Codes over lattices and applications to biomedical measurements

• Grant number: 13/10110-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2013
• End date: January 31, 2014
• Field of knowledge: Engineering - Electrical Engineering - Telecommunications
• Principal Investigator: Marcelo Firer
• Grantee: Cornelia ROssing
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Most of the common imaging techniques, e.g. magnetic resonance imaging (MRI), nuclear magnetic resonance (NMR), or computerized tomography (CT) behave linearly in their first order approximation. Our idea is to improve image quality by introducing coding theory for the measurement. The linearity of the system then allows us to correct occurring errors instead of only reducing them what is done so far. The scenario is as follows: The system F (with a single pulse response f) is exposed to an excitation s and the system response r=F(s) + t = fs + t is measured, the problem here is that the measurement is disturbed, thus instead of fs we receive fs + t where t represents what is called noise, the common distortion of the signal. The main idea now is to use a linear block code with generator polynomial s. In terms of coding theory we encode the message f using s and sent the codeword fs. The receiver obtains r=fs+t and because of the character of the noise a decoder can retrieve the original information fs. This way we expect to be able to retrieve the system response without noise and therefore to improve the image quality. For a higher image quality we need to find suitable linear block codes and decoder. Our main focus here will be on the codes, we expect good results from codes introduced by lattices, in particular Craig's lattices. (AU)