Real-Space Inversion and Super-Resolution of Ultrafast Scattering using Natural Scattering Kernels

Directly resolving in real-space multiple atomic motions using ultrafast x-ray or electron scattering is generally limited by the finite detector range. As a result, signal interpretation mostly relies on modeling and simulations of specific excitation pathways. Here, we introduce an approach to resolve ultrafast diffuse scattering signals in real space below the diffraction limit, and recover multiple atomic motions de-novo, using a scattering basis representation that is composed of the measurement parameters and constraints, and the subsequent inversion analysis. We leverage signal priors, such as smoothness and sparsity to deconvolve the spatially transformed signals using convex optimization. We validate the approach on simulated and experimental data, demonstrate super-resolution in real space, and discuss the recovery accuracy and resolution limits vs signal fidelity.Comment: 6 pages, 4 figure

Beyond the current noise limit in imaging through turbulent medium

Shift-and-add is an approach employed to mitigate the phenomenon of resolution degradation in images acquired through a turbulent medium. Using this technique, a large number of consecutive short exposures is registered below the coherence time of the atmosphere or other blurring medium. The acquired images are shifted to the position of the brightest speckle and stacked together to obtain high-resolution and high signal-to-noise frame. In this paper we present a highly efficient method for determination of frames shifts, even if in a single frame the object cannot be distinguished from the background noise. The technique utilizes our custom genetic algorithm, which iteratively evolves a set of image shifts. We used the maximal energy of stacked images as an objective function for shifts estimation and validate the efficiency of the method on simulated and real images of simple and complex sources. Obtained results confirmed, that our proposed method allows for the recovery of spatial distribution of objects even only 2% brighter than their background. The presented approach extends significantly current limits of image reconstruction with the use of shift-and-add method. The applications of our algorithm include both the optical and the infrared imaging. Our method may be also employed as a digital image stabilizer in extremely low light level conditions in professional and consumer applications.Comment: 8 pages, 4 figure

Dynamic super-resolution in particle tracking problems

Particle tracking in biological imaging is concerned with reconstructing the trajectories, locations, or velocities of the targeting particles. The standard approach of particle tracking consists of two steps: first reconstructing statically the source locations in each time step, and second applying tracking techniques to obtain the trajectories and velocities. In contrast, the dynamic reconstruction seeks to simultaneously recover the source locations and velocities from all frames, which enjoys certain advantages. In this paper, we provide a rigorous mathematical analysis for the resolution limit of reconstructing source number, locations, and velocities by general dynamical reconstruction in particle tracking problems, by which we demonstrate the possibility of achieving super-resolution for the dynamic reconstruction. We show that when the location-velocity pairs of the particles are separated beyond certain distances (the resolution limits), the number of particles and the location-velocity pair can be stably recovered. The resolution limits are related to the cut-off frequency of the imaging system, signal-to-noise ratio, and the sparsity of the source. By these estimates, we also derive a stability result for a sparsity-promoting dynamic reconstruction. In addition, we further show that the reconstruction of velocities has a better resolution limit which improves constantly as the particles moving. This result is derived by an observation that the inherent cut-off frequency for the velocity recovery can be viewed as the total observation time multiplies the cut-off frequency of the imaging system, which may lead to a better resolution limit as compared to the one for each diffraction-limited frame. It is anticipated that this observation can inspire new reconstruction algorithms that improve the resolution of particle tracking in practice

Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Power Spectra and WMAP-Derived Parameters

(Abridged) We present the angular power spectra derived from the 7-year maps and discuss the cosmological conclusions that can be inferred from WMAP data alone. The third acoustic peak in the TT spectrum is now well measured by WMAP. In the context of a flat LambdaCDM model, this improvement allows us to place tighter constraints on the matter density from WMAP data alone, and on the epoch of matter-radiation equality, The temperature-polarization (TE) spectrum is detected in the 7-year data with a significance of 20 sigma, compared to 13 sigma with the 5-year data. The low-l EE spectrum, a measure of the optical depth due to reionization, is detected at 5.5 sigma significance when averaged over l = 2-7. The BB spectrum, an important probe of gravitational waves from inflation, remains consistent with zero. The upper limit on tensor modes from polarization data alone is a factor of 2 lower with the 7-year data than it was using the 5-year data (Komatsu et al. 2010). We test the parameter recovery process for bias and find that the scalar spectral index, ns, is biased high, but only by 0.09 sigma, while the remaining parameters are biased by < 0.15 sigma. The improvement in the third peak measurement leads to tighter lower limits from WMAP on the number of relativistic degrees of freedom (e.g., neutrinos) in the early universe: Neff > 2.7 (95% CL). Also, using WMAP data alone, the primordial helium mass fraction is found to be YHe = 0.28+0.14-0.15, and with data from higher-resolution CMB experiments included, we now establish the existence of pre-stellar helium at > 3 sigma (Komatsu et al. 2010).Comment: 22 pages, 14 figures, version accepted to Astrophysical Journal Supplement Series, added high-l EE detection, consolidated parameter recovery simulation