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Reconstruction of Binary Functions and Shapes From Incomplete Frequency Information

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1 Author(s)
Yu Mao ; Inst. for Math. & Its Applic., Univ. of Minnesota, Minneapolis, MN, USA

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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Information Theory, IEEE Transactions on  (Volume:58 ,  Issue: 6 )