Sampling systems matched to input processes and image classes

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dc.contributor.advisor Rao, Raghuveer
dc.contributor.author Bopardikar, Ajit
dc.date.accessioned 2011-12-06T19:31:46Z
dc.date.available 2011-12-06T19:31:46Z
dc.date.issued 2000-05-01
dc.identifier.uri http://hdl.handle.net/1850/14436
dc.description.abstract This dissertation investigates sampling and reconstruction of wide sense stationary (WSS) random processes from their sample "random variables". In this context, two types of sampling systems are studied, namely, interpolation and approximation sampling systems. We aim to determine the properties of the filters in these systems that minimize the mean squared error between the input process and the process reconstructed from its samples. More specifically, for the interpolation sampling system we seek and obtain a closed form expression for an interpolation filter that is optimal in this sense. Likewise, for the approximation sampling system we derive a closed form expression for an optimal reconstruction filter given the statistics of the input process and the antialiasing filter. Using these expressions we show that Meyer-type scaling functions and wavelets arise naturally in the context of subsampled bandlimited processes. We also derive closed form expressions for the mean squared error incurred by both the sampling systems. Using the expression for mean squared error we show that for an approximation sampling system, minimum mean squared error is obtained when the antialiasing filter and the reconstruction filter are spectral factors of an ideal brickwall-type filter. Similar results are derived for the discrete-time equivalents of these sampling systems. Finally, we give examples of interpolation and approximation sampling filters and compare their performance with that of some standard filters. The implementation of these systems is based on a novel framework called the perfect reconstruction circular convolution (PRCC) filter bank framework. The results obtained for the one dimensional case are extended to the multidimensional case. Sampling a multidimensional random field or image class has a greater degree of freedom and the sampling lattice can be defined by a nonsingular matrix D. The aim is to find optimal filters in multidimensional sampling systems to reconstruct the input image class from its samples on a lattice defined by D. Closed form expressions for filters in multidimensional interpolation and approximation sampling systems are obtained as are expressions for the mean squared error incurred by each system. For the approximation sampling system it is proved that the antialiasing and reconstruction filters that minimize the mean squared error are spectral factors of an ideal brickwall-type filter whose support depends on the sampling matrix D. Finally. we give examples of filters in the interpolation and approximation sampling systems for an image class derived from a LANDSAT image and a quincunx sampling lattice. The performance of these filters is compared with that of some standard filters in the presence of a quantizer. en_US
dc.language.iso en_US en_US
dc.subject Image class en_US
dc.subject Input process en_US
dc.subject Sampling system en_US
dc.subject Wide sense stationary en_US
dc.subject WSS en_US
dc.subject.lcc TA1637 .B66 2000
dc.subject.lcsh Image processing--Digital techniques--Mathematical models en_US
dc.subject.lcsh Electric filters, Digital--Mathematical models en_US
dc.subject.lcsh Sampling (Statistics) en_US
dc.subject.lcsh Signal processing--Statistical methods en_US
dc.subject.lcsh Numerical analysis en_US
dc.title Sampling systems matched to input processes and image classes en_US
dc.type Thesis en_US
dc.description.college College of Science en_US
dc.description.department Chester F. Carlson Center for Imaging Science en_US

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