Variational Uncalibrated Photometric Stereo under General Lighting

Photometric stereo (PS) techniques nowadays remain constrained to an ideal laboratory setup where modeling and calibration of lighting is amenable. To eliminate such restrictions, we propose an efficient principled variational approach to uncalibrated PS under general illumination. To this end, the Lambertian reflectance model is approximated through a spherical harmonic expansion, which preserves the spatial invariance of the lighting. The joint recovery of shape, reflectance and illumination is then formulated as a single variational problem. There the shape estimation is carried out directly in terms of the underlying perspective depth map, thus implicitly ensuring integrability and bypassing the need for a subsequent normal integration. To tackle the resulting nonconvex problem numerically, we undertake a two-phase procedure to initialize a balloon-like perspective depth map, followed by a "lagged" block coordinate descent scheme. The experiments validate efficiency and robustness of this approach. Across a variety of evaluations, we are able to reduce the mean angular error consistently by a factor of 2-3 compared to the state-of-the-art.Comment: Haefner and Ye contributed equall

Gravitational wave radiometry: Mapping a stochastic gravitational wave background

The problem of the detection and mapping of a stochastic gravitational wave background (SGWB), either of cosmological or astrophysical origin, bears a strong semblance to the analysis of CMB anisotropy and polarization. The basic statistic we use is the cross-correlation between the data from a pair of detectors. In order to `point' the pair of detectors at different locations one must suitably delay the signal by the amount it takes for the gravitational waves (GW) to travel to both detectors corresponding to a source direction. Then the raw (observed) sky map of the SGWB is the signal convolved with a beam response function that varies with location in the sky. We first present a thorough analytic understanding of the structure of the beam response function using an analytic approach employing the stationary phase approximation. The true sky map is obtained by numerically deconvolving the beam function in the integral (convolution) equation. We adopt the maximum likelihood framework to estimate the true sky map that has been successfully used in the broadly similar, well-studied CMB map making problem. We numerically implement and demonstrate the method on simulated (unpolarized) SGWB for the radiometer consisting of the LIGO pair of detectors at Hanford and Livingston. We include `realistic' additive Gaussian noise in each data stream based on the LIGO-I noise power spectral density. The extension of the method to multiple baselines and polarized GWB is outlined. In the near future the network of GW detectors, including the Advanced LIGO and Virgo detectors that will be sensitive to sources within a thousand times larger spatial volume, could provide promising data sets for GW radiometry.Comment: 24 pages, 19 figures, pdflatex. Matched version published in Phys. Rev. D - minor change

A Two-stage Method for Inverse Medium Scattering

We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer support, and one resolution enhancing step with mixed regularization. The first step is strictly direct and of sampling type, and faithfully detects the scatterer support. The second step is an innovative application of nonsmooth mixed regularization, and it accurately resolves the scatterer sizes as well as intensities. The model is efficiently solved by a semi-smooth Newton-type method. Numerical results for two- and three-dimensional examples indicate that the approach is accurate, computationally efficient, and robust with respect to data noise.Comment: 18 pages, 5 figure

Real-time Microphone Array Processing for Sound-field Analysis and Perceptually Motivated Reproduction

This thesis details real-time implementations of sound-field analysis and perceptually motivated reproduction methods for visualisation and auralisation purposes. For the former, various methods for visualising the relative distribution of sound energy from one point in space are investigated and contrasted; including a novel reformulation of the cross-pattern coherence (CroPaC) algorithm, which integrates a new side-lobe suppression technique. Whereas for auralisation applications, listening tests were conducted to compare ambisonics reproduction with a novel headphone formulation of the directional audio coding (DirAC) method. The results indicate that the side-lobe suppressed CroPaC method offers greater spatial selectivity in reverberant conditions compared with other popular approaches, and that the new DirAC formulation yields higher perceived spatial accuracy when compared to the ambisonics method

A novel prestack sparse azimuthal AVO inversion

In this paper we demonstrate a new algorithm for sparse prestack azimuthal AVO inversion. A novel Euclidean prior model is developed to at once respect sparseness in the layered earth and smoothness in the model of reflectivity. Recognizing that methods of artificial intelligence and Bayesian computation are finding an every increasing role in augmenting the process of interpretation and analysis of geophysical data, we derive a generalized matrix-variate model of reflectivity in terms of orthogonal basis functions, subject to sparse constraints. This supports a direct application of machine learning methods, in a way that can be mapped back onto the physical principles known to govern reflection seismology. As a demonstration we present an application of these methods to the Marcellus shale. Attributes extracted using the azimuthal inversion are clustered using an unsupervised learning algorithm. Interpretation of the clusters is performed in the context of the Ruger model of azimuthal AVO

Large-angle anomalies in the CMB

We review the recently found large-scale anomalies in the maps of temperature anisotropies in the cosmic microwave background. These include alignments of the largest modes of CMB anisotropy with each other and with geometry and direction of motion of the Solar System, and the unusually low power at these largest scales. We discuss these findings in relation to expectation from standard inflationary cosmology, their statistical significance, the tools to study them, and the various attempts to explain them.Comment: Review in the Advances in Astronomy special issue "Testing the Gaussianity and Statistical Isotropy of the Universe" (eds. D. Huterer, E. Komatsu and S. Shandera); 16 pages, 7 figures. v2 matches the published versio