A global robust M-estimation scheme for maximum a posteriori (MAP) image super-resolution, which efficiently addresses the presence of outliers in the low resolution images is proposed in this work. In iterative MAP image super-resolution, the objective function to be minimized involves the highly resolved image, a parameter controlling the step size of the iterative algorithm and a parameter w...

Stochastic inverse problems in heat conduction with consideration of uncertainties in the measured temperature data, temperature sensor locations and thermophysical properties are addressed using a Bayesian statistical inference method. Both parameter estimation and thermal history reconstruction problems, including boundary heat flux and heat source reconstruction, are studied. Probabilistic s...

This paper presents a Basis Pursuit DeNoising (BPDN) sparse estimation approach as a regularization technique in a predictor-based subspace method for the identification of Linear ParameterVarying (LPV) state-space systems. It is known that in this identification method, the choice of the past window of a state predictor factorization will influence the conditioning of the main parameter estima...

We present a normalized LMS (NLMS) algorithm with robust regularization. Unlike conventional NLMS with the fixed regularization parameter, the proposed approach dynamically updates the regularization parameter. By exploiting a gradient descent direction, we derive a computationally efficient and robust update scheme for the regularization parameter. In simulation, we demonstrate the proposed al...

The problem of designing the regularization term and regularization parameter for linear regression models is discussed. Previously, we derived an approximation to the generalization error called the subspace information criterion (SIC), which is an unbiased estimator of the generalization error with finite samples under certain conditions. In this paper, we apply SIC to regularization learning...

Image deconvolution is still to be a challenging illposed problem for recovering a clear image from a given blurry image, when the point spread function is known. Although competitive deconvolution methods are numerically impressive and approach theoretical limits, they are becoming more complex, making analysis, and implementation difficult. Furthermore, accurate estimation of the regularizati...

In this work we present an inverse finite-element modeling framework for constitutive modeling and parameter estimation of soft tissues using full-field volumetric deformation data obtained from 3D ultrasound. The finite-element model is coupled to full-field visual measurements by regularization springs attached at nodal locations. The free ends of the springs are displaced according to the lo...

A constrained moving horizon observer is developed for nonlinear discrete-time systems. The algorithm is proved to converge exponentially under a detectability assumption and the data being exciting at all time. However, in many practical estimation problems, such as combined state and parameter estimation, the data may not be exciting for every period of time. The algorithm therefore has regul...

Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The penalty term is usually weighted by a tuning parameter and encourages certain constraints on the parameters to be estimated. Particular choices of constraints...

The Bayesian LASSO (BL) has been pointed out to be an effective approach to sparse model representation and successfully applied to quantitative trait loci (QTL) mapping and genomic breeding value (GBV) estimation using genome-wide dense sets of markers. However, the BL relies on a single parameter known as the regularization parameter to simultaneously control the overall model sparsity and th...