A recurring task in image processing, approximation theory, and the numerical solution of partial differential equations is to reconstruct a piecewise-smooth real-valued function f (x), where x ∈ R N , from its truncated Fourier transform (its truncated spectrum). An essential step is edge detection for which a variety of one-dimensional schemes have been developed over the last few decades. Mo...

There are several different types of wavefront sensors that can be used to measure the phase of an input beam. While they have widely varying modes of operation, they all require some computational overhead in order to deconstruct the phase from an optical measurement which reduces the sensing speed. Furthermore, zonal detection methods, such as the Shack-Hartmann wavefront sensor (SHWFS) are n...

Wavefront computations, characterized by a data dependent flow of computation across a data space, are receiving increasing attention as an important class of parallel computations. Though sophisticated compiler optimizations can often produce efficient pipelined implementations from sequential representations, we argue that a language-based approach to representing wavefront computations is a ...

The slope detection and ranging (SLODAR) method recovers atmospheric turbulence profiles from time averaged spatial cross correlations of wavefront slopes measured by Shack-Hartmann wavefront sensors. The Palomar multiple guide star unit (MGSU) was set up to test tomographic multiple guide star adaptive optics and provided an ideal test bed for SLODAR turbulence altitude profiling. We present t...

We introduce a multigrid preconditioned conjugate gradient (MGCG) iterative scheme for computing open loop wavefront reconstructors in the adaptive optics (AO) system of large telescopes. We present numerical simulations which indicate that our MGCG method has a rapid convergence rate for a wide range of sub-aperture gradient measurement signal-to-noise ratios. The cost per iteration is order N...

Small-scale neuronal networks may impose widespread effects on large network dynamics. To unravel this relationship, we analyzed eight multiscale recordings of spontaneous seizures from four patients with epilepsy. During seizures, multiunit spike activity organizes into a submillimeter-sized wavefront, and this activity correlates significantly with low-frequency rhythms from electrocorticogra...

A recurring task in image processing, approximation theory, and the numerical solution of partial differential equations is to reconstruct a piecewise-smooth real-valued function f(x), where x ∈ R , from its truncated Fourier transform (its truncated spectrum). An essential step is edge detection for which a variety of one-dimensional schemes have been developed over the last few decades. Most ...