Reconstruction of diffusions using spectral data from timeseries

Reconstruction of Diffusions Using Spectral Data from Timeseries

Abstract. A numerical technique for the reconstruction of diffusion processes (diffusions, in short) from data is presented. The drift and diffusion coefficients of the generator of the diffusion are found by minimizing an object function which measures the difference between the eigenspectrum of the operator and a reference eigenspectrum. The reference spectrum can be obtained, in discretized ...

Image Reconstruction from Incomplete Data

Image Reconstruction from Incomplete Data

Reconstruction of tridiagonal matrices from spectral data

Jacobi matrices are parametrized by their eigenvalues and norming constants (first coordinates of normalized eigenvectors): this coordinate system breaks down at reducible tridiagonal matrices. The set of real symmetric tridiagonal matrices with prescribed simple spectrum is a compact manifold, admitting an open covering by open dense sets Uπ Λ centered at diagonal matrices Λπ , where π spans t...

On Reconstruction from Non-uniform Spectral Data

Abstract This paper addresses the reconstruction of compactly supported functions from non-uniform samples of their Fourier transform. We briefly investigate the consequences of acquiring non-uniform spectral data. We summarize two often applied reconstruction methods, convolutional gridding and uniform re-sampling, and investigate the reconstruction accuracy as it relates to sampling density. ...