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

在本研究计画中，我们设计并分析反问题的数值演算法。这些问题最初来自紧算子的反演，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，并给出其数学基础。此外，我们还将算法推广到多媒体信息系统中，提出了新的数学模型，使数据项能够进行语义解释，正则化的基本操作是根据约束条件选择合适的子空间。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，即内容和语境的关系。将该模型应用于元数据库系统和多媒体数据关联检索等实际信息系统中，提出了处理个体差异的学习机制和实现真实的实时信息检索的加速方法。我们实际上将这种方法应用于语义图像搜索，多语言Meta搜索，包括音乐，颜色等的媒体搜索。

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.