In many applications of solving ill-posed problems there are a number of regularization methods to choose from as well as a free regularization parameter. The choice of the method and regularization can add bias if deblurred images are based on what the researcher expects. The presented project develops a tool for method choice and parameter selection by using a set of three statistical diagnos...

the methods applied to regularization of the ill-posed problems can be classified under “direct” and “indirect” methods. practice has shown that the effects of different regularization techniques on an ill-posed problem are not the same, and as such each ill-posed problem requires its own investigation in order to identify its most suitable regularization method. in the geoid computations witho...

In order to obtain better generalization performance in supervised learning, model parameters should be determined appropriately, i.e., they should be determined so that the generalization error is minimized. However, since the generalization error is inaccessible in practice, the model parameters are usually determined so that an estimator of the generalization error is minimized. The regulari...

In view of its ongoing importance for a variety of practical applications, feature selection via `1-regularization methods like the lasso has been subject to extensive theoretical as well empirical investigations. Despite its popularity, mere `1-regularization has been criticized for being inadequate or ineffective, notably in situations in which additional structural knowledge about the predic...

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...