Collaborative Research on Numerical Methods for Image Processing

小行星9806413 图像处理问题的数值解会产生非常大的非对称线性系统，其解对下列参数极其敏感： 数据中的扰动。为了避免或至少控制灾难性的 由于这种不稳定性的影响，需要正则化。正则化 产生对不准确性不太敏感的稍微修改的问题 在数据中。 研究人员和他的同事的研究目的是开发有效和高效的正则化方法来解决大型 在图像处理应用中出现的非对称线性系统， 以及开发用于图像压缩的新算法。新 数值方法将在医学成像数据上进行测试， 应用于介入磁共振成像， 凯斯西储大学生物医学工程系。

9806413 Reichel The numerical solution of image processing problems gives rise to very large nonsymmetric linear systems whose solutions are extremely sensitive to perturbations in the data. To avoid or at least contain the disastrous effects of such instability, regularization is required. Regularization yields slightly modified problems which are less sensitive to inaccuracies in the data. The aim of the research by the investigator and his colleague is to develop effective and efficient regularization methods for the solution of large nonsymmetric linear systems that arise in image processing applications, as well as to develop new algorithms for image compression. The new numerical methods will be tested on medical imaging data and will be applied to interventional magnetic resonance imaging in collaboration with the department for Biomedical Engineering at Case Western Reserve University.