Donoho, David L. | Search NASA

NASA NTRS1993

The quasi-periodic oscillations and very low frequency noise of Scorpius X-1 as transient chaos - A dripping handrail?

We present evidence that the quasi-periodic oscillations (QPO) and very low frequency noise (VLFN) characteristic of many accretion sources are different aspects of the same physical process. We analyzed a long, high time resolution EXOSAT observation of the low-mass X-ray binary (LMXB) Sco X-1. The X-ray luminosity varies stochastically on time scales from milliseconds to hours. The nature of this variability - as quantified with both power spectrum analysis and a new wavelet technique, the scalegram - agrees well with the dripping handrail accretion model, a simple dynamical system which exhibits transient chaos. In this model both the QPO and VLFN are produced by radiation from blobs with a wide size distribution, resulting from accretion and subsequent diffusion of hot gas, the density of which is limited by an unspecified instability to lie below a threshold.

Scargle, Jeffrey D.↗

NASA NTRS1992

Superresolution via sparsity constraints

The problem of recovering a measure mu supported on a lattice of span Delta is considered under the condition that measurements are only available concerning the Fourier Transform at frequencies of Omega or less. If Omega is much smaller than the Nyquist frequency pi/Delta and the measurements are noisy, then stable recovery of mu is generally impossible. It is shown here that if, in addition, it is known that mu satisfies certain sparsity constraints, then stable recovery is possible. This finding validates practical efforts in spectroscopy, seismic prospecting, and astronomy to provide superresolution by imposing support limitations in reconstruction.

Donoho, David L.↗