Search results for "POLYNOMIAL REGRESSION"
showing 10 items of 27 documents
Non-separable local polynomial regression cell-average multiresolution operators. Application to compression of images
2016
Abstract Cell-average multiresolution Harten׳s algorithms have been satisfactorily used to compress data. These schemes are based on two operators: decimation and prediction. The accuracy of the method depends on the prediction operator. In order to design a precise function, local polynomial regression has been used in the last years. This paper is devoted to construct a family of non-separable two-dimensional linear prediction operators approximating the real values with this procedure. Some properties are proved as the order of the scheme and the stability. Some numerical experiments are performed comparing the new methods with the classical linear method.
Non-linear Local Polynomial Regression Multiresolution Methods Using $$\ell ^1$$-norm Minimization with Application to Signal Processing
2015
Harten’s Multiresolution has been developed and used for different applications such as fast algorithms for solving linear equations or compression, denoising and inpainting signals. These schemes are based on two principal operators: decimation and prediction. The goal of this paper is to construct an accurate prediction operator that approximates the real values of the signal by a polynomial and estimates the error using \(\ell ^1\)-norm in each point. The result is a non-linear multiresolution method. The order of the operator is calculated. The stability of the schemes is ensured by using a special error control technique. Some numerical tests are performed comparing the new method with…
Non-consistent cell-average multiresolution operators with application to image processing
2016
In recent years different techniques to process signal and image have been designed and developed. In particular, multiresolution representations of data have been studied and used successfully for several applications such as compression, denoising or inpainting. A general framework about multiresolution representation has been presented by Harten (1996) 20. Harten's schemes are based on two operators: decimation, D , and prediction, P , that satisfy the consistency property D P = I , where I is the identity operator. Recently, some new classes of multiresolution operators have been designed using learning statistical tools and weighted local polynomial regression methods obtaining filters…
A Comparison between Three Meta-Modeling Optimization Approaches to Design a Tube Hydroforming Process
2012
Computer aided procedures to design and optimize forming processes have become crucial research topics as the industrial interest in cost and time reduction has been increasing. A standalone numerical simulation approach could make the design too time consuming while meta-modeling techniques enables faster approximation of the investigated phenomena, reducing the simulation time. Many researchers are, nowadays, facing such research challenge by using various approaches. Response surface method (RSM) is probably the most known one, since its effectiveness was demonstrated in the past years. The effectiveness of RSM depends both on the definition of the Design of Experiments (DoE) and the acc…
Permutation Tests in Linear Regression
2015
Exact permutation tests are available only in rather simple linear models. The problem is that, although standard assumptions allow permuting the errors of the model, we cannot permute them in practice, because they are unobservable. Nevertheless, the residuals of the model can be permuted. A proof is given here which shows that it is possible to approximate the unobservable permutation distribution where the true errors are permuted by permuting the residuals. It is shown that approximation holds asymptotically and almost surely for certain quadratic statistics as well as for statistics which are expressible as the maximum of appropriate linear functions. The result is applied to testing t…
Polynomial Fuzzy Models for Nonlinear Control: A Taylor Series Approach
2009
Classical Takagi-Sugeno (T-S) fuzzy models are formed by convex combinations of linear consequent local models. Such fuzzy models can be obtained from nonlinear first-principle equations by the well-known sector-nonlinearity modeling technique. This paper extends the sector-nonlinearity approach to the polynomial case. This way, generalized polynomial fuzzy models are obtained. The new class of models is polynomial, both in the membership functions and in the consequent models. Importantly, T-S models become a particular case of the proposed technique. Recent possibilities for stability analysis and controller synthesis are also discussed. A set of examples shows that polynomial modeling is…
Determination of thermometric parameters from the conductance curve of the normal metal based tunnel junction array
1997
Abstract We propose a method for extracting thermometric parameters from the measured conductance curve, against bias voltage, of a tunnel junction array. Instead of fitting the whole theoretical conductance curve to the experiment, we perform several polynomial fits to selected bias regions. The advantages of this method is that polynomial fits are linear in their fitting parameters whereas the theoretical form for the conductance is inherently nonlinear. This way the proposed method is about three orders of magnitude faster than the nonlinear fit. Optimizing this polynomial fit procedure is discussed.
Polynomial Regression and Measurement Error
2020
Many of the phenomena of interest in information systems (IS) research are nonlinear, and it has consequently been recognized that by applying linear statistical models (e.g., linear regression), we may ignore important aspects of these phenomena. To address this issue, IS researchers are increasingly applying nonlinear models to their datasets. One popular analytical technique for the modeling and analysis of nonlinear relationships is polynomial regression, which in its simplest form fits a "U-shaped" curve to the data. However, the use of polynomial regression can be problematic when the independent variables are contaminated with measurement error, and the implications of error can be m…
Investigation of Inspiratory Pressure-Volume Curves on Mechanically Ventilated Patients Using Least Square Polynomial Fit
1988
Abstract An on-line method for the registration of pressure volume 1 oops TrT mechanically ventilated patients was developed using a personal computer with analog/digital interface. A third order polynomial function was fitted to the measured inspiratory pressure volume pairs. The significance of the fitting procedure was calculated using regression ANOVA. The inflection point of the pressure-volume curve was determinated by calculating the root of the second derivative of the polynomial. The method was teseted on 20 patients without major pulmonary dysfunction and on 6 patients with severe ARDS.
Generalized wavelets design using Kernel methods. Application to signal processing
2013
Abstract Multiresolution representations of data are powerful tools in signal processing. In Harten’s framework, multiresolution transforms are defined by predicting finer resolution levels of information from coarser ones using an operator, called the prediction operator, and defining details (or wavelet coefficients) that are the difference between the exact values and the predicted values. In this paper we present a multiresolution scheme using local polynomial regression theory in order to design a more accurate prediction operator. The stability of the scheme is proved and the order of the method is calculated. Finally, some results are presented comparing our method with the classical…