Reconstruction of Binary Functions and Shapes from Incomplete Frequency Information

Details Reconstruction of Binary Functions and Shapes from Incomplete Frequency Information Reconstruction of Binary Functions and Shapes from Incomplete Frequency Information

2011-04-04

arxiv.org/abs/1104.0446v3

IEEE Transactions on Information Theory, vol. 58, no. 6, 2012

Computer Science

Information Theory

IEEE Transactions on Information Theory, 2012

Scientific paper

10.1109/TIT.2012.2190041

The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization problem. We further prove that if a binary function is spatially structured (e.g. a general black-white image or an indicator function of a shape), then it can be recovered from very few low frequency measurements in general. These results would lead to efficient methods of sensing, characterizing and recovering a binary signal or a shape as well as other applications like deconvolution of binary functions blurred by a low-pass filter. Numerical results are provided to demonstrate the theoretical arguments.

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