When the path integral method of anomaly evaluation is applied to chiral gauge theories, two different types of gauge anomaly, i.e., the consistent form and the covariant form, appear depending on the regularization scheme for the Jacobian factor. We clarify the relation between the regularization scheme and the Pauli–Villars–Gupta (PVG) type Lagrangian level regularization. The conventional PV...

The reconstruction of an image u(x, y) that describes a real scene from experimental data (observed image) I(x, y) can be identified as an inverse problem. This problem is generally ill-posed in the sense of Hadamard. The regularization of an inverse problem in image processing requires smoothing homogeneous areas of the object without degrading edges. The location of these edges are unknown an...

In sensitivity encoding reconstruction, the issue of ill conditioning becomes serious and thus the signal-to-noise ratio becomes poor when a large acceleration factor is employed. Total variation (TV) regularization has been used to address this issue and shown to better preserve sharp edges than Tikhonov regularization but may cause blocky effect. In this article, we study nonlocal TV regulari...

The objectives of this chapter are: (i) to introduce a concise overview of regularization; (ii) to define and to explain the role of a particular type of regularization called total variation norm (TV-norm) in computer vision tasks; (iii) to set up a brief discussion on the mathematical background of TV methods; and (iv) to establish a relationship between models and a few existing methods to s...

In this paper the training of Least Squares Support Vector Machines (LS-SVMs) for classification and regression and the determination of its regularization constants is reformulated in terms of additive regularization. In contrast with the classical Tikhonov scheme, a major advantage of this additive regularization mechanism is that it enables to achieve computational fusion of the training and...

SENSE reconstruction suffers from an ill-conditioning problem, which increasingly lowers the signal-to-noise ratio (SNR) as the reduction factor increases. Ill-conditioning also degrades the convergence behavior of iterative conjugate gradient reconstructions for arbitrary trajectories. Regularization techniques are often used to alleviate the ill-conditioning problem. Based on maximum a poster...

Graph cut minimization formulates the segmentation problem as the liner combination of data and smoothness terms. The smoothness term is included in the energy formulation through a regularization parameter. We propose that the trade-off between the data and the smoothness terms should not be balanced by the same regularization parameter for the whole image. In order to validate the proposed id...

We formulate a principle for classification with the knowledge of the marginal distribution over the data points (unlabeled data). The principle is cast in terms of Tikhonov style regularization where the regularization penalty articulates the way in which the marginal density should constrain otherwise unrestricted conditional distributions. Specifically, the regularization penalty penalizes a...