Researcher Information

Abstract

This project builds a mathematical model that obtains parameters and statistical properties of residuals taken from a picture in JPEG format, to later simulate replicas of the original picture. The importance of this problem stems from the large amount of bandwidth required to transmit a high resolution picture over the Internet. The mathematical model built from this picture and its set of residuals has a much smaller magnitude than the original picture elements (pixels). This implies that if one were to transmit the parameters alone, a high compression rate would be achieved, thus saving bandwidth. In order to replicate the picture, the receiver has to randomly generate a set of residuals (inputs) with the same statistical properties as those from the received mathematical model, and process them in order to get the output. The output of the model will be a replica of the original picture. As an alternative approach, one can also transmit the residuals of the model, which will still require less bandwidth than the original picture. Real examples will be presented.

Faculty Sponsors

Dr. José Ramos

Project Type

Event

Location

Alvin Sherman Library

Start Date

4-13-2012 1:00 PM

End Date

4-13-2012 5:30 PM

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Apr 13th, 1:00 PM Apr 13th, 5:30 PM

Mathematical Modeling, Simulation, and Compression of Images

Alvin Sherman Library

This project builds a mathematical model that obtains parameters and statistical properties of residuals taken from a picture in JPEG format, to later simulate replicas of the original picture. The importance of this problem stems from the large amount of bandwidth required to transmit a high resolution picture over the Internet. The mathematical model built from this picture and its set of residuals has a much smaller magnitude than the original picture elements (pixels). This implies that if one were to transmit the parameters alone, a high compression rate would be achieved, thus saving bandwidth. In order to replicate the picture, the receiver has to randomly generate a set of residuals (inputs) with the same statistical properties as those from the received mathematical model, and process them in order to get the output. The output of the model will be a replica of the original picture. As an alternative approach, one can also transmit the residuals of the model, which will still require less bandwidth than the original picture. Real examples will be presented.