One-dimensional Hadamard naturalness-preserving transform reconstruction of signals degraded by nonstationary noise processes

The problem of reconstructing a time-varying one-dimensional signal from segments of its Hadamard naturalness preserving transform (NPT) is considered. Closed-form reconstruction formulas are derived for specific formats of available Hadamard NPT segments. Two fast reconstruction schemes, which in a single iteration provide the same solution as the general iterative reconstruction algorithm, are introduced for these formats. Simulation results of the algorithms when applied to first-order Gauss-Markov and image signals are good. However, the reconstruction of speech signals is poor due to the poor estimates derived from the available segments of the transformed signal. The reconstruction algorithm is proposed for interframe two-layer packet transmission of image signals over an Orwell-ring-based network. Good pictorial results are obtained at up to 50% packet loss rate