Linear Reconstruction of Non-Stationary Image Ensembles Incorporating Blur and Noise Models

Two new linear reconstruction techniques are developed to improve the resolution of images collected by ground-based telescopes imaging through atmospheric turbulence. The classical approach involves the application of constrained least squares (CLS) to the deconvolution from wavefront sensing (DWFS) technique. The new algorithm incorporates blur and noise models to select the appropriate regularization constant automatically. In all cases examined, the Newton-Raphson minimization converged to a solution in less than 10 iterations. The non-iterative Bayesian approach involves the development of a new vector Wiener filter which is optimal with respect to mean square error (MSE) for a non-stationary object class degraded by atmospheric turbulence and measurement noise. This research involves the first extension of the Wiener filter to account properly for shot noise and an unknown, random optical transfer function (OTF). The vector Wiener filter provides superior reconstructions when compared to the traditional scalar Wiener filter for a non-stationary object class. In addition, the new filter can provide a superresolution capability when the object\u27s Fourier domain statistics are known for spatial frequencies beyond the OTF cutoff. A generalized performance and robustness study of the vector Wiener filter showed that MSE performance is fundamentally limited by object signal-to-noise ratio (SNR) and correlation between object pixels

Frame Selection Performance Limits for Statistical Image Reconstruction of Adaptive Optics Compensated Images

The U.S. Air Force uses adaptive optics systems to collect images of extended objects beyond the atmosphere. These systems use wavefront sensors and deformable mirrors to compensate for atmospheric turbulence induced aberrations. Adaptive optics greatly enhance image quality; however, wavefront aberrations are not completely eliminated. Therefore, post-detection processing techniques are employed to further improve the compensated images. Typically, many short exposure images are collected, recentered to compensate for tilt, and then averaged to overcome randomness in the images and improve signal-to-noise ratio. Experience shows that some short exposure images in a data set are better than others. Frame selection exploits this fact by using a quality metric to discard low quality frames. A composite image is then created by averaging only the best frames. Performance limits associated with the frame selection technique are investigated in this thesis. Limits imposed by photon noise result in a minimum object brightness of visual magnitude +8 for point sources and +4 for a typical satellite model. Effective average point spread functions for point source and extended objects after frame selection processing are almost identical across a wide range of conditions. This discovery allows the use of deconvolution techniques to sharpen images after using the frame selection technique. A new post-detection processing method, frame weighting, is investigated and may offer some improvement for dim objects during poor atmospheric seeing. Frame selection is demonstrated for the first time on actual imagery from an adaptive optics system. Data analysis indicates that signal-to-noise ratio improvements are degraded for exposure times longer than that allowed to freeze individual realizations of the turbulence effects

Optical coherence tomography with a Fizeau interferometer configuration

We report the investigation of a Fizeau interferometer-based OCT system. A secondary processing interferometer is necessary in this configuration, to compensate the optical path difference formed in the Fizeau interferometer between the end of the fibre and the sample. The Fizeau configuration has the advantage of 'downlead insensitivity', which eliminates polarisation fading. An optical circulator is used in our system to route light efficiently from the source to the sample, and backscattered light from the sample and the fibre end through to the Mach-Zehnder processing interferometer. The choice of a Mach- Zehnder processing interferometer, from which both antiphase outputs are available, facilitates the incorporation of balanced detection, which often results in a large improvement in the Signal-to-Noise ratio (SNR) compared with the use of a single detector. Balanced detection comprises subtraction of the two antiphase interferometer outputs, implying that the signal amplitude is doubled and the noise is well reduced. It has been discerned that the SNR drops when the refractive index variation at a boundary is small. Several OCT images of samples (resin, resin + crystals, fibre composite) are presented

Inversely Unstable Solutions of Two-Dimensional Systems on Genus-p Surfaces and the Topology of Knotted Attractors

In this paper, we will show that a periodic nonlinear, time-varying dissipative system that is defined on a genus-p surface contains one or more invariant sets which act as attractors. Moreover, we shall generalize a result in [Martins, 2004] and give conditions under which these invariant sets are not homeomorphic to a circle individually, which implies the existence of chaotic behaviour. This is achieved by studying the appearance of inversely unstable solutions within each invariant set.Comment: 19 pages with 20 figures, AMS La-TeX, to be published in International Journal of Bifurcation and Chao

Spaceborne radar observations: A guide for Magellan radar-image analysis

Geologic analyses of spaceborne radar images of Earth are reviewed and summarized with respect to detecting, mapping, and interpreting impact craters, volcanic landforms, eolian and subsurface features, and tectonic landforms. Interpretations are illustrated mostly with Seasat synthetic aperture radar and shuttle-imaging-radar images. Analogies are drawn for the potential interpretation of radar images of Venus, with emphasis on the effects of variation in Magellan look angle with Venusian latitude. In each landform category, differences in feature perception and interpretive capability are related to variations in imaging geometry, spatial resolution, and wavelength of the imaging radar systems. Impact craters and other radially symmetrical features may show apparent bilateral symmetry parallel to the illumination vector at low look angles. The styles of eruption and the emplacement of major and minor volcanic constructs can be interpreted from morphological features observed in images. Radar responses that are governed by small-scale surface roughness may serve to distinguish flow types, but do not provide unambiguous information. Imaging of sand dunes is rigorously constrained by specific angular relations between the illumination vector and the orientation and angle of repose of the dune faces, but is independent of radar wavelength. With a single look angle, conditions that enable shallow subsurface imaging to occur do not provide the information necessary to determine whether the radar has recorded surface or subsurface features. The topographic linearity of many tectonic landforms is enhanced on images at regional and local scales, but the detection of structural detail is a strong function of illumination direction. Nontopographic tectonic lineaments may appear in response to contrasts in small-surface roughness or dielectric constant. The breakpoint for rough surfaces will vary by about 25 percent through the Magellan viewing geometries from low to high Venusian latitudes. Examples of anomalies and system artifacts that can affect image interpretation are described

Maternal Behavior Potentially Affecting Offspring Survivability: a Comparison Between Meishan and Yorkshire X Landrace (YL) Sows

This study was designed to examine differences in maternal behavior between two breeds, the Meishan breed from China and the Yorkshire/Landrace (YL) cross. This was a preliminary trial aimed at gathering data to appropriately design a more extensive study. Identification of maternal behavioral contributions to piglet survivability may assist in reducing production losses caused by the sow.</p