Inverse problems in image processing

Animesh Khemka, Purdue University

Abstract

In this dissertation, we focus on inverse problems related to image processing. We have studied two separate inverse problems and developed two different reconstruction algorithms which can be applied to the two cases. First, we consider the problem of monitoring the concentration and dispersion of pollutants in the atmosphere using a collection of randomly scattered sensors. The sensors are capable of only indicating that the concentration has exceeded a randomly selected threshold and providing this information through a transponder-like mechanism to an airborne imaging radar. We use this information to estimate the concentration as well as the time and location of the pollutant source. We use the Expectation-Maximization algorithm to find the maximum likelihood estimate of the quantities of interest and determine the accuracy of this technique using standard atmospheric dispersion models. Second, we focus on image interpolation. We have developed a method to select the best interpolation algorithm for different regions of an image. In particular, we segment the image into graphical and natural regions and use the appropriate algorithm for each region. The natural regions are interpolated using a current state-of-the-art algorithm. However, when applied to graphical images, the current state-of-the-art interpolators tend to produce artifacts at edge discontinuities. Thus, we developed a novel approach which we call Low Entropy Interpolation (LEI) algorithm for the graphical images. The LEI algorithm is highly non-linear and produces very sharp edges with very few defects necessary for good quality interpolation of graphical images.

Degree

Ph.D.

Advisors

Bell, Purdue University.

Subject Area

Electrical engineering

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