We derive sharp performance bounds for least squares regression with L1 regularization from parameter estimation accuracy and feature selection quality perspectives. The main result proved for L1 regularization extends a similar result in [Ann. Statist. 35 (2007) 2313–2351] for the Dantzig selector. It gives an affirmative answer to an open question in [Ann. Statist. 35 (2007) 2358–2364]. Moreo...

Waves from a sparse set of source hidden in additive noise are observed by a sensor array. We treat the estimation of the sparse set of sources as a generalized complex-valued LASSO problem. The corresponding dual problem is formulated and it is shown that the dual solution is useful for selecting the regularization parameter of the LASSO when the number of sources is given. The solution path o...

This paper reports studies on the influence of the regularization parameter and the first estimate on the performance of iterative image restoration algorithms. We discuss regularization parameter estimation methods that have been developed for the linear Tikhonov-Miller filter to restore images distorted by additive Gaussian noise. We have performed experiments on synthetic data to show that t...

Regularization approaches for the limited-angle reconstruction problem in digital breast tomosynthesis are widelyused. Though, their benefits depend largely upon a suitable regularization parameter estimation. We aim to evaluate the reconstruction quality of precise small contrast features objectively with the help of an automated process. These features were represented by so-called Landolt ri...

We treat the estimation of a sparse set of sources emitting plane waves observed by a sensor array as a complex-valued LASSO (c–LASSO) problem where the usual l1-norm constraint is replaced by the l1-norm of a matrix D times the solution vector. When the sparsity order is given, algorithmically selecting a suitable value for the c–LASSO regularization parameter remains a challenging task. The c...

A parameter of an econometric model is identified if there is a one-to-one or many-to-one mapping from the population distribution of the available data to the parameter. Often, this mapping is obtained by inverting a mapping from the parameter to the population distribution. If the inverse mapping is discontinuous, then estimation of the parameter usually presents an illposed inverse problem. ...