in this paper the 3d inversion of gravity data using two different regularization methods, namely tikhonov regularization and truncated singular value decomposition (tsvd), is considered. the earth under the survey area is modeled using a large number of rectangular prisms, in which the size of the prisms are kept fixed during the inversion and the values of densities of the prisms are the mode...

A main problem in adaptive optics is to reconstruct the phase spectrum given noisy phase differences. We present an efficient approach to solve the least-squares minimization problem resulting from this reconstruction, using either a truncated singular value decomposition (TSVD)-type or a Tikhonov-type regularization. Both of these approaches make use of Kronecker products and the generalized s...

In the solution of ill-posed problems by means of regularization methods, a crucial issue is the computation of the regularization parameter. In this work, we focus on the Truncated Singular Value Decomposition (TSVD) and Tikhonov method, and we define a method for computing the regularization parameter based on the behavior of Fourier coefficients. We compute a safe index for truncating the TS...

Truncated Singular Value Decomposition (TSVD) regularization method have been used by Zhao et al. [ " Kronecker product approximations for image restoration with new mean boundary conditions " (2011), Applied Mathematical Modelling, Vol. 36, pp. 225-237]. In this report, I propose an alternative regularization the Tikhonov method. The new regularization method gives better relative error when a...

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...

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...

Considering non-negative characteristic of the particle size distribution (PSD), based on trust-regionreflective Newton method, two non-negative regularization methods of truncated singular value decomposition (TSVD) and Tikhonov (TIK) for photon correlation spectroscopy (PCS) are proposed in this paper. Combining two regularization parameter criterions of GCV and L-curve, two non-negative regu...

We consider regularization methods for numerical solution of linear illposed problems, in particular, image deblurring, when the singular value decomposition (SVD) of the operator is available. We assume that the noise-free problem satisfies the discrete Picard condition and define the Picard parameter, the index beyond which the data, expressed in the coordinate system of the SVD, are dominate...

In this work, a data acquisition approach for the inverse problem in electrocardiography using a low cost wireless acquisition system is presented. Obtaining an image of the electrical activity on the heart surface is important in the study and diagnosis of heart disease. In addition, an introduction to the mathematical problem is presented describing two regularization methods: the Tikhonov me...

The PP-TSVD algorithm is a regularization algorithm based on the truncated singular value decomposition (TSVD) that computes piecewise polynomial (PP) solutions without any a priori information about the locations of the break points. Here we describe an extension of this algorithm designed for two-dimensional inverse problems based on a Kronecker-product formulation. We illustrate its use in c...