论文标题
贝叶斯框架中形状识别逆问题的稳定性
Stabilities of Shape Identification Inverse Problems in a Bayesian Framework
论文作者
论文摘要
在贝叶斯框架中研究了一般形状识别逆问题。这个问题需要从有限维观察数据中确定欧几里得空间中域的未知形状，并具有一些高斯随机噪声。然后，研究后验的稳定性以进行观察数据。对于空间的每个点，考虑到观察数据，该点包含在未知域中的条件概率。还研究了此概率分布的稳定性。作为我们反问题的模型问题，考虑了热问题。这个问题需要从热导体表面某些部分的温度数据中确定热导体中腔体未知形状。要将上述稳定性结果应用于此模型问题，需要远期操作员的可测量性和一些界限。这些属性显示了。
A general shape identification inverse problem is studied in a Bayesian framework. This problem requires the determination of the unknown shape of a domain in the Euclidean space from finite-dimensional observation data with some Gaussian random noise. Then, the stability of posterior is studied for observation data. For each point of the space, the conditional probability that the point is included in the unknown domain given the observation data is considered. The stability is also studied for this probability distribution. As a model problem for our inverse problem, a heat inverse problem is considered. This problem requires the determination of the unknown shape of cavities in a heat conductor from temperature data of some portion of the surface of the heat conductor. To apply the above stability results to this model problem, one needs the measurability and some boundedness of the forward operator. These properties are shown.
