A control problem in medical image processing

抛物控制问题的偏微分方程可以用来模拟各种图像处理应用。在这个项目中，我们研究了医学成像中的一个特定的原型任务：乳腺癌的早期诊断依赖于对乳房x线摄影图像的适当检查，即乳房的x线扫描。医疗评价过程分为非常短的确认阶段和核查阶段。在验证阶段，专家向前移动（近距离）和向后移动（正常），从而交替检查小细节（潜在的钙化，小肿瘤），并在器官的一般形态中捕捉关键模式位置的总体印象。验证阶段可以通过切换不同的精细或粗糙的图像表示来支持近距离或正常的子阶段。数学模型导致抛物线控制问题。在这个项目中，我们想要结合反问题的正则化理论的结果，以及最近在图像处理中使用1齐次惩罚项去噪的一些结果，以研究图像处理（乳房x光检查，x射线图像）中的抛物线控制问题。我们与来自MeVis/CeVis的合作伙伴以及不来梅乳房x光检查项目共同努力。

Parabolic control problems for PDEs can be used to model a variety of image processing applications. In this project we investigate a particular prototypical task in medical imaging: The diagnosis of breast cancer at an early stage relies on an appropriate examination of mammography images, i. e. X-ray scans of the breast. The medical evaluation process is divided into a very short recognition phase and a verification phase. During the verification phase the expert shifts forwards ( close up ) and backwards ( normal ), thereby alternating in examining small details (potential calcifications, small tumors), and in catching an overall impression of the location of critical patterns within the general morphology of the organ. The verification phase can be supported by switching between different fine or coarse scale presentations of the image for close up or normal subphases. The mathematical model leads to a parabolic control problem. In this project we want to combine ¿ results from regularization theory for inverse problems, ¿ some recent results in image processing for denoising with 1-homogeneous penalty terms in order to investigate this parabolic control problem in image processing (mammography screening, X-ray images). We work together with our cooperation partners from MeVis/CeVis and the Mammograhie Screening Bremen-project.