Modern Convex Optimization to Medical Image Analysis

Recently, diagnosis, therapy and monitoring of human diseases involve a variety of imaging modalities, such as magnetic resonance imaging(MRI), computed tomography(CT), Ultrasound(US) and Positron-emission tomography(PET) as well as a variety of modern optical techniques. Over the past two decade, it has been recognized that advanced image processing techniques provide valuable information to physicians for diagnosis, image guided therapy and surgery, and monitoring of the treated organ to the therapy. Many researchers and companies have invested significant efforts in the developments of advanced medical image analysis methods; especially in the two core studies of medical image segmentation and registration, segmentations of organs and lesions are used to quantify volumes and shapes used in diagnosis and monitoring treatment; registration of multimodality images of organs improves detection, diagnosis and staging of diseases as well as image-guided surgery and therapy, registration of images obtained from the same modality are used to monitor progression of therapy. These challenging clinical-motivated applications introduce novel and sophisticated mathematical problems which stimulate developments of advanced optimization and computing methods, especially convex optimization attaining optimum in a global sense, hence, bring an enormous spread of research topics for recent computational medical image analysis. Particularly, distinct from the usual image processing, most medical images have a big volume of acquired data, often in 3D or 4D (3D + t) along with great noises or incomplete image information, and form the challenging large-scale optimization problems; how to process such poor 'big data' of medical images efficiently and solve the corresponding optimization problems robustly are the key factors of modern medical image analysis.