Naturalness-preserving transform (NPT) reconstruction of signals degraded by non-stationary noise processes

Under adverse channel signaling conditions, segments of a transmitted signal could be rendered unusable. Hadamard naturalness-preserving transform (NPT) preprocessing is investigated for such applications. The problem of reconstructing a one-dimensional signal from segments of its Hadamard NPT is considered. The solution requires an estimate of the signal amplitude over the available transform segments. Closed-form reconstruction formulas are derived for specific formats of NPT segments. In the general case, an iterative reconstruction scheme is investigated. Simulation results are presented