Image Reconstruction After Transform Coding Using Relative Entropy and Maximum Entropy

Presented are two new methods based on entropy for reconstructing images compressed with the Discrete Cosine transform. One method is based upon a sequential implementation of the Minimum Relative Entropy Principle; the other is based upon the Maximum Entropy Principle. These will be compared with each other and with the conventional method employing the Inverse Discrete Cosine transform. Chapter 2 describes the traditional use of the Discrete Cosine transform for image compression. Chapter 3 explains the theory and implementation of the entropy-based reconstructions. It introduces a fast algorithm for the Maximum Entropy Principle. Chapter 4 compares the numerical performance of the three reconstruction methods. Chapter 5 shows the theoretical convergence limit of the iterative implementation of the Minimum Relative Entropy Principle to equal the limit of the convergence of the Maximum Relative Entropy method. Preliminary results of this thesis were presented at Southeastern \u2787 in Tampa. Final results will be presented at the Annual Meeting of the American Optical Society in Rochester on October 19, 1987

Persistent global power fluctuations near a dynamic transition in electroconvection

This is a study of the global fluctuations in power dissipation and light transmission through a liquid crystal just above the onset of electroconvection. The source of the fluctuations is found to be the creation and annihilation of defects. They are spatially uncorrelated and yet temporally correlated. The temporal correlation is seen to persist for extremely long times. There seems to be an especially close relation between defect creation/annihilat ion in electroconvection and thermal plumes in Rayleigh-B\'enard convection

A Stochastic Description of Dictyostelium Chemotaxis

Chemotaxis, the directed motion of a cell toward a chemical source, plays a key role in many essential biological processes. Here, we derive a statistical model that quantitatively describes the chemotactic motion of eukaryotic cells in a chemical gradient. Our model is based on observations of the chemotactic motion of the social ameba Dictyostelium discoideum, a model organism for eukaryotic chemotaxis. A large number of cell trajectories in stationary, linear chemoattractant gradients is measured, using microfluidic tools in combination with automated cell tracking. We describe the directional motion as the interplay between deterministic and stochastic contributions based on a Langevin equation. The functional form of this equation is directly extracted from experimental data by angle-resolved conditional averages. It contains quadratic deterministic damping and multiplicative noise. In the presence of an external gradient, the deterministic part shows a clear angular dependence that takes the form of a force pointing in gradient direction. With increasing gradient steepness, this force passes through a maximum that coincides with maxima in both speed and directionality of the cells. The stochastic part, on the other hand, does not depend on the orientation of the directional cue and remains independent of the gradient magnitude. Numerical simulations of our probabilistic model yield quantitative agreement with the experimental distribution functions. Thus our model captures well the dynamics of chemotactic cells and can serve to quantify differences and similarities of different chemotactic eukaryotes. Finally, on the basis of our model, we can characterize the heterogeneity within a population of chemotactic cells

Iterative Reconstruction Of Transform-Coded Images Using Relative Entropy.

A universal method of decoding transform-coded images using the principle of minimum relative entropy (MREP) is considered that was previously introduced by the authors. Here they examine the MREP\u27s iterative convergence properties by applying it to image data compressed by the discrete cosine transform and running the MREP iterative algorithm until it stabilizes

Reconstruction Of Transform-Coded Images By Entropy Methods

A new, universal approach to reconstructing transform-coded images is proposed. The method views the images as a probability mass function (pmf), allowing the retained coefficients of a transform (Karhunen-Loeve, discrete cosine, slant, etc.) to be thought of as averages of the basis functions over the pmf. This sets the stage for reconstructing the original images by using the maximum entropy principle (MEP) and the minimum relative entropy principle (MREP) with the retained coefficients as constraints in the extremizations. A formulation combining the two methods is also proposed, resulting in a reconstruction algorithm that is fast, proceeding in an iterative way using the estimate from each coefficient as a prior pmf for the next one via the MREP. The proposed approaches are illustrated with images compressed by discrete cosine transform coding, and the results are compared with standard reconstruction using the inverse discrete cosine transform

A scanning PIV method for fine-scale turbulence measurements

A hybrid technique is presented that combines scanning PIV with tomographic reconstruction to make spatially and temporally resolved measurements of the fine-scale motions in turbulent flows. The technique uses one or two high-speed cameras to record particle images as a laser sheet is rapidly traversed across a measurement volume. This is combined with a fast method for tomographic reconstruction of the particle field for use in conjunction with PIV cross-correlation. The method was tested numerically using DNS data and with experiments in a large mixing tank that produces axisymmetric homogeneous turbulence at Rλ≃219. A parametric investigation identifies the important parameters for a scanning PIV set-up and provides guidance to the interested experimentalist in achieving the best accuracy. Optimal sheet spacings and thicknesses are reported, and it was found that accurate results could be obtained at quite low scanning speeds. The two-camera method is the most robust to noise, permitting accurate measurements of the velocity gradients and direct determination of the dissipation rate.</p