Model Based Reconstruction for Missing Data

Abstract

The previous chapter has introduced a number of simple but effective techniques for missing data removal. Those techniques were designed by exploiting the particular features of blotches, mainly temporal discontinuity. The methods employed were direct, in that they examined quantities which could be specifically related to the feature in question. The systems contained modules which addressed each problem as it arose. For example it was recognized that motion correction was vital for better image reconstruction and so a method was developed to correct motion, and kept separate from the subsequent image reconstruction. This chapter presents a framework for coherent decision making with respect to the missing data problem. It results in a process which identifies the missing regions at the same time as correcting the motion and image information. The framework employs models for the degradation process as well as the image sequence, in a quantitative fashion, in contrast to their use as ‘mission statements’ in the previous chapter. In some sense the model based technique presented here is a generalization of the methods introduced in the previous chapter, and the connections are explored after the technique is presented.