Engineering topics
Recht, Benjamin
Publications and source records attributed to Recht, Benjamin.
Superresolution without separation
Abstract This article provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination of $M$ shifted copies of a known waveform with unknown shifts and amplitudes, and one only observes a finite collection of evaluations of this signal. We characterize properties of the base waveform such that the exact translations and amplitudes can be recovered from $2M+1$ observations. This recovery can be achieved by solving a weighted version of basis pursuit over a continuous dictionary. Our analysis shows that $\ell_1$-based methods enjoy the same separation-free recovery guarantees as polynomial root finding techniques, such as de Prony’s method or Vetterli’s method for signals of finite rate of innovation. Our proof techniques combine classical polynomial interpolation techniques with contemporary tools from compressed sensing.
Well-Being Tracking via Smartphone-Measured Activity and Sleep: Cohort Study
Automatically tracking mental well-being could facilitate personalization of treatments for mood disorders such as depression and bipolar disorder. Smartphones present a novel and ubiquitous opportunity to track individuals’ behavior and may be useful for inferring and automatically monitoring mental well-being. The aim of this study was to assess the extent to which activity and sleep tracking with a smartphone can be used for monitoring individuals’ mental well-being.