Space-efficient algorithms in computer algebra and image processing applications

我们建议研究的问题，在一些领域，包括计算机代数，图像集压缩，数学文件分析。我们的主要重点是技术，有效地减少空间需求的算法的执行和存储的data.In许多重要的问题，在计算机代数，输入的大小和最终所需的结果是相对较小的，但中间结果可能会显着增长，在许多算法。我们的目标是开发算法，不仅是空间效率，但也考虑到底层系统中的内存管理。在图像集压缩中，单独压缩每个图像并不利用图像之间存在的冗余。我们计划研究技术来压缩一组图像，以及图像集的动态更新的问题。我们特别关注卫星和医学图像，其中图像之间存在大量的冗余。许多数学文献仅以扫描数字图像的数字形式提供。我们打算建立一个系统，分析这些图像，并将它们存储在一个结构化的形式，供其他工具使用。特别感兴趣的是认识和利用数学中的抽象概念，如矩阵结构（例如Toeplitz，Hankel等）。和算法描述。这样的系统可以用来建立一个数学知识的数字图书馆，以有效地存储和使用的其他计算机代数系统。

We propose to study problems in a number of areas including computer algebra, image set compression, and mathematical document analysis. Our main focus is on techniques for efficiently reducing the space requirement for both the execution of algorithms and the storage of data.In many important problems in computer algebra, the sizes of the input and the final desired results are relatively small, but intermediate results may grow significantly in many algorithms. Our goal is to develop algorithms that are not only space efficient, but also take memory management in the underlying system into account. We expect that more practical algorithms will be developed as a result.In image set compression, compressing each image individually does not exploit the redundancy that exists between images. We plan to examine techniques to compress a set of images as well as the problem of dynamic updates to image set. We particularly focus on satellite and medical images in which substantial redundancy among images is known to exist.Many mathematical documents are available in digital form only as scanned digital images. We intend to build a system that analyzes these images and store them in a structured form for use by other tools. Of particular interests are recognizing and utilizing abstract concepts in mathematics such as matrix structures (e.g. Toeplitz, Hankel, etc.) and algorithm descriptions. Such a system can be used to build a digital library of mathematical knowledge to be stored efficiently and used by other computer algebra systems.