Optimum processors for pattern recognition with nonoverlapping target and scene noise

In this dissertation, we are concerned with the detection of a known two-dimensional signal, with possibly an unknown illumination or strength, in the presence of noise, using optical pattern recognition techniques.^ Part I: Optimum receivers for pattern recognition with nonoverlapping target and scene noise. In the first part, we design optimum receivers for pattern recognition problems with nonoverlapping target and scene noise. The design of the receivers is based on hypothesis testing. We show that a noise-free target in the presence of spatially nonoverlapping scene noise can be detected with no error by operations that are independent of the scene-noise statistics. The operations performed by the optimum receiver for this case are two correlations and a subtraction which can be implemented with an optical processor. We also design the optimum receiver for detecting a noisy target in nonoverlapping colored background noise. We show that in this receiver the input signal must pass through a prewhitening process in addition to the operations performed by the optimum receiver designed for a noise-free target.^ Part II: Statistical analysis and design of nonlinear joint transform correlators. We investigate the performance of the optical nonlinear joint transform correlators (JTC) for target detection in the presence of colored background noise. We also investigate the sensitivity of the binary nonlinear JTC, using different thresholding methods for binarization in the Fourier plane, under unknown illumination conditions. Finally we introduce a technique to select the support area in the Fourier plane of a binary JTC to design a ternary JTC. We show that the ternary JTC, under certain conditions, can have a better noise performance compared with a binary JTC.