Fast level set estimation from projection measurements

Estimation of the level set of a function (i.e., regions where the function exceeds some value) is an important problem with applications in digital elevation maps, medical imaging, and astronomy. In many applications, however, the function of interest is acquired through indirect measurements, such as tomographic projections, coded-aperture measurements, or pseudo-random projections associated with compressed sensing. This paper describes a new methodology and associated theoretical analysis for rapid and accurate estimation of the level set from such projection measurements. The proposed method estimates the level set from projection measurements without an intermediate function reconstruction step, thereby leading to significantly faster computation. In addition, the coherence of the projection operator and McDiarmid´s inequality are used to characterize the estimator´s performance.