The inner mass power spectrum of galaxies using strong gravitational lensing: beyond linear approximation

In the last decade the detection of individual massive dark matter sub-halos has been possible using potential correction formalism in strong gravitational lens imaging. Here we propose a statistical formalism to relate strong gravitational lens surface brightness anomalies to the lens potential fluctuations arising from dark matter distribution in the lens galaxy. We consider these fluctuations as a Gaussian random field in addition to the unperturbed smooth lens model. This is very similar to weak lensing formalism and we show that in this way we can measure the power spectrum of these perturbations to the potential. We test the method by applying it to simulated mock lenses of different geometries and by performing an MCMC analysis of the theoretical power spectra. This method can measure density fluctuations in early type galaxies on scales of 1-10 kpc at typical rms-levels of a percent, using a single lens system observed with the Hubble Space Telescope with typical signal-to-noise ratios obtained in a single orbit

Dynamic Iterative Pursuit

For compressive sensing of dynamic sparse signals, we develop an iterative pursuit algorithm. A dynamic sparse signal process is characterized by varying sparsity patterns over time/space. For such signals, the developed algorithm is able to incorporate sequential predictions, thereby providing better compressive sensing recovery performance, but not at the cost of high complexity. Through experimental evaluations, we observe that the new algorithm exhibits a graceful degradation at deteriorating signal conditions while capable of yielding substantial performance gains as conditions improve.Comment: 6 pages, 7 figures. Accepted for publication in IEEE Transactions on Signal Processin