Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing

We demonstrate that sub-wavelength optical images borne on partially-spatially-incoherent light can be recovered, from their far-field or from the blurred image, given the prior knowledge that the image is sparse, and only that. The reconstruction method relies on the recently demonstrated sparsity-based sub-wavelength imaging. However, for partially-spatially-incoherent light, the relation between the measurements and the image is quadratic, yielding non-convex measurement equations that do not conform to previously used techniques. Consequently, we demonstrate new algorithmic methodology, referred to as quadratic compressed sensing, which can be applied to a range of other problems involving information recovery from partial correlation measurements, including when the correlation function has local dependencies. Specifically for microscopy, this method can be readily extended to white light microscopes with the additional knowledge of the light source spectrum.Comment: 16 page

Role of Alpha Oscillations During Short Time Memory Task Investigated by Graph Based Partitioning

In this study, we investigate the clustering pattern of alpha band (8 Hz - 12 Hz) electroencephalogram (EEG) oscillations obtained from healthy individuals during a short time memory task with 3 different memory loads. The retention period during which subjects were asked to memorize a pattern in a square matrix is analyzed with a graph theoretical approach. The functional coupling among EEG electrodes are quantified via mutual information in the time-frequency plane. A spectral clustering algorithm followed by bootstrapping is used to parcellate memory related circuits and for identifying significant clusters in the brain. The main outcome of the study is that the size of the significant clusters formed by alpha oscillations decreases as the memory load increases. This finding corroborates the active inhibition hypothesis about alpha oscillations

A survey of uncertainty principles and some signal processing applications

The goal of this paper is to review the main trends in the domain of uncertainty principles and localization, emphasize their mutual connections and investigate practical consequences. The discussion is strongly oriented towards, and motivated by signal processing problems, from which significant advances have been made recently. Relations with sparse approximation and coding problems are emphasized

Scattering of gravitational radiation. Intensity fluctuations

Aims. The effect of gravitational microlensing on the intensity of gravitational radiation as it propagates through an inhomogeneous medium is considered. Lensing by both stars and a power law spectrum of density perturbations is examined. Methods. The long wavelengths characteristic of gravitational radiation mandate a statistical, physical-optics approach to treat the effect of the lensing. Results. A model for the mass power spectrum of a starfield, including the effects of clustering and allowing for a distribution of stellar masses, is constructed and used to determine both the amplitude of fluctuations in the gravitational wave strain and its associated temporal fluctuation spectrum. For a uniformly distributed starfield the intensity variance scales linearly with stellar density, σ, but is enhanced by a factor ≳σr^2_F when clustering is important, where r_F is the Fresnel scale. The effect of lensing by a power law mass spectrum, applicable to lensing by small scale fluctuations in gas and dark matter, is also considered. For power law mass density spectra with indices steeper than −2 the wave amplitude exhibits rms fluctuations 1.3^(1/4)(D_(eff)/1 Gpc)^(1/2)%, where is the variance in the mass surface density measured in M^2_⊙ pc^(−4) and D_(eff) is the effective distance to the lensing medium. For shallower spectra the amplitude of the fluctuations depends additionally on the inner length scale and power law index of the density fluctuations. The intensity fluctuations are dominated by temporal fluctuations on long timescales. For lensing material moving at a speed v across the line of sight the fluctuation timescale exceeds v^(−1)(D_(eff)λ)^(1/2). Lensing by small scale structure induces at most ≈15% rms variations if the line of sight to a gravitational wave source intersects a region with densities ~100 M_⊙ pc^(−2), which are typically encountered in the vicinity of galaxy clusters

Microarcsecond Radio Imaging using Earth Orbit Synthesis

The observed interstellar scintillation pattern of an intra-day variable radio source is influenced by its source structure. If the velocity of the interstellar medium responsible for the scattering is comparable to the earth's, the vector sum of these allows an observer to probe the scintillation pattern of a source in two dimensions and, in turn, to probe two-dimensional source structure on scales comparable to the angular scale of the scintillation pattern, typically $\sim 10 \mu$as for weak scattering. We review the theory on the extraction of an ``image'' from the scintillation properties of a source, and show how earth's orbital motion changes a source's observed scintillation properties during the course of a year. The imaging process, which we call Earth Orbit Synthesis, requires measurements of the statistical properties of the scintillations at epochs spread throughout the course of a year.Comment: ApJ in press. 25 pages, 7 fig