Reconstruction of Binary Functions and Shapes from Incomplete Frequency Information

The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct the binary signal from incomplete frequency measurements via solving a simple linear optimization problem. We further prove that if the binary function is spatially structured, e.g. a general black-write 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 function from low-pass filter. Numerical results are demonstrated to validate the theoretical arguments.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Yu Mao
• Keywords: Binary Function, Binary Signal, CORR 2011, Education, Frequency Measurements