Methods for Solving Inverse Problems Involving Words
解决涉及单词的反问题的方法
基本信息
- 批准号:1211884
- 负责人:
- 金额:$ 27.83万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2012
- 资助国家:美国
- 起止时间:2012-07-01 至 2016-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
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.
在这个项目中,PI将对一种类型的反问题进行研究,其中所需的未知数是离散变量。这项工作代表了一个偏离经典的反问题,其中的未知数是连续变量。 描述未知事物的一种方法是称它为一个由许多字母组成的“单词”。 在这些问题中,给出了与未知词相关的测量数据。 目标是从数据中确定单词。 给定一组允许构成单词的字符,可以构成的可能的n字母单词的数量仍然非常大。 然而,它是有限的。 在这项工作中采取的方法是利用一个词是如何形成的结构。 我们的目标是设计专门的算法是快速和强大的。 这项工作的目标应用包括条形码阅读和RFID(射频识别),其中隐藏的字是由ASCII字符组成的产品代码。 这类反问题需要新的方法和新技术的发展。 从稀疏表示使用字典,编码理论和信号处理的想法将在这项工作中。 这项工作的目的是开发具有理想的数学特性的实用算法。这项工作的最终目标是创造新的技术,使工业和商业的差异。条形码和RFID,用于识别商店和仓库中的产品,是供应链管理的重要组成部分。 它们还用于跟踪产品的生命周期。 需要一种用于手持式激光扫描仪的算法,该算法可以读取损坏或脏的条形码,并且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阅读方法。 这项建议的研究成果有可能在商业上产生影响。 该方法可以改进在销售点和仓库中的产品的识别和跟踪,并且能够改进库存控制和供应链管理。 希望拟议的工作将产生可衡量的经济影响。 PI计划在本科阶段的课堂上使用条形码解码作为工业数学的范例。 这门学科非常令人兴奋和容易理解,涉及广泛的知识,从编码理论到信号处理,从测量科学到建模。 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。PI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。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Fadil Santosa其他文献
Rational design of a diffractive homogenizer for a laser beam
- DOI:
10.1023/a:1020352911182 - 发表时间:
2002-01-01 - 期刊:
- 影响因子:1.400
- 作者:
Svetlana Rudnaya;David Misemer;Fadil Santosa - 通讯作者:
Fadil Santosa
Determination of a Small Elliptical Anomaly in Electrical Impedance Tomography using Minimal Measurements
使用最小测量确定电阻抗断层扫描中的小椭圆异常
- DOI:
- 发表时间:
2024 - 期刊:
- 影响因子:0
- 作者:
Gaoming Chen;Fadil Santosa;Aseel Titi - 通讯作者:
Aseel Titi
Seismic signatures of pore fluid mobility in heterogeneous reservoirs
非均质储层孔隙流体流动性的地震特征
- DOI:
10.1190/image2023-3908530.1 - 发表时间:
2023 - 期刊:
- 影响因子:0
- 作者:
Qiuzi Li;Brent Wheelock;Tuan Tran;Fadil Santosa - 通讯作者:
Fadil Santosa
Crack determination from boundary measurements—Reconstruction using experimental data
- DOI:
10.1007/bf00567084 - 发表时间:
1993-09-01 - 期刊:
- 影响因子:2.400
- 作者:
Valdis Liepa;Fadil Santosa;Michael Vogelius - 通讯作者:
Michael Vogelius
Fadil Santosa的其他文献
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{{ truncateString('Fadil Santosa', 18)}}的其他基金
Collaborative Research: Internship Network in the Mathematical Sciences
合作研究:数学科学实习网络
- 批准号:
2015441 - 财政年份:2020
- 资助金额:
$ 27.83万 - 项目类别:
Continuing Grant
Collaborative Research: Internship Network in the Mathematical Sciences
合作研究:数学科学实习网络
- 批准号:
2053549 - 财政年份:2020
- 资助金额:
$ 27.83万 - 项目类别:
Continuing Grant
The Institute for Mathematics and its Applications
数学及其应用研究所
- 批准号:
0931945 - 财政年份:2010
- 资助金额:
$ 27.83万 - 项目类别:
Continuing Grant
Inverse design methods for optical applications
光学应用的逆向设计方法
- 批准号:
0807856 - 财政年份:2008
- 资助金额:
$ 27.83万 - 项目类别:
Standard Grant
Inverse Problems in Industrial Applications
工业应用中的反问题
- 批准号:
0504185 - 财政年份:2005
- 资助金额:
$ 27.83万 - 项目类别:
Standard Grant
Institute for Mathematics and its Applications
数学及其应用研究所
- 批准号:
0439734 - 财政年份:2005
- 资助金额:
$ 27.83万 - 项目类别:
Continuing Grant
Mathematical Sciences: Use of Enhancement Techniques and A Priori Information in Electrical Impedance Tomography
数学科学:增强技术和先验信息在电阻抗断层扫描中的应用
- 批准号:
9796009 - 财政年份:1996
- 资助金额:
$ 27.83万 - 项目类别:
Standard Grant
University - Industry Cooperative Research Programs in the Mathematical Sciences: Postdoctoral Research in Geophysical Exploration
数学科学产学合作研究项目:地球物理勘探博士后研究
- 批准号:
9626832 - 财政年份:1996
- 资助金额:
$ 27.83万 - 项目类别:
Standard Grant
Mathematical Sciences/GIG:Infrastructure Needs for Preparing Students for the Industrial and Business Workforce
数学科学/GIG:为学生进入工业和商业劳动力做好准备的基础设施需求
- 批准号:
9631347 - 财政年份:1996
- 资助金额:
$ 27.83万 - 项目类别:
Continuing Grant
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