Coarse structures involving low electrical contrasts can be profitably imaged by means of cheap and relatively simple methods such as travel time tomography, whereas fine structure involving sub-wavelength detail can only be recovered by inverting full-waveform data. Despite its complexity and high computation costs, full-waveform inversion of GPR data has become a popular tool for high-resolut...

We document the calibration of the local volatility in terms of local and implied instantaneous variances; we first explore the theoretical properties of the method for a particular class of volatilities. We confirm the theoretical results through a numerical procedure which uses a Gauss-Newton style approximation of the Hessian in the framework of a sequential quadratic programming (SQP) appro...

PURPOSE An emerging topic in diffusion magnetic resonance is imaging blood microcirculation alongside water diffusion using the intravoxel incoherent motion (IVIM) model. Recently, a combined IVIM diffusion tensor imaging (IVIM-DTI) model was proposed, which accounts for both anisotropic pseudo-diffusion due to blood microcirculation and anisotropic diffusion due to tissue microstructures. In t...

We investigate a new algorithm for computing regularized solutions of the 2-D magnetotelluric inverse problem. The algorithm employs a nonlinear conjugate gradients (NLCG) scheme to minimize an objective function that penalizes data residuals and second spatial derivatives of resistivity. We compare this algorithm theoretically and numerically to two previous algorithms for constructing such “m...

We consider a problem of simultaneous reduction of a sequence of matrices by means of orthogonal transformations. We show that such reduction can be performed by a series of the deflation steps. At each deflation step a simultaneous eigenvalue problem, which is a direct generalization of the generalized eigenvalue problem, is solved. A fast variant of Gauss-Newton algorithm for its solution was...

The implementation of geostatistical approach to solve inverse problems [8], such as estimating hydraulic conductivity from measurements of head, is expensive for problems discretized on fine grids. Dimensionality reduction techniques such as representing the random field via Karhunen-Loève expansion, are frequently used in such a context. We show how to combine an efficient method to compute t...

Control theory has become a focus of research for evaluation and synthesis of numerical algorithms. In this paper, a finite-time version of the continuous Newton method is proposed using finite-time stability theory. Moreover, robustness of the proposed method under computational errors is discussed. It is also shown that the proposed approach can change the singularity structure of the Newton ...

Abstract: Time-domain testing of A/D converter in single tone mode amounts to the identification of fundamental and harmonic tones in noise. The variable projection method reduces this problem to frequency estimation by minimising a onedimensional function. In this paper it is shown that the bias due to ignoring the harmonic distortion effect is negligible, and this approximation leads to fast ...