Applications of the random neural network to some inverse problems in image processing

Inverse problems arise in many fields and are important in practical applications to science and engineering. The techniques used today for solving inverse problems are as multivariate as the problems themselves. In this dissertation, we approach solving some inverse problems which arise in imaging by using neural network based methods. Random neural network (RNN) is chosen as the neural network model to be used in this work since it is closer to biophysical reality and mathematically more tractable than standard neural methods.; The first problem that we have studied is the sensor image fusion problem. The role of neural networks in fusion is to reconstitute a visually understandable representation of the scene taken from two or more sensors. The network is trained to produce a non-linear mapping from the sensor output images to get a fused image such that the fused image is closer to the real image than each individual sensor image.; The second problem we have worked on is the land mine detection problem. In my master's thesis [94], we have developed a novel technique called the δ-technique which is based on measuring differences in reflected (or induced) energy in contiguous areas and is shown to be an effective and computationally very fast approach to accurately detecting mines and significantly reducing false alarms. In this work, we consider improvements on this approach using neural network techniques and an additional measured statistic which we call the S-statistic. Two neural network based techniques are developed for mine detection and false alarm filtering. In the first approach, the novel S-statistic is combined with the δ-Technique, in an RNN design. In the second approach, an RNN is trained using a 3 x 3 block measurement window, and then applied as a post-processor for the δ-Technique. It is shown through the use of experimental data that both RNN detectors offer a robust non-parametric technique for mine detection.; The third problem is related to semiconductor fabrication metrology. It is crucial to locate defects (i.e. abnormal features) on the wafer during the manufacturing process. The most obvious way to identify abnormal features is to examine cross-section images or profiles. Since acquiring cross-section image is destructive, the problem is then deducing a chip's vertical cross-section from two-dimensional top-down scanning electron microscopy (SEM) images of the chip surface. We propose two neural network based approaches: One of the approaches is to directly map from SEM intensity waveform to profile. The other one is based on physics of the image formation in SEM. Both methods are trained and tested on real experimental data. Reconstructed profile images from both approaches can be used by a failure analysis engineer to identify abnormal features from normal ones.