Project Details
Projekt
A control problem in medical image processing
Applicant
Professor Dr. Peter Maaß
Subject Area
Mathematics
Term
from 2005 to 2009
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 18078967
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.
DFG Programme
Priority Programmes
