Numerical Algorithm for Inverse Problems and its Application to Multimedia Information Systems.

在这个研究项目中，我们设计并分析了反问题的数值算法。该问题最初来源于紧算子的反演，其典型例子是第一类Fredholm积分方程。我们的主题包括发展稳定的数值算法并给出它的数学基础。并将该算法扩展到多媒体信息系统中，提出了一种新的数学模型，实现了数据项的语义解释。正则化的基本操作是根据约束选择合适的子空间。我们将此操作推广到语义解释，其中约束对应于上下文。我们可以用这个模型来处理意义，即内容和上下文的关系。该模型应用于实际的信息系统，包括元数据库系统和多媒体数据的关联搜索。我们还开发了一种处理个体差异的学习机制和一种实现实时信息检索的加速方法。我们实际将此方法应用于语义图像搜索、多语言元搜索、媒体搜索（包括音乐、颜色等）。

In this research project, we designed and analyzed numerical algorithm for inverse problems. The problems originally comes from inversion of compact operators whose typical example is Fredholm integral equations of the first kind. Our main theme includes developing stable numerical algorithm and giving its mathematical foundations. Moreover we extended our algorithms to multimedia information system and proposed new mathematical model which enables semantic interpretation of data items.The essential operation of regularization is that selecting an appropriate subspace according to the constraint. We generalized this operation to semantic interpretation where the constraint corresponds to context. We can deal with meaning which is the relation of content and the context using the model. This model is applied to actual information systems including meta-database systems and associative search for multimedia data.We also developed a learning mechanism to deal with individual differences and an accelerating method to realize real time information retrieval. We actually applied this method to semantic image search, multilingual meta search, media search including music, colours and so on.