Fast linear least-squares method for ultrasound attenuation and backscatter estimation

Ultrasonics ◽  
2021 ◽  
pp. 106503
Author(s):  
Jasleen Birdi ◽  
Arun Muraleedharan ◽  
Jan D’hooge ◽  
Alexander Bertrand
Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 278
Author(s):  
Ming-Feng Yeh ◽  
Ming-Hung Chang

The only parameters of the original GM(1,1) that are generally estimated by the ordinary least squares method are the development coefficient a and the grey input b. However, the weight of the background value, denoted as λ, cannot be obtained simultaneously by such a method. This study, therefore, proposes two simple transformation formulations such that the unknown parameters, and can be simultaneously estimated by the least squares method. Therefore, such a grey model is termed the GM(1,1;λ). On the other hand, because the permission zone of the development coefficient is bounded, the parameter estimation of the GM(1,1) could be regarded as a bound-constrained least squares problem. Since constrained linear least squares problems generally can be solved by an iterative approach, this study applies the Matlab function lsqlin to solve such constrained problems. Numerical results show that the proposed GM(1,1;λ) performs better than the GM(1,1) in terms of its model fitting accuracy and its forecasting precision.


2010 ◽  
Vol 22 (1) ◽  
pp. 155-158
Author(s):  
宣科 Xuan Ke ◽  
王琳 Wang Lin ◽  
李川 Li Chuan ◽  
李为民 Li Weimin ◽  
王季刚 Wang Jigang ◽  
...  

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 708
Author(s):  
Ju-Hyeon Seong ◽  
Seung-Hyun Lee ◽  
Kyoung-Kuk Yoon ◽  
Dong-Hoan Seo

Geomagnetic fingerprint has been actively studied because of the high signal stability and positioning resolution even when the time has elapsed. However, since the measured three-axis geomagnetism signals at one position are irregular according to the change of the azimuth angle, a large-sized database which is stored magnitudes per angles is required for robust and accurate positioning against the change of the azimuth angle. To solve this problem, this paper proposes a novel approach, an elliptic coefficient map based geomagnetic fingerprint. Unlike the general fingerprint, which stores strength or magnitude of the geomagnetism signals depending on the position, the proposed algorithm minimized the size of databased by storing the Ellipse coefficient map through the ellipse equation derived from the characteristics of 2-D magnetic vectors depending on the position. In addition, the curvature bias of ellipse was reduced by applying the normalized linear least-squares method to 2-D geomagnetic characteristics and the positioning accuracy was improved by applying the weighted geomagnetic signal equalization method.


2020 ◽  
Vol 28 (2) ◽  
pp. 307-312
Author(s):  
Leonid L. Frumin

AbstractA generalization of the linear least squares method to a wide class of parametric nonlinear inverse problems is presented. The approach is based on the consideration of the operator equations, with the selected function of parameters as the solution. The generalization is based on the two mandatory conditions: the operator equations are linear for the estimated parameters and the operators have discrete approximations. Not requiring use of iterations, this approach is well suited for hardware implementation and also for constructing the first approximation for the nonlinear least squares method. The examples of parametric problems, including the problem of estimation of parameters of some higher transcendental functions, are presented.


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