Low Space-bandwidth Product Signal Extrapolation Using a New Robust Iterative Random Grain Allocation Scheme

Abstract

Abstract The extrapolation in the space domain of a partially observed low space-bandwidth product (SBP) sequence or, equivalently, the resolution of the Fourier spectra in the frequency domain, in the presence of appreciable noise, is considered. The unknown sequence estimate is based on a number of acquired samples on a given measurement interval and the prior knowledge of the signal frequency bandlimit. Using an approach similar to a Monte-Carlo method, the extrapolated sequence samples are constructed from variably sized elementary grains. The new iterative algorithm, at each iteration step, based on a random-number generator, decides both the sample position to be considered and the sign of a grain that might be added to the current sample value. A sample update in each iteration step is either accepted or rejected in accordance with an appropriate decision rule. While exploiting the extrapolated sequence frequency bandlimit as a constraint, this decision rule is based on a non-increasing l1-norm of ...