 3-D position calculation of each marker. These positions and the positions of the markers referenced in the planar target coordinate frame are used for pose estimation by using least-squares fitting algorithm to obtain the position and orientation of the planar target. The system can be applied for robot tracking as shown in the experiments. The experimental results validate the system’s ability to estimate object pose in real-time with minimum system frequency of 25 Hz.