Wavelet thresholding as introduced by Donoho and Johnstone (1994) provides a simple technique which involves thresholding the output of the Discrete Wavelet Transform (DWT) of the data of interest, as a way of removing noise from the signal. They show that their estimators are asymptotically minimax for a wide range of norms and spaces. This convergence requires strong regularization or thresho...

Penalized spline criteria involve the function of goodness of fit and penalty, which in the penalty function contains smoothing parameters. It serves to control the smoothness of the curve that works simultaneously with point knots and spline degree. The regression function with two predictors in the non-parametric model will have two different non-parametric regression functions. Therefore, we...

Likelihood-based estimators with conventional regularization methods generally produces images with nonuniform and anisotropic spatial resolution properties. Previous work on penalty design for penalizedlikelihood estimators has led to statistical reconstruction methods that yield approximately uniform “average” resolution. However some asymmetries in the local point-spread functions persist. S...

In this paper, we present an algorithm to solve the inequality constrained multi-objective programming (MP) by using a penalty function with objective parameters and constraint penalty parameter. First, the penalty function with objective parameters and constraint penalty parameter for MP and the corresponding unconstraint penalty optimization problem (UPOP) is defined. Under some conditions, a...

We present an interior-point penalty method for nonlinear programming (NLP), where the merit function consists of a piecewise linear penalty function (PLPF) and an `2-penalty function. The PLPF is defined by a set of penalty parameters that correspond to break points of the PLPF and are updated at every iteration. The `2-penalty function, like traditional penalty functions for NLP, is defined b...