scholarly journals Stochastic piecewise linear function fitting with application to ultrasound shear wave imaging

2014 ◽  
Author(s):  
Atul Ingle ◽  
Tomy Varghese ◽  
William Sethares ◽  
James Bucklew
Keyword(s):  
Linear Function ◽  
Shear Wave ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Shear Wave Imaging ◽  
Function Fitting ◽  
Wave Imaging

scholarly journals MINLP formulations for continuous piecewise linear function fitting

2021 ◽  
Author(s):  
Noam Goldberg ◽  
Steffen Rebennack ◽  
Youngdae Kim ◽  
Vitaliy Krasko ◽  
Sven Leyffer
Keyword(s):  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Mixed Integer ◽  
Function Fitting ◽  
Computational Performance ◽  
Integer Nonlinear Programming ◽  
Minlp Model ◽  
Necessary Constraints ◽  
Continuous Piecewise Linear Function

AbstractWe consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. 10.1007/s10589-014-9647-y) for piecewise linear function fitting. We show that this MINLP model is incomplete and can result in a piecewise linear curve that is not the graph of a function, because it misses a set of necessary constraints. We provide two counterexamples to illustrate this effect, and propose three alternative models that correct this behavior. We investigate the theoretical relationship between these models and evaluate their computational performance.

A Comparison of Two Mixed-Integer Linear Programs for Piecewise Linear Function Fitting

2021 ◽  
Author(s):  
John Alasdair Warwicker ◽  
Steffen Rebennack
Keyword(s):  
Linear Programming ◽  
Linear Function ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Mixed Integer ◽  
Data Sets ◽  
Binary Variables ◽  
Function Fitting

The problem of fitting continuous piecewise linear (PWL) functions to discrete data has applications in pattern recognition and engineering, amongst many other fields. To find an optimal PWL function, the positioning of the breakpoints connecting adjacent linear segments must not be constrained and should be allowed to be placed freely. Although the univariate PWL fitting problem has often been approached from a global optimisation perspective, recently, two mixed-integer linear programming approaches have been presented that solve for optimal PWL functions. In this paper, we compare the two approaches: the first was presented by Rebennack and Krasko [Rebennack S, Krasko V (2020) Piecewise linear function fitting via mixed-integer linear programming. INFORMS J. Comput. 32(2):507–530] and the second by Kong and Maravelias [Kong L, Maravelias CT (2020) On the derivation of continuous piecewise linear approximating functions. INFORMS J. Comput. 32(3):531–546]. Both formulations are similar in that they use binary variables and logical implications modelled by big-[Formula: see text] constructs to ensure the continuity of the PWL function, yet the former model uses fewer binary variables. We present experimental results comparing the time taken to find optimal PWL functions with differing numbers of breakpoints across 10 data sets for three different objective functions. Although neither of the two formulations is superior on all data sets, the presented computational results suggest that the formulation presented by Rebennack and Krasko is faster. This might be explained by the fact that it contains fewer complicating binary variables and sparser constraints. Summary of Contribution: This paper presents a comparison of the mixed-integer linear programming models presented in two recent studies published in the INFORMS Journal on Computing. Because of the similarity of the formulations of the two models, it is not clear which one is preferable. We present a detailed comparison of the two formulations, including a series of comparative experimental results across 10 data sets that appeared across both papers. We hope that our results will allow readers to take an objective view as to which implementation they should use.

FROM THE BOREHOLE WALL INTO THE FORMATION – COMBINING BOREHOLE IMAGES WITH DEEP SHEAR WAVE IMAGING TECHNOLOGY

2019 ◽  
Author(s):  
Stefan Schimschal ◽  
Stephen Fayers ◽  
Nicklas Ritzmann ◽  
Martin Cox ◽  
Iain Whyte
Keyword(s):  
Shear Wave ◽  
Borehole Wall ◽  
Imaging Technology ◽  
Shear Wave Imaging ◽  
Wave Imaging

scholarly journals Natural shear wave imaging using vocal tract vibrations: Introducing vocal passive elastography (V-PE) to thyroid elasticity mapping

2021 ◽  
Vol 118 (2) ◽  
pp. 023702
Author(s):  
Steve Beuve ◽  
Samuel Callé ◽  
Elise Khoury ◽  
Emmanuel Gilles Simon ◽  
Jean-Pierre Remenieras
Keyword(s):  
Shear Wave ◽  
Vocal Tract ◽  
Shear Wave Imaging ◽  
Wave Imaging

A Color-Doppler Shear-Wave-Imaging Phase-reconstruction Method Using Four Color Flow Images

2016 ◽  
Vol 39 (3) ◽  
pp. 172-188
Author(s):  
Naoki Sunaguchi ◽  
Yoshiki Yamakoshi ◽  
Takahito Nakajima
Keyword(s):  
Image Quality ◽  
Shear Wave ◽  
Initial Phase ◽  
Color Doppler ◽  
Reconstruction Method ◽  
Phase Reconstruction ◽  
Color Flow ◽  
Shear Wave Imaging ◽  
Wave Imaging ◽  
Phase Map

This study investigates shear wave phase map reconstruction using a limited number of color flow images (CFIs) acquired with a color Doppler ultrasound imaging instrument. We propose an efficient reconstruction method to considerably reduce the number of CFIs required for reconstruction and compare this method with Fourier analysis-based color Doppler shear wave imaging. The proposed method uses a two-step phase reconstruction process, including an initial phase map derived from four CFIs using an advanced iterative algorithm of optical interferometry. The second step reduces phase artifacts in the initial phase map using an iterative correction procedure that cycles between the Fourier and inverse Fourier domains while imposing directional filtering and total variation regularization. We demonstrate the efficacy of this method using synthetic and experimental data of a breast phantom and human breast tissue. Our results show that the proposed method maintains image quality and reduces the number of CFIs required to four; previous methods have required at least 32 CFIs to achieve equivalent image quality. The proposed method is applicable to real-time shear wave elastography using a continuous shear wave produced by a mechanical vibrator.

scholarly journals DESIGN OF TIME DELAYED CHAOTIC CIRCUIT WITH THRESHOLD CONTROLLER

2011 ◽  
Vol 21 (03) ◽  
pp. 725-735 ◽  
Author(s):  
K. SRINIVASAN ◽  
I. RAJA MOHAMED ◽  
K. MURALI ◽  
M. LAKSHMANAN ◽  
SUDESHNA SINHA
Keyword(s):  
Numerical Simulations ◽  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Operational Amplifiers ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Oscillator ◽  
Threshold Values ◽  
Chaotic Circuit

A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.

Real time quantitative elastography using Supersonic Shear wave Imaging

2010 ◽  
Author(s):  
Mickael Tanter ◽  
Mathieu Pernot ◽  
Gabriel Montaldo ◽  
Jean-Luc Gennisson ◽  
Eric Bavu ◽  
...  
Keyword(s):  
Real Time ◽  
Shear Wave ◽  
Shear Wave Imaging ◽  
Wave Imaging

Suppression of the influence of surface waves on shear wave imaging for buried pipe location

2021 ◽  
pp. 104517
Author(s):  
Shuan Yan ◽  
Hongyong Yuan ◽  
Yan Gao ◽  
Boao Jin ◽  
Lizheng Deng ◽  
...  
Keyword(s):  
Surface Waves ◽  
Shear Wave ◽  
Buried Pipe ◽  
Shear Wave Imaging ◽  
Wave Imaging

Far _ Near Wellbore Fracture Characterization Using High Resolution Borehole Images and Deep Shear Wave Imaging

2020 ◽  
Author(s):  
N. Kerrouche ◽  
A. Alhammadi ◽  
A. AlMershed ◽  
H. Al-Khateeb ◽  
D.N. Tiwary ◽  
...  
Keyword(s):  
High Resolution ◽  
Shear Wave ◽  
Fracture Characterization ◽  
Shear Wave Imaging ◽  
Wave Imaging
Sign in / Sign up

Export Citation Format

Share Document