We study the stability in the Cauchy Problem for the Helmholtz equation in dependence of the wave number k. For simple geometries, we show analytically that this problem is getting more stable with increasing k. In more detail, there is a subspace of the data space on which the Cauchy Problem is well posed, and this subspace grows with larger k. We call this a subspace of stability. For more ge...

Inference of model parameters is one step in an engineering process often ending in predictions that support decision in the form of design or control. Incorporation of end goals into the inference process leads to more efficient goal-oriented algorithms that automatically target the most relevant parameters for prediction. In the linear setting the control-theoretic concepts underlying balance...

other fields. However, the spectral properties of the Laplace Transform tend to complicate its numerical treatment; therefore, the closely related “Truncated” Laplace Transforms are often used in applications. We have constructed efficient algorithms for the evaluation of the left singular functions and singular values of the Truncated Laplace Transform. Together with the previously introduced ...

F. Zanderigo, A. Bertoldo, G. Pillonetto, C. Cobelli Information Engineering, University of Padova, Padova, Italy, Italy, Information Engineering, University of Padova, Padova, ITALY, Italy Introduction. Bolus tracking MRI allows to quantify cerebral blood flow (CBF), volume (CBV) and mean transit time (MTT) by deconvolution from arterial input function, AIF(t), and tissue concentration, C(t), ...

A new method based on singular value decomposition (SVD) was applied to the denoising of time-resolved spectral matrix (TRSM), which obtained by a streak camera. The least informative principal components (PCs) were filtered out using Tikhonov regularization principle. for determining quasi-optimal parameter suggested. SVD compared with moving average time direction (MATD) smoothing TRSM. Numer...

A damage detection algorithm is presented based on updating a finite element model with measured eigenfrequencies and mode shapes. The update needs regularization because it is an ill-posed problem. Tikhonov regularization and truncated singular value decomposition are commonly used regularization techniques for linear problems. These techniques can also be used for nonlinear updating problems,...

The following is a list of the major changes since Version 2.0 of the package. Replaced gsvd by cgsvd which has a diierent sequence of output arguments. Removed the obsolete function csdecomp (which replaced the function csd) Deleted the function mgs. Changed the storage format of bidiagonal matrices to sparse, instead of a dense matrix with two columns. Removed the obsolete function bsvd. Adde...

Tikhonov regularization of linear discrete ill-posed problems often is applied with a finite difference regularization operator that approximates a low-order derivative. These operators generally are represented by banded rectangular matrices with fewer rows than columns. They therefore cannot be applied in iterative methods that are based on the Arnoldi process, which requires the regularizati...

This paper presents an imaging approach for Multiple Input Output Ground Penetrating Radar (MIMO GPR) systems working in down-looking contactless mode. The exploits a linear approximation of the scattering phenomenon and is based on ray-based propagation model, which takes into account presence air-soil interface. Accordingly, Interface Reflection Point concept extended to case MIMO GPR. propos...

We present a method to solve the inverse problem in pulsed photothermal radiometry sPPTRd that exploits advantages of truncated singular value decomposition sT-SVDd while imposing a non-negativity constraint to the solution. The presented method is a hybrid in the sense that it expresses the solution vector as a linear superposition of right singular vectors, but with a non-negative constraint ...