We review the information approach to regularization parameter selection and its information complexity extension for the solution of discrete ill posed problems. An information criterion for regularization parameter selection was first proposed by Shibata in the context of ridge regression as an extension of Takeuchi’s information criterion. In the information approach, the regularization para...

This paper considers subset selection in the presence of noise via algorithms that minimize diversity measures. This leads to iterative procedures like regularized FOCUSS in which each iteration involves the solution to a regularized least squares problem. Several di erent methods for choosing the regularization parameter such as the discrepancy principle and the L-curve technique are evaluated...

This article discusses the problem of choosing a regularization parameter in the group Lasso proposed by Yuan and Lin (2006), an l1-regularization approach for producing a block-wise sparse model that has been attracted a lot of interests in statistics, machine learning, and data mining. It is important to choose an appropriate regularization parameter from a set of candidate values, because it...

In dynamic MRI, sufficient temporal resolution can often only be obtained using imaging protocols which produce undersampled data for each image in the time series. This has led to popularity of compressed sensing (CS) based reconstructions. One problem CS approaches is determining regularization parameters, control balance between fidelity and regularization. We propose a data-driven approach ...

Abstract This paper considers large-scale linear ill-posed inverse problems whose solutions can be represented as sums of smooth and piecewise constant components. To solve such we consider regularizers consisting two terms that must balanced. Namely, a Tikhonov term guarantees the smoothness solution component, while total-variation (TV) regularizer promotes blockiness non-smooth component. A ...

This thesis focuses on developing computational methods and the general theory of automatic smoothing and variable selection via regularization. Methods of regularization are a commonly used technique to get stable solution to ill-posed problems such as nonparametric regression and classification. In recent years, methods of regularization have also been successfully introduced to address a cla...

This paper discusses iterative methods for the solution of very large severely ill-conditioned linear systems of equations that arise from the discretization of linear ill-posed problems. The right-hand side vector represents the given data and is assumed to be contaminated by errors. Solution methods proposed in the literature employ some form of ltering to reduce the in uence of the error in ...