Reconstruction of Multidimensional Signals from Zero Crossings.
MASSACHUSETTS INST OF TECH CAMBRIDGE RESEARCH LAB OF ELECTRONICS
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This thesis addresses the problem of reconstruction of multidimensional signals from zero crossing or threshold crossing information. The basic theoretical result shows that most two-dimensional, periodic, bandlimited signals are uniquely specified wtih zero crossings or with crossings of an arbitrary threshold. This result also applies to finite length signals and to situations where only a discrete set of zero crossing points are available. Additional results show that signals of higher dimensions and nonperiodic signals are also uniquely specified with zero crossings or threshold crossings. By applying the duality of the Fourier transform in a straight-forward way, it is also shown that finite-length signals are uniquely specified with zero crossings or sign formation in the Fourier domain under analogous sets of conditions. A problem distinct from that of uniquely specifying signals with zero crossings is that of developing specific algorithms for recovering signals from zero crossing information once it is known that the signals satisfy the appropriate constraints. Two algorithms for recovering signals from zero crossings or threshold crossings are presented and one is successfully used to recover example images from threshold crossings. The thesis concludes with suggestions for future research including possible applications of these results. Additional keywords electrical engineering theorems equations.
- Theoretical Mathematics
- Non-Radio Communications