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

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Bajwa, Waheed U. Krishnamurthy, Kalyani Willett, Rebecca
Copyright Year	2013
Abstract	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 $\ell_1$-norm of the discretized function.
Starting Page	2047
Ending Page	2074
Page Count	28
File Format	PDF
DOI	10.1137/120891927
e-ISSN	19364954
Journal	SIAM Journal on Imaging Sciences (SJISBI)
Issue Number	4
Volume Number	6
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2013-10-22
Access Restriction	Subscribed
Subject Keyword	Computational difficulty of problems Inverse problems Image processing performance guarantees projection measurements Norms of matrices, numerical range, applications of functional analysis to matrix theory level set estimation Physics, astronomy, technology, engineering compressive sensing
Content Type	Text
Resource Type	Article

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