Iterative region of interest reconstruction in emission tomography

Ma, Jun

doi:10.1109/isbi.2010.5490106

Cited by 1 publication

(1 citation statement)

References 6 publications

(17 reference statements)

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“…First, level set estimation without reconstruction of f would allow design of sequential measurement schemes optimally adapted to the function of interest. For instance, in tomography we would like to estimate the level set, S * , quickly from an initial set of observations so that additional observations focused on S * can be collected immediately, resulting in an overall low radiation dose [26,32,31]. Some recent works [19,18] have provided theoretical characterizations of the significant benefits associated with certain sequential measurement schemes; the method proposed in this paper may facilitate the use of such schemes in timesensitive or computational-resource limited applications.…”

Section: Introductionmentioning

confidence: 99%

Level Set Estimation from Projection Measurements: Performance Guarantees and Fast Computation

Krishnamurthy¹,

Bajwa²,

Willett³

2013

SIAM J. Imaging Sci.

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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 mapping, medical imaging, astronomy, etc. In many applications, the function of interest is not observed directly. Rather, it is acquired through (linear) projection measurements, such as tomographic projections, interferometric measurements, coded-aperture measurements, and random projections associated with compressed sensing. This paper describes a new methodology for rapid and accurate estimation of the level set from such projection measurements. The key defining characteristic of the proposed method, called the projective level set estimator, is its ability to estimate the level set from projection measurements without an intermediate reconstruction step. This leads to significantly faster computation relative to heuristic "plug-in" methods that first estimate the function, typically with an iterative algorithm, and then threshold the result. The paper also includes a rigorous theoretical analysis of the proposed method, which utilizes results from the literature on concentration of measure and characterizes the estimator's performance in terms of geometry of the measurement operator and 1-norm of the discretized function.

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