Methods for Solving Inverse Problems Involving Words

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

In this project, the PI will conduct research on a type of inverse problems in which the desired unknown is a discrete variable. This work represents a departure from classical inverse problems where the unknowns are continuous variables. One way to describe the unknown is to call it a "word" consisting of a number of letters. In these problems one is given measured data which is related to the unknown word. The object is to determine the word from the data. Given a set of characters that are permitted in forming a word, the number of possible n-letter words that can be formed is still very large. However, it is finite. The approach taken in this work is to exploit the structure of how a word is formed. The goal is to devise specialized algorithms which are fast and robust. Target applications for this work include bar code reading and RFID (Radio-frequency identification) where the hidden words are product codes consisting of ASCII characters. This class of inverse problems requires new approaches and development of new techniques. Ideas from sparse representation using dictionaries, coding theory, and signal processing will be employed in this work. The aim of this effort is to develop practical algorithms that have desirable mathematical properties. The ultimate goal of this work is to create new technologies that will make a difference in industry and commerce. Bar codes and RFID, used to identify products in stores and warehouses, are important elements in supply chain management. They are also used to track the life-cycle of products. There is a need for algorithms for hand-held laser scanners that can read bar codes that are damaged or dirty, and work in poor conditions. There is also a need for RFID reading methods that can deal with multiple tags that are near each other. The products of research from this proposal have the potential to make a difference in commerce. The methods may improve identification and tracking of products at points of sale and in warehouses, and may be able to improve inventory control and supply-chain management. It is hoped that the work being proposed will have a measurable economic impact. The PI plans to use bar code decoding as exemplar of industrial mathematics in the classroom at the undergraduate level. The subject is perticularly exciting and accessible, and involves a breadth of knowledge, from coding theory to signal processing, from measurement science to modeling. Bar code decoding demonstrates the utility and importance of mathematics in our daily lives. The PI has a track record of working with high-school students and undergraduates, and intends to engage students at these level, and at the graduate level, in the proposed work.