Learning nonlocal regularization operators

نویسندگان

چکیده

<p style='text-indent:20px;'>A learning approach for determining which operator from a class of nonlocal operators is optimal the regularization an inverse problem investigated. The considered motivated by use squared fractional order Sobolev seminorms as operators. First fundamental results theory with local are extended to case. Then framework based on bilevel optimization strategy developed allows choose given i) respect suitable performance measure training set, and ii) enjoy particularly favorable properties. Results numerical experiments also provided.</p>

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Adaptation for Regularization Operators in Learning Theory

We consider learning algorithms induced by regularization methods in the regression setting. We show that previously obtained error bounds for these algorithms using a-priori choices of the regularization parameter, can be attained using a suitable a-posteriori choice based on validation. In particular, these results prove adaptation of the rate of convergence of the estimators to the minimax r...

متن کامل

Abelian Anomalies in Nonlocal Regularization

Nonlocal regularization of QED is shown to possess an axial anomaly of the same form as other regularization schemes. The Noether current is explicitly constructed and the symmetries are shown to be violated, whereas the identities constructed when one properly considers the contribution from the path integral measure are respected. We also discuss the barrier to quantizing the fully gauged chi...

متن کامل

Optimal Rates for Regularization Operators in Learning Theory

We develop some new error bounds for learning algorithms induced by regularization methods in the regression setting. The “hardness” of the problem is characterized in terms of the parameters r and s, the first related to the “complexity” of the target function, the second connected to the effective dimension of the marginal probability measure over the input space. We show, extending previous ...

متن کامل

Anomalies for Nonlocal Dirac Operators

The anomalies of a very general class of non local Dirac operators are computed using the ζ-function definition of the fermionic determinant and an asymmetric version of the Wigner transformation. For the axial anomaly all new terms introduced by the non locality can be brought to the standard minimal Bardeen’s form. Some extensions of the present techniques are also commented.

متن کامل

Image Recovery via Nonlocal Operators

This paper considers two nonlocal regularizations for image recovery, which exploit the spatial interactions in images. We get superior results using preprocessed data as input for the weighted functionals. Applications discussed include image deconvolution and tomographic reconstruction. The numerical results show our method outperforms some previous ones.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Mathematical Control and Related Fields

سال: 2022

ISSN: ['2156-8499', '2156-8472']

DOI: https://doi.org/10.3934/mcrf.2021003