scholarly journals Hermite Interpolation Based Interval Shannon-Cosine Wavelet and Its Application in Sparse Representation of Curve

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 1
Author(s):  
Aiping Wang ◽  
Li Li ◽  
Shuli Mei ◽  
Kexin Meng
Keyword(s):  
Wavelet Transform ◽  
Hermite Interpolation ◽  
Boundary Effect ◽  
Absolute Error ◽  
Maximum Error ◽  
Reconstruction Method ◽  
Infinite Domain ◽  
Curve Reconstruction ◽  
Piecewise Function ◽  
Almost All

Using the wavelet transform defined in the infinite domain to process the signal defined in finite interval, the wavelet transform coefficients at the boundary are usually very large. It will bring severe boundary effect, which reduces the calculation accuracy. The construction of interval wavelet is the most common method to reduce the boundary effect. By studying the properties of Shannon-Cosine interpolation wavelet, an improved version of the wavelet function is proposed, and the corresponding interval interpolation wavelet based on Hermite interpolation extension and variational principle is designed, which possesses almost all of the excellent properties such as interpolation, smoothness, compact support and normalization. Then, the multi-scale interpolation operator is constructed, which can be applied to select the sparse feature points and reconstruct signal based on these sparse points adaptively. To validate the effectiveness of the proposed method, we compare the proposed method with Shannon-Cosine interpolation wavelet method, Akima method, Bezier method and cubic spline method by taking infinitesimal derivable function cos(x) and irregular piecewise function as an example. In the reconstruction of cos(x) and piecewise function, the proposed method reduces the boundary effect at the endpoints. When the interpolation points are the same, the maximum error, average absolute error, mean square error and running time are 1.20 × 10−4, 2.52 × 10−3, 2.76 × 10−5, 1.68 × 10−2 and 4.02 × 10−3, 4.94 × 10−4, 1.11 × 10−3, 9.27 × 10−3, respectively. The four indicators mentioned above are all lower than the other three methods. When reconstructing an infinitely derivable function, the curve reconstructed by our method is smoother, and it satisfies C2 and G2 continuity. Therefore, the proposed method can better realize the reconstruction of smooth curves, improve the reconstruction efficiency and provide new ideas to the curve reconstruction method.

Spatial Dynamic Analysis of a Mangeove Patch Based on Unmanned Aerial Vehicle: A Case Study in Pear Bay in Guangxi, China

2021 ◽  
Author(s):  
Xin Lin ◽  
Chungan Li ◽  
Mei Zhou ◽  
Wenhai Liang ◽  
Biao Li
Keyword(s):  
Unmanned Aerial Vehicle ◽  
Spatial Dynamics ◽  
Absolute Error ◽  
Maximum Error ◽  
Canopy Height ◽  
Accurate Information ◽  
Maximum Absolute Error ◽  
Patch Area ◽  
Maximum Increase ◽  
Aerial Vehicle

Abstract This study investigated the short-term spatial variability of an mangrove patch, located in the Pearl Bay in Guangxi, China. Unmanned aerial vehicle (UAV) imagery covering the period from March 2015 to October 2017 were used and the following models were developed: two annual ultra-high resolution spatial resolution digital orthophoto maps (DOMs), two digital elevation models (DEMs), two digital surface models (DSMs), two canopy height models (CHMs), and a canopy height difference model (d-CHM). Using these models, the spatial dynamics of the extent and canopy height of the patch were analyzed. The resolution of the DOMs was 0.1 m, with an average geometrical error of 0.17 m and a maximum error of 0.44 m. The resolutions of DEMs, DSMs, CHMs, d-CHM were all 1 m. The average elevation errors of CHM in 2015 and 2017 were 0.002 m and -0.001 m, respectively, with maximum absolute errors of 0.034 m and 0.030 m, respectively. The average elevation error of d-CHM was -0.003 m and the maximum absolute error was 0.036 m, and the data quality were rated as good. From 2015 to 2017, the area of the mangrove patch increased from 8.16 ha to 8.79 ha, with an average annual increase of 3.7%. Specifically, the areas of expansion, shrinkage, and maximum seaward expansion were 6356 m2, 19 m2, and 24 m, respectively. The driving factor for the variability was natural processes. Stand canopy height exhibited a particular trend of decrease from northwest to southeast (horizontal; parallel to the seawall) and from the land to the sea (vertically; perpendicular to the seawall). From 2015 to 2017, 88.2% of the patch area showed increased canopy height, with an average increase of 0.78 m and a maximum increase of 3.2 m. In contrast, 11.8% of the patch area showed decreased canopy height with a maximum decrease of 3.1 m. The main reason for the decrease in canopy height was the death of trees caused by serious insect plagues. On the other hand, the reason for the increase in height could be attributed to the natural growth of mangrove trees, but further studies are required to verify the cause. UAV remote sensing has an incomparable advantage over traditional methods in that it provides extremely detailed and highly accurate information for in-depth study of the spatial evolution of mangrove patches, which would significantly contribute towards the protection and management of mangroves.

scholarly journals Multi-Perspective Ultrasound Imaging Technology of the Breast with Cylindrical Motion of Linear Arrays

2019 ◽  
Vol 9 (3) ◽  
pp. 419 ◽  
Author(s):  
Chang Liu ◽  
Binzhen Zhang ◽  
Chenyang Xue ◽  
Wendong Zhang ◽  
Guojun Zhang ◽  
...  
Keyword(s):  
Chest Wall ◽  
Ultrasound Imaging ◽  
Ultrasonic Transducer ◽  
Absolute Error ◽  
Data Reconstruction ◽  
Reconstruction Method ◽  
Water Tank ◽  
Volume Data ◽  
Imaging Technology ◽  
Linear Arrays

In this paper, we propose a multi-perspective ultrasound imaging technology with the cylindrical motion of four piezoelectric micromachined ultrasonic transducer (PMUT) rotatable linear arrays. The transducer is configured in a cross shape vertically on the circle with the length of the arrays parallel to the z axis, roughly perpendicular to the chest wall. The transducers surrounded the breast, which achieves non-invasive detection. The electric rotary table drives the PMUT to perform cylindrical scanning. A breast model with a 2 cm mass in the center and six 1-cm superficial masses were used for the experimental analysis. The detection was carried out in a water tank and the working temperature was constant at 32 °C. The breast volume data were acquired by rotating the probe 90° with a 2° interval, which were 256 × 180 A-scan lines. The optimized segmented dynamic focusing technology was used to improve the image quality and data reconstruction was performed. A total of 256 A-scan lines at a constant angle were recombined and 180 A-scan lines were recombined according to the nth element as a dataset, respectively. Combined with ultrasound imaging algorithms, multi-perspective ultrasound imaging was realized including vertical slices, horizontal slices and 3D imaging. The seven masses were detected and the absolute error of the size was approximately 1 mm where even the image of the injection pinhole could be seen. Furthermore, the breast boundary could be seen clearly from the chest wall to the nipple, so the location of the masses was easier to confirm. Therefore, the validity and feasibility of the data reconstruction method and imaging algorithm were verified. It will be beneficial for doctors to be able to comprehensively observe the pathological tissue.

scholarly journals Phylogenetic Reconstruction Based on Synteny Block and Gene Adjacencies

2020 ◽  
Vol 37 (9) ◽  
pp. 2747-2762 ◽  
Author(s):  
Guénola Drillon ◽  
Raphaël Champeimont ◽  
Francesco Oteri ◽  
Gilles Fischer ◽  
Alessandra Carbone
Keyword(s):  
Chromosomal Rearrangements ◽  
Phylogenetic Reconstruction ◽  
Simulated Data ◽  
Synteny Block ◽  
Data Sets ◽  
Reconstruction Method ◽  
Reconstruction Methods ◽  
Wide Range ◽  
Genomic Markers ◽  
Almost All

Abstract Gene order can be used as an informative character to reconstruct phylogenetic relationships between species independently from the local information present in gene/protein sequences. PhyChro is a reconstruction method based on chromosomal rearrangements, applicable to a wide range of eukaryotic genomes with different gene contents and levels of synteny conservation. For each synteny breakpoint issued from pairwise genome comparisons, the algorithm defines two disjoint sets of genomes, named partial splits, respectively, supporting the two block adjacencies defining the breakpoint. Considering all partial splits issued from all pairwise comparisons, a distance between two genomes is computed from the number of partial splits separating them. Tree reconstruction is achieved through a bottom-up approach by iteratively grouping sister genomes minimizing genome distances. PhyChro estimates branch lengths based on the number of synteny breakpoints and provides confidence scores for the branches. PhyChro performance is evaluated on two data sets of 13 vertebrates and 21 yeast genomes by using up to 130,000 and 179,000 breakpoints, respectively, a scale of genomic markers that has been out of reach until now. PhyChro reconstructs very accurate tree topologies even at known problematic branching positions. Its robustness has been benchmarked for different synteny block reconstruction methods. On simulated data PhyChro reconstructs phylogenies perfectly in almost all cases, and shows the highest accuracy compared with other existing tools. PhyChro is very fast, reconstructing the vertebrate and yeast phylogenies in <15 min.

Optimization of a neuro-human thermal model using a genetic algorithm

2020 ◽  
pp. 1420326X2097519
Author(s):  
Mohamad El Kadri ◽  
Fabrice De Oliveira ◽  
Christian Inard ◽  
François Demouge
Keyword(s):  
Genetic Algorithm ◽  
Thermal Model ◽  
Absolute Error ◽  
Maximum Error ◽  
Male Students ◽  
Local Skin ◽  
Active Systems ◽  
Physiological Variables ◽  
Human Thermal Model ◽  
Skin Temperatures

A neuro-human thermal model was optimized to increase the prediction accuracy of the physiological variables of a group of 15 healthy male students exposed to transient environmental conditions. The effect of both the passive and active systems parameters was studied using a sensitivity analysis, and the parameters that had the most influence on the neuro-human thermal model outputs were established. A genetic algorithm was then used to optimize the model in order to determine the parameters that corresponded to the studied population. The results showed that the optimization increased the precision of the neuro-human thermal model. The mean absolute error and the maximum error between the experimental data and the numerical results for mean skin temperature were 0.13°C and 0.56°C, respectively, and we obtained 0.03°C and 0.11°C, respectively, for rectal temperature. These results show that the neuro-human thermal model can be accurately adjusted for the rectal, mean and local skin temperatures of a targeted population by using a genetic algorithm to determine the values of the parameters that correspond to this population.

scholarly journals ANALYSIS OF LUMBOSACRAL LORDOSIS USING STANDING LATERAL RADIOGRAPHS THROUGH CURVE RECONSTRUCTION

2002 ◽  
Vol 14 (04) ◽  
pp. 149-156 ◽  
Author(s):  
RUEY-MO LIN ◽  
RONG-SHEAN LEE ◽  
YING-MING HUANG ◽  
SHOU-I CHEN ◽  
CHIN-YIN YU
Keyword(s):  
Age Groups ◽  
Lumbosacral Spine ◽  
Reconstruction Method ◽  
Lumbar Curve ◽  
Curve Reconstruction ◽  
Practical Applications ◽  
Geometric Characteristics ◽  
Gender And Age ◽  
Lumbosacral Lordosis ◽  
Lower Lumbar

The consensus of the normal magnitude of lumbosacral curve has not been achieved. The Cobb's angle cannot depict the whole contour of this curve. For practical applications, a clearer image of these curves and their aging changes should be further investigated. This study aimed to provide a more consolidate concept of normal lumbosacral curves for clinician through a computerized reconstruction method. Standing lateral radiographs of lumbosacral spine in 82 normal adults were used for reconstructing the sagittal lumbosacral curves. The geometric characteristics of these curves according to the gender and age groups were studied. Using standing lateral radiographs, reconstruction of the lumbosacral curves was performed through digitization, programming and computation. These curves and related parameters were normalized and averaged for analyzing the differences of gender and age. The most anteriorward and horizontal vertebrae usually occurred on the L4 and L3 in any gender and age groups. The sacral inclination angle did not change obviously with the increasing ages. A tendency of L1 shifting backward was noted in the age groups of 40 to 60 and above 60 years old. The sagittal lumbosacral curves can be easily reconstructed by digitizing lateral radiographs, The aging changes of lumbosacral curves could be qualitatively described as the flattening of lower lumbar curve and the rearward inclination of upper lumbar curve. The changes occurred obviously above 40 years old. Although individual variations existed, the aging changes and the geometric characteristics such as the most anteriorward or horizontal vertebrae could be used as an important guideline during therapy or surgical correction.

scholarly journals Diagnosis and Optimization of Ensemble Forecasts

2008 ◽  
Vol 136 (3) ◽  
pp. 1054-1074 ◽  
Author(s):  
Tomislava Vukicevic ◽  
Isidora Jankov ◽  
John McGinley
Keyword(s):  
Initial Conditions ◽  
Forecast Error ◽  
Absolute Error ◽  
Ensemble Forecast ◽  
Stochastic Representation ◽  
Ensemble Forecasts ◽  
Ensemble Technique ◽  
Consensus Forecasts ◽  
Almost All ◽  
The Impact

Abstract In the current study, a technique that offers a way to evaluate ensemble forecast uncertainties produced either by initial conditions or different model versions, or both, is presented. The technique consists of first diagnosing the performance of the forecast ensemble and then optimizing the ensemble forecast using results of the diagnosis. The technique is based on the explicit evaluation of probabilities that are associated with the Gaussian stochastic representation of the weather analysis and forecast. It combines an ensemble technique for evaluating the analysis error covariance and the standard Monte Carlo approach for computing samples from a known Gaussian distribution. The technique was demonstrated in a tutorial manner on two relatively simple examples to illustrate the impact of ensemble characteristics including ensemble size, various observation strategies, and configurations including different model versions and varying initial conditions. In addition, the authors assessed improvements in the consensus forecasts gained by optimal weighting of the ensemble members based on time-varying, prior-probabilistic skill measures. The results with different observation configurations indicate that, as observations become denser, there is a need for larger-sized ensembles and/or more accuracy among individual members for the ensemble forecast to exhibit prediction skill. The main conclusions relative to ensembles built up with different physics configurations were, first, that almost all members typically exhibited some skill at some point in the model run, suggesting that all should be retained to acquire the best consensus forecast; and, second, that the normalized probability metric can be used to determine what sets of weights or physics configurations are performing best. A comparison of forecasts derived from a simple ensemble mean to forecasts from a mean developed from variably weighting the ensemble members based on prior performance by the probabilistic measure showed that the latter had substantially reduced mean absolute error. The study also indicates that a weighting scheme that utilized more prior cycles showed additional reduction in forecast error.

SMAP revisited and revised

Geophysics ◽  
1992 ◽  
Vol 57 (2) ◽  
pp. 258-262 ◽  
Author(s):  
David L. Brumbaugh
Keyword(s):  
Linear Programming ◽  
Absolute Error ◽  
Maximum Error ◽  
Seismic Interpretation ◽  
Programming Technique ◽  
Adjustment Procedure ◽  
Uniform Grids ◽  
Programming Techniques ◽  
Original Procedure ◽  
Seismic Lines

The original seismic mis‐tie adjustment procedure (SMAP) is restricted to uniform grids of 2-D seismic lines. In many areas, uniform grids do not occur, especially with multiple‐vintage coverage. An alternative method is proposed still using linear programming techniques to simultaneously minimize the maximum error and absolute error sum, but extending the technique to handle any 2-D seismic grid orientation. Horizons can be treated individually or in combination, with certain restrictions. The original procedure also has some poorly imposed constraints. SAS/OR™ software improves upon the original SMAP results. A comparison is made between a 2-D seismic interpretation corrected with the new algorithm and a 3-D seismic interpretation covering the same area, showing an excellent correlation between the two structural pictures. 2-D seismic interpretation is still a viable tool, and improved maps can be made through this linear programming technique for minimizing mis‐ties.

scholarly journals On the Discrete Harmonic Wavelet Transform

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Carlo Cattani ◽  
Aleksey Kudreyko
Keyword(s):  
Wavelet Transform ◽  
Absolute Error ◽  
Harmonic Wavelet ◽  
The Absolute

The discrete harmonic wavelet transform has been reviewed and applied towards given functions. The absolute error of reconstruction of the functions has been computed.

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