Robust reconstruction of spherical signals with finite rate of innovation

Abstract

We develop a robust method for the accurate reconstruction of non-bandlimited finite rate of innovation signals composed of finite number of Diracs. For the recovery of parameters of K Diracs defining the signal, the proposed method requires more than (K + √K) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> samples of the signal band-limited in harmonic domain such that the spherical harmonic transform can be computed using the samples. In comparison with the existing methods, the proposed method is robust in a sense that it does not require all Diracs to have distinct colatitude parameter. We first estimate the N number of Diracs which do not have distinct colatitude parameter. Once N is determined, the proposed method requires, at most, N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> +N/2 + 1 unique and intelligently chosen rotations of the signal to recover all parameters accurately. We also provide illustrations to demonstrate the accurate reconstruction using the proposed method.