A l-norm penalized orthogonal forward regression (l-POFR) algorithm is proposed based on the concept of leaveone-out mean square error (LOOMSE). Firstly, a new l-norm penalized cost function is defined in the constructed orthogonal space, and each orthogonal basis is associated with an individually tunable regularization parameter. Secondly, due to orthogonal computation, the LOOMSE can be anal...

From a set of shifted, blurred, and decimated image , super-resolution image reconstruction can get a high-resolution image. So it has become an active research branch in the field of image restoration. . In general, super-resolution image restoration is an ill-posed problem. Prior knowledge about the image can be combined to make the problem well-posed, which contributes to some regularization...

For a convex class of functions F , a regularization functions Ψ(·) and given the random data (Xi, Yi) N i=1, we study estimation properties of regularization procedures of the form f̂ ∈ argmin f∈F ( 1 N N ∑ i=1 ( Yi − f(Xi) )2 + λΨ(f) ) for some well chosen regularization parameter λ. We obtain bounds on the L2 estimation error rate that depend on the complexity of the “true model” F ∗ := {f ∈ ...

This article addresses improvements on the design of the adaptive normalized matched filter (ANMF) for radar detection. It is well-acknowledged that the estimation of the noise-clutter covariance matrix is a fundamental step in adaptive radar detection. In this paper, we consider regularized estimation methods which force by construction the eigenvalues of the scatter estimates to be greater th...

Abstract. The χ-principle generalizes the Morozov discrepancy principle to the augmented residual of the Tikhonov regularized least squares problem. For weighting of the data fidelity by a known Gaussian noise distribution on the measured data and, when the stabilizing, or regularization, term is considered to be weighted by unknown inverse covariance information on the model parameters, the mi...

Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. The Golub-Kahan iterative bidiagonalization is used to project the problem onto a subspace and regularization then applied to find a subspace approximation to the full problem. Determination of the regularization parameter for the projected problem by unbiased predictive risk estimation, generalized...

We address the problem of adaptive regularization in image restoration by adopting a neural-network learning approach. Instead of explicitly specifying the local regularization parameter values, they are regarded as network weights which are then modified through the supply of appropriate training examples. The desired response of the network is in the form of a gray level value estimate of the...

Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. The Golub-Kahan iterative bidiagonalization is used to project the problem onto a subspace and regularization then applied to find a subspace approximation to the full problem. Determination of the regularization parameter for the projected problem by unbiased predictive risk estimation, generalized...

We address discrete nonlinear inverse problems with weighted least squares and Tikhonov regularization. Regularization is a way to add more information to the problem when it is ill-posed or ill-conditioned. However, it is still an open question as to how to weight this information. The discrepancy principle considers the residual norm to determine the regularization weight or parameter, while ...

We address discrete nonlinear inverse problems with weighted least squares and Tikhonov regularization. Regularization is a way to add more information to the problem when it is ill-posed or ill-conditioned. However, it is still an open question as to how to weight this information. The discrepancy principle considers the residual norm to determine the regularization weight or parameter, while ...