Parallel Imaging Problem

Metric Labeling problems have been introduced as a model for understanding noisy data with pair-wise relations between the data points. One application of labeling problems with pair-wise relations is image understanding, where the underlying assumption is that physically close pixels are likely to belong to the same object. In this paper we consider a variant of this problem, we will call Parallel Imaging, where instead of directly observing the noisy data, the data undergoes a simple linear transformation first, such as adding different images. This class of problems arises in a wide range of imaging problems. Our study has been motivated by the Parallel Imaging problem in Magnetic Resonance Image (MRI) reconstruction. We give a constant factor approximation algorithm for the case of speedup of two with the truncated linear metric, motivated by the MRI reconstruction problem. Our method uses local search and graph cut techniques.