Linear regression analysis using the relative squared error

Simulated Annealing-Based Image Reconstruction for Patients With COVID-19 as a Model for Ultralow-Dose Computed Tomography

“…The other competing cost functions that have produced outclass results are RMSE and MAE whereas rest of the cost functions seem requiring more annealing time to reach the acceptable image quality. Keeping in view the image quality with reduced number of views, significant reduction in radiation dose to the patients has been observed in case of lung biopsy sample images acquired using low-dose CT-guidance producing equivalent diagnostic accuracy images to standard dose CT-guidance (Arnold and Stahlecker, 2002).…”

A surprising property of uniformly best linear affine estimation in linear regression when prior information is fuzzy

“…In the relative squared error approach proposed by Arnold and Stahlecker (2000), the quadratic form of the denominator is presupposed to be p.d. Subsequently, this assumption was weakened; the denominator of the relative squared error in Arnold and Stahlecker (2002) is merely assumed to be n.n.d. Now, it is an interesting question to be left for future research, whether Wilczyń ski's generalization can also be applied to the case of an n.n.d.…”

“…(10) is a special case of the solution of a slightly more general constrained minimization problem investigated in Arnold and Stahlecker (2002), where a relative squared error approach to linear regression analysis is presented. That minimization problem is also mentioned and discussed in Schönfeld (2004).…”

Design and performance of an wide-range real-time NFM system using higher order Campbell mode

“…The counting rate values of counting mode were taken as Campbell r in the overlap region. Since the calibration interval spans an order of magnitude, the linear fitting based on the ordinary least square method will make the counting result of 10 5 cps heavier, selecting the linear regression analysis algorithm using the relative squared error [23] makes full use of the results of the whole calibration interval.…”

“…Particularly, paralyzable model and non-paralyzable model were also introduced in counting mode to correct and improve the counting rate. The linear regression analysis algorithm using the relative squared error [23] was applied to calibrate the Campbell results, which improve the accuracy of the Campbell mode. The calibration algorithm runs in real-time (figure 8).…”