Related papers: Numerical Methods for the Inverse Nonlinear Fourie…
Random coupled parabolic partial differential models are solved numerically using random cosine Fourier transform together with non Gaussian random numerical integration that capture the highly oscillatory behavior of the involved…
We consider a particular approach to the regularization of the inverse problem of computerized tomography. This approach is based on notions pertaining to Fourier synthesis. It refines previous contributions, in which the preprocessing of…
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…
The pseudo-polar Fourier transform is a specialized non-equally spaced Fourier transform, which evaluates the Fourier transform on a near-polar grid, known as the pseudo-polar grid. The advantage of the pseudo-polar grid over other…
The inversion of nabla Laplace transform, corresponding to a causal sequence, is considered. Two classical methods, i.e., residual calculation method and partial fraction method are developed to perform the inverse nabla Laplace transform.…
Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…
A three-point iterative method for solving scalar non-linear equations was selected and then adapted to solve systems of non-linear equations. Subsequently, by applying Taylor's theorem to functions of $\R^{n}$ in $\R^{n}$, it is shown that…
A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…
Resampling by interpolation is the traditional method to process interferograms from non-uniformly sampled Fourier transform spectrometers. The non-uniform fast Fourier transform (NUFFT) is an alternative approach that has been mostly…
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…
We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is…
The paper discusses numerical implementations of various inversion schemes for generalized V-line transforms on vector fields introduced in [6]. It demonstrates the possibility of efficient recovery of an unknown vector field from five…
Iterative Fast Fourier Transform methods are useful for calculating the fields in composite materials and their macroscopic response. By iterating back and forth until convergence, the differential constraints are satisfied in Fourier…
In the paper we present some new inversion formulas and two new formulas for Stirling numbers.
Real life signals are in general non--stationary and non--linear. The development of methods able to extract their hidden features in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem…
We propose a new class of semi-implicit methods for solving nonlinear fractional differential equations and study their stability. Several versions of our new schemes are proved to be unconditionally stable by choosing suitable parameters.…
Given a binary nonlinear code, we provide a deterministic algorithm to compute its weight and distance distribution, and in particular its minimum weight and its minimum distance, which takes advantage of fast Fourier techniques. This…
In this paper we established a class of optimal fourth-order methods which is obtained by existing third-order method for solving nonlinear equations for simple roots by using weight functions. Some physical examples are given to illustrate…
Nonlinear inverse problems have complicated landscapes. Hence the calculation with naive iterative schemes (e.g., Gauss-Newton or conjugate gradients) is trapped in local minima. The (first) Born approximation can avoid this trapping but…
In the present work, firstly, we use a minimax equality to prove the existence of a solution of certain system of varitional equations and we provide a numerical approximation of such a solution. Then, we propose a numerical method to solve…