Introduction: Unfolding X-ray spectrum is a powerful tool for quality control of X-ray tubes. Generally, the acquisition of the X-ray spectrum in diagnostic radiology departments is complicated and difficult due to high photon flux. Measurement of x ray spectra using radiation detectors could not be performed accurately, because of the pulse pile up. Therefore, indirect methods...

In this paper, the Method of Fundamental Solutions (MFS) is extended to solve some special cases of the problem of transient heat conduction in functionally graded materials. First, the problem is transformed to a heat equation with constant coefficients using a suitable new transformation and then the MFS together with the Tikhonov regularization method is used to solve the resulting equation.

| The reconstruction of impedance distribution in electrical impedance tomography (EIT) is a nonlinear ill-posed inverse problem. In order to obtain stable solution the problem has to be regularized. One of the most common methods for this is the generalized Tikhonov reg-ularization. The regularization matrices that are usually used with the Tikhonov method are more or less ad hoc and the assoc...

Reconstructing ionospheric electron density (IED) is an ill-posed inverse problem, with classical Tikhonov regularization tending to smooth IED structures. By contrast, total variation (TV) regularization effectively resists noise and preserves discontinuities of the IED. In this paper, we regularize the inverse problem by incorporating both Tikhonov and TV regularization. A specific formulatio...

We consider the problem of Tikhonov regularization with a general convex loss function: this formalism includessupport vector machines and regularized least squares. For a family of kernels that includes the Gaussian, parameterized by a “bandwidth” parameter σ, we characterize the limiting solution as σ → ∞. In particular, we show that if we set the regularization parameter λ = λ̃σ, the regulari...

For good image quality using ultrasound inverse scattering, one alternately solves the well-posed forward scattering equation for an estimated total field and the ill-posed inverse scattering equation for the desired object property function. In estimating the total field, error or noise contaminates the coefficients of both matrix and data of the inverse scattering equation. Previous work on i...

Modern imaging technologies have been at the forefront of scientific research and medical diagnosis. Typically, the cost of producing these images is quite high, while device defects, environmental variations, as well as movements generated by the objects being imaged, may result in noisy, poor-quality images. As a method to improve the cost-benefit of imaging technologies, image deblurring has...

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...

Classification based on Low-Rank Representation (LRR) has been a hot-topic in the field of pattern classification. However, LRR may not be able to fuse the local and global information of data completely and fail to represent nonlinear samples. In this paper, we propose a kernel locality preserving low-rank representation with Tikhonov regularization (KLP-LRR) for face recognition. KLP-LRR is a...