The use of interval -related expert knowledge in processing 2-D and 3-D data, with an emphasis on applications to geosciences and biosciences

Processing different types of data is one of the main applications of computers, the application for which computers have been originally designed. The more data we need to process, the more computing power we need and thus, the more important it is to use (and design) faster algorithms for data processing. Even processing 1-D data often is very time-consuming, but processing 2-D data (e.g., images) and 3-D data is where we really encounter the limits of the current computer hardware abilities. Data processing algorithms sometimes produce results which contradict the expert knowledge – because this knowledge was not taken into account in the algorithm. For example, a mathematical solution to a seismic inverse problem may lead to un-physically large values of density inside the Earth. At present, in such situations, researchers try to repeatedly modify (“hack”) the process until the results produced by the algorithm agree with this expert knowledge. This process takes up a lot of expert time and – because of the need for numerous iterations – a lot of computer time. To avoid this long, ad-hoc process, it is desirable to explicitly incorporate the expert knowledge into the algorithms, so that the results are always consistent with the expert’s knowledge. Expert knowledge often comes in the form of bounds (i.e., intervals) on the actual values of the physical quantities. In this dissertation, we describe how this intervalrelated expert knowledge can be used in processing 2-D and 3-D data. In data processing, one can distinguish between two types of situations: simpler situations when we directly measure the data that needs to be processed, and more complex situations when the data points can only be measured indirectly, i.e., when these points themselves need to be determined from the measurement results. In this dissertation, we consider both types of data processing. For the case of directly measured 2-D and 3-D data (e.g., images), one of the main problems usually is referencing these images. For the