We use blind deconvolution methods in optical diffusion tomography to reconstruct images of objects imbedded in or located behind turbid media from continuous-wave measurements of the scattered light transmitted through the media. In particular, we use a blind deconvolution imaging algorithm to determine both a deblurred image of the object and the depth of the object inside the turbid medium. ...

We provide a data mine of proven results for multiple zeta values (MZVs) of the form ζ(s1,s2, . . . ,sk) = ∑n1>n2>...>nk>0 { 1/(n1 1 ...n sk k ) } with weight w = ∑i=1 si and depth k and for Euler sums of the form ∑n1>n2>...>nk>0 { (ε1 1 ...ε nk 1 )/(n s1 1 ...n sk k ) } with signs εi = ±1. Notably, we achieve explicit proven reductions of all MZVs with weights w≤ 22, and all Euler sums with we...

Depth estimation has been used widely as a tool for rapid interpretion of large-scale potential-field data in applications such as mapping basement relief. Nearly all of these techniques rely on the analysis of the local shape of the anomalous field in determining the depth and location of the subsurface sources. These methods focus on the phase information at the expense of the amplitude of th...

We present a method for estimating the point spread function of a terahertz imaging system designed to operate in reflection mode. The method is based on imaging phantoms with known geometry, which have patterns with sharp edges at all orientations. The point spread functions are obtained by a deconvolution technique in the Fourier domain. We validate our results by using the estimated point sp...

y(t0) = y0 Here f(t, y) is a given function, t0 is a given initial time and y0 is a given initial value for y. The unknown in the problem is the function y(t). Two obvious considerations in deciding whether or not a given algorithm is of any practical value are (a) the amount of computational effort required to execute the algorithm and (b) the accuracy that this computational effort yields. Fo...

In this investigation we propose a computational approach for solution of optimal control problems for vortex systems with compactly supported vorticity. The problem is formulated as PDE–constrained optimization in which the solutions are found using a gradient–based descent method. Recognizing such Euler flows as free– boundary problems, the proposed approach relies on shape differentiation co...

y(t0) = y0 Here f(t, y) is a given function, t0 is a given initial time and y0 is a given initial value for y. The unknown in the problem is the function y(t). Two obvious considerations in deciding whether or not a given algorithm is of any practical value are (a) the amount of computational effort required to execute the algorithm and (b) the accuracy that this computational effort yields. Fo...

8. First-Order Equations: Numerical Methods 8.1. Numerical Approximations 2 8.2. Explicit and Implicit Euler Methods 3 8.3. Explicit One-Step Methods Based on Taylor Approximation 4 8.3.1. Explicit Euler Method Revisited 4 8.3.2. Local and Global Errors 4 8.3.3. Higher-Order Taylor-Based Methods (not covered) 5 8.4. Explicit One-Step Methods Based on Quadrature 6 8.4.1. Explicit Euler Method Re...