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- Long memory (2)
- Wavelet (2)
- 0-1 step function (1)
- AIC (1)
- Augmented Lagrangian method (1)
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- Bar code (1)
- Bayesian inference (1)
- Bayesian method (1)
- Constrained optimization (1)
- Copula density estimation (1)
- Cross-validation (CV) (1)
- Discrete wavelet transform (DWT) (1)
- I(d) process (1)
- LARS (1)
- Lasso (1)
- MCMC (1)
- Maximum penalized likelihood estimation (1)
- Nonlinear least squares (1)
- Total variation (1)
- Wavelet deconvolution (1)
Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
Change Point Estimation Of Bilevel Functions, Leming Qu, Yi-Cheng Tu
Change Point Estimation Of Bilevel Functions, Leming Qu, Yi-Cheng Tu
Leming Qu
Reconstruction of a bilevel function such as a bar code signal in a partially blind deconvolution problem is an important task in industrial processes. Existing methods are based on either the local approach or the regularization approach with a total variation penalty. This article reformulated the problem explicitly in terms of change points of the 0-1 step function. The bilevel function is then reconstructed by solving the nonlinear least squares problem subject to linear inequality constraints, with starting values provided by the local extremas of the derivative of the convolved signal from discrete noisy data. Simulation results show a considerable …
Inversion For Non-Smooth Models With Physical Bounds, Partha S. Routh, Leming Qu, Mrinal K. Sen, Phil D. Anno
Inversion For Non-Smooth Models With Physical Bounds, Partha S. Routh, Leming Qu, Mrinal K. Sen, Phil D. Anno
Leming Qu
Geological processes produce structures at multiple scales. A discontinuity in the subsurface can occur due to layering, tectonic activities such as faulting, folding and fractures. Traditional approaches to invert geophysical data employ smoothness constraints. Such methods produce smooth models and thefore sharp contrasts in the medium such as lithological boundaries are not easily discernible. The methods that are able to produce non-smooth models, can help interpret the geological discontinuity. In this paper we examine various approaches to obtain non-smooth models from a finite set of noisy data. Broadly they can be categorized into approaches: (1) imposing non-smooth regularization in the …
Rayleigh Wave Dispersion Curve Inversion: Occam Versus The L1-Norm, Matthew M. Haney, Leming Qu
Rayleigh Wave Dispersion Curve Inversion: Occam Versus The L1-Norm, Matthew M. Haney, Leming Qu
Leming Qu
We compare inversions of Rayleigh wave dispersion curves for shear wave velocity depth profiles based on the L2-norm (Occam's Inversion) and L1-norm (TV Regularization). We forward model Rayleigh waves using a finite-element method instead of the conventional technique based on a recursion formula and root-finding. The forward modeling naturally leads to an inverse problem that is overparameterized in depth. Solving the inverse problem with Occam's Inversion gives the smoothest subsurface model that satisfies the data. However, the subsurface need not be smooth and we therefore also solve the inverse problem with TV Regularization, a procedure that does not penalize discontinuities. …
Bayesian Wavelet Estimation Of Long Memory Parameter, Leming Qu
Bayesian Wavelet Estimation Of Long Memory Parameter, Leming Qu
Leming Qu
A Bayesian wavelet estimation method for estimating parameters of a stationary I(d) process is represented as an useful alternative to the existing frequentist wavelet estimation methods. The effectiveness of the proposed method is demonstrated through Monte Carlo simulations. The sampling from the posterior distribution is through the Markov Chain Monte Carlo (MCMC) easily implemented in the WinBUGS software package.
Copula Density Estimation By Total Variation Penalized Likelihood With Linear Equality Constraints, Leming Qu, Wotao Yin
Copula Density Estimation By Total Variation Penalized Likelihood With Linear Equality Constraints, Leming Qu, Wotao Yin
Leming Qu
A copula density is the joint probability density function (PDF) of a random vector with uniform marginals. An approach to bivariate copula density estimation is introduced that is based on a maximum penalized likelihood estimation (MPLE) with a total variation (TV) penalty term. The marginal unity and symmetry constraints for copula density are enforced by linear equality constraints. The TV-MPLE subject to linear equality constraints is solved by an augmented Lagrangian and operator-splitting algorithm. It offers an order of magnitude improvement in computational efficiency over another TV-MPLE method without constraints solved by log-barrier method for second order cone program. A …
Wavelet Reconstruction Of Nonuniformly Sampled Signals, Leming Qu, Partha S. Routh, Phil D. Anno
Wavelet Reconstruction Of Nonuniformly Sampled Signals, Leming Qu, Partha S. Routh, Phil D. Anno
Leming Qu
For the reconstruction of a nonuniformly sampled signal based on its noisy observations, we propose a level dependent l1 penalized wavelet reconstruction method. The LARS/Lasso algorithm is applied to solve the Lasso problem. The data adaptive choice of the regularization parameters is based on the AIC and the degrees of freedom is estimated by the number of nonzero elements in the Lasso solution. Simulation results conducted on some commonly used 1_D test signals illustrate that the proposed method possesses good empirical properties.
Wavelet Deconvolution In A Periodic Setting Using Cross-Validation, Leming Qu, Partha S. Routh, Kyungduk Ko
Wavelet Deconvolution In A Periodic Setting Using Cross-Validation, Leming Qu, Partha S. Routh, Kyungduk Ko
Leming Qu
The wavelet deconvolution method WaveD using band-limited wavelets offers both theoretical and computational advantages over traditional compactly supported wavelets. The translation-invariant WaveD with a fast algorithm improves further. The twofold cross-validation method for choosing the threshold parameter and the finest resolution level in WaveD is introduced. The algorithm’s performance is compared with the fixed constant tuning and the default tuning in WaveD.
Wavelet-Based Bayesian Estimation Of Partially Linear Regression Models With Long Memory Errors, Kyungduk Ko, Leming Qu, Marina Vannucci
Wavelet-Based Bayesian Estimation Of Partially Linear Regression Models With Long Memory Errors, Kyungduk Ko, Leming Qu, Marina Vannucci
Leming Qu
In this paper we focus on partially linear regression models with long memory errors, and propose a wavelet-based Bayesian procedure that allows the simultaneous estimation of the model parameters and the nonparametric part of the model. Employing discrete wavelet transforms is crucial in order to simplify the dense variance-covariance matrix of the long memory error. We achieve a fully Bayesian inference by adopting a Metropolis algorithm within a Gibbs sampler. We evaluate the performances of the proposed method on simulated data. In addition, we present an application to Northern hemisphere temperature data, a benchmark in the long memory literature.