Compressed Sensing for Surface Characterization and Metrology

Surface metrology is the science of measuring small-scale features on surfaces. In this paper, a novel compressed sensing (CS) theory is introduced for the surface metrology to reduce data acquisition. We first describe that the CS is naturally fit to surface measurement and analysis. Then, a geomet...

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Bibliographic Details
Published in:IEEE transactions on instrumentation and measurement 2010-06, Vol.59 (6), p.1600-1615
Main Author: Ma, Jianwei
Format: Article
Language:English
Subjects:
Algorithms
Atomic measurements
Compressed
Compressed sensing
Compressed sensing (CS)/compressive sampling
Computational efficiency
curvelets
Data acquisition
Detection
Earth Sciences
Environmental Sciences
Geophysics
Global Changes
incomplete measurement
Metrology
Physics
Protocols
Recovery
Sampling
Sampling methods
Sciences of the Universe
sparse recovery
Studies
surface characterization
Surface fitting
surface metrology
Surface texture
Surface waves
Theorems
Transforms
wave atoms
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Summary:Surface metrology is the science of measuring small-scale features on surfaces. In this paper, a novel compressed sensing (CS) theory is introduced for the surface metrology to reduce data acquisition. We first describe that the CS is naturally fit to surface measurement and analysis. Then, a geometric-wavelet-based recovery algorithm is proposed for scratched and textural surfaces by solving a convex optimal problem with sparse constrained by curvelet transform and wave atom transform. In the framework of compressed measurement, one can stably recover compressible surfaces from incomplete and inaccurate random measurements by using the recovery algorithm. The necessary number of measurements is far fewer than those required by traditional methods that have to obey the Shannon sampling theorem. The compressed metrology essentially shifts online measurement cost to computational cost of offline nonlinear recovery. By combining the idea of sampling, sparsity, and compression, the proposed method indicates a new acquisition protocol and leads to building new measurement instruments. It is very significant for measurements limited by physical constraints, or is extremely expensive. Experiments on engineering and bioengineering surfaces demonstrate good performances of the proposed method.
ISSN:0018-9456
1557-9662
DOI:10.1109/TIM.2009.2027744