Methods for Solving Inverse Problems Involving Words

在这个项目中，PI将对一类期望未知量为离散变量的反问题进行研究。这项工作与未知数为连续变量的经典反问题有所不同。描述未知事物的一种方法是将其称为由多个字母组成的“单词”。在这些问题中，给出的是与未知词有关的测量数据。目的是从数据中确定单词。在给定一组允许组成单词的字符的情况下，可以形成的可能的n字母单词的数量仍然非常大。然而，它是有限的。这项工作所采取的方法是探索一个词是如何构成的结构。其目标是设计出快速而健壮的专门算法。这项工作的目标应用包括条形码读取和RFID(射频识别)，其中隐藏的单词是由ASCII字符组成的产品代码。这类逆问题需要新的方法和新技术的发展。这项工作将使用字典稀疏表示、编码理论和信号处理的思想。这项工作的目的是开发具有理想数学特性的实用算法。这项工作的最终目标是创造将在工业和商业中产生影响的新技术。条形码和RFID用于识别商店和仓库中的产品，是供应链管理中的重要元素。它们还用于跟踪产品的生命周期。需要手持式激光扫描仪的算法，这种扫描仪可以读取损坏或肮脏的条形码，并在恶劣的条件下工作。还需要能够处理彼此靠近的多个标签的RFID读取方法。来自这项提议的研究产品有可能在商业上有所不同。这些方法可以改进对销售点和仓库中产品的识别和跟踪，并可能能够改善库存控制和供应链管理。希望拟议中的工作将产生可衡量的经济影响。PI计划在本科水平的课堂上使用条形码解码作为工业数学的范例。这门学科特别令人兴奋和容易理解，涉及从编码理论到信号处理、从测量科学到建模的广泛知识。条形码解码展示了数学在我们日常生活中的实用性和重要性。国际学生联合会有与高中生和本科生合作的记录，并打算让这些级别的学生和研究生参与拟议的工作。

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.